Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Halc on 19/10/2018 12:54:07

This thread is meant to investigate relativistic limits on the acceleration of large objects. To drive the points home, my objects will be large and fast, but never with impossible properties like being massless, infinite rigidity, or with instantaneous acceleration, all of which can be shown to violate fixed speed of light.
Consider a long object, say a light year in length, which is fairly fragile in that it will allow only negligible physical compression or stretching before it breaks. Hence the force of propulsion is spread as needed over the entire length of the object. Our engines/railguns are as powerful as they need to be.
For slow accelerations, the clock at the front of the object will get ahead of the ones further back, so the acceleration further forward run is lower, but for a longer time. If the rear acceleration takes 10 years (measured in local accelerating frame) to get up to say .866c, the front acceleration will take place for 10.866 years to get to that speed iff it ignites and ceases at the same time (object frame) as the rear acceleration. The points in between can accelerate proportionally. In this way, the entire object might be under acceleration at once, but only in the object's own frame.
That seems viable for only slow accelerations, and even then, in any other frame, part of the object is accelerating and the part of it not, so right there it seems on first glance to be putting strain on our object, but I cannot prove that since the two parts are always separated in a spacelike manner, and so cannot directly effect each other.
Scaling up the acceleration demonstrates the limits if not the deficiencies of my proposed methods. Clearly at some point there is strain the way I am doing it. Is there a strainfree way of accelerating a long object? More exactly, is there a way to do it that never changes the object's proper length?
There is proof of sorts that there is a correct solution, since if there is compression or tension somewhere in the object, we could compensate for that with a thrust function that applies more or less force at points further forward. There must be a solution that involves zero strain, but even then the length of the object puts an absolute limit on the magnitude of the acceleration.
Edit: There seems to be nothing impossible about near instantaneous acceleration. Many of my examples assume as a limit an acceleration to a desired speed in negligible time. If this is found to violate finite light speed or some other law, kindly post details since it will effect my answers for minimum time to get a big thing somewhere.
Update, Feb 2019: I think I found that very violation. See post 97. Infinite acceleration makes the speed undefined, and without a defined speed, the proper length is undefined. Acceleration can be arbitrarily high, but not infinite.

As always, I don't know :)
But depending on definitions, you take something that compress under acceleration and put it as close as you can to lightspeed. Presuming that bonds microscopically holds relative time dilation's and length contractions there should be no problem. Otherwise you need a infinitely rigid structure to make it work, which would make that 'rocket' into a singularity of its own.
A interesting question here would be to presume that there can be objects coasting, aka uniformly relatively moving, close to light speed. That way you can avoid the acceleration and just question where the difference lies.
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the real point of 'c' is that it is observer dependent.
either one ignore it or acknowledge it.
if you accept that as something that defines your universe, as well as every one else's 'universe' then 'c' is a constant.
Yes, it's local, but so are all experiments proving it to be a constant.
And so is 'repeatable experiments'.
That's where 'physics' comes from

A very funny thing is considering a 'black hole' spinning at the speed of light, or let's put it just under that limit. If you want to argue that it is 'space' doing it, what about the black hole?
does it even need to spin?

But depending on definitions, you take something that compress under acceleration and put it as close as you can to lightspeed.
I'm not attempting to get close to lightspeed. I'm trying to accelerate a long thing, something that cannot take stress.
Presuming that bonds microscopically holds relative time dilation's and length contractions there should be no problem. Otherwise you need a infinitely rigid structure to make it work, which would make that 'rocket' into a singularity of its own.
No rigidity at all. That was the point of the thread. I said up front that infinite or massless things destroy the point being made.
A interesting question here would be to presume that there can be objects coasting, aka uniformly relatively moving, close to light speed. That way you can avoid the acceleration and just question where the difference lies.
I will get to that. How long of a coasting object can exist? It doesn't even have to move, which it doesn't anyway since it has to have a frame in which it is stationary. Think about it. Go for really long lengths.
A very funny thing is considering a 'black hole' spinning at the speed of light,
Speed of light isn't a rate of spin. Black holes don't spin at a 'speed' nor at a particular angular velocity. They have a particular angular momentum.
does it even need to spin?
Yes it does. Conservation laws demand it. It means that Hawking radiation needs to preserve it, as do gravity waves given off by objects spinning in.

For slow accelerations, the clock at the front of the ship will get ahead of the ones further back,
How?

For slow accelerations, the clock at the front of the ship will get ahead of the ones further back,
How?
Gravity and acceleration are locally indistinguishable, so the front clock is functionally identical to one higher up in a building in a uniform gravitational field, and the clocks up there go faster since they're less dilated by gravity.
Similarly for any accelerating observer, clocks in the direction of acceleration advance, and those behind fall further behind (even into negative territory). The Andromeda 'paradox' illustrates this quite well. Small acceleration, but multiplied by large distance.

Hmm, would you mind expanding a little on this one Halc?
" A very funny thing is considering a 'black hole' spinning at the speed of light, "
Speed of light isn't a rate of spin. Black holes don't spin at a 'speed' nor at a particular angular velocity. They have a particular angular momentum. ""
Never said that the speed of light is a angular momentum? But if something as a wheel, moves around with a point marked at its circumference, where we find that point to move at a same or slightly less speed as measured for light. Then you can make a comparison I think? https://www.universetoday.com/109308/howfastdoblackholesspin/

Also I would slightly alter that statement of yours that conservation laws demand the black hole to spin :)
In this case, as I questioned what spins I would put it as conservation laws demands 'something' to spin, suggesting it then to be the space around it. Now, if we find a black hole spinning faster than its allowed " The speed limit is set by the event horizon, eventually, at a high enough spin, reaches the singularity. You can’t have what’s called a naked singularity. You can’t have a singularity exposed to the rest of the Universe. That would mean that the singularity itself could emit energy or light and somebody outside could actually see it. And that can’t happen. " :)
Wouldn't that be interesting?

If the ship cannot tolerate longitudinal stress, it cannot be accelerated by a finite number of engines since the thrust of each engine must be transmitted to the intervening material by stress.
Therefore the ship must be modelled as an array of infintesimal elements, each with its own engine and some means of ensuring that they work together in complete synchronism. Thus the entire ship must accelerate as a single entity. There being no change in length, there can be no relative velocity or acceleration between the front and the back of the ship and thus no change in perceived clock rates between observers on the ship.
This is quite different from a rigid rod, propelled from one end. The propulsive force is transmitted at the speed of sound in the rod which leads to mechanical compression and loss of synchronism way in excess of any relativistic effect, and is the reason that pushrods were abandoned in favour of overhead camshafts in highrevving engines.

Gravity and acceleration are locally indistinguishable, so the front clock is functionally identical to one higher up in a building in a uniform gravitational field, and the clocks up there go faster since they're less dilated by gravity.
If the front and back of the ship are not accelerating at (at least very nearly) the same rate, you are tearing your ship apart.
There is a tiny gravitational effect due to the mass of the ship which means that the middle of the ship (where the fore and aft masses cancel out) are subject to a smaller field than the ends but that's hardly going to matter.

Never said that the speed of light is a angular momentum? But if something as a wheel, moves around with a point marked at its circumference, where we find that point to move at a same or slightly less speed as measured for light. Then you can make a comparison I think?
Wheels have different properties. Earth is a wheel, and in the rotating frame of Earth, yes, there is a circumference where stuff moves at light speed, and there is stuff beyond that circumference. It means that all stars but our own move at greater than light speed in that rotating frame, which isn't a contradiction since laws are different in such frames.
The link you provide is interesting, but it says that physicists use units for angular momentum that are cast in terms of mass, not in terms of speed. So it is unclear how the author suddenly assigns a speed to a spin rate.
I find the concept of the naked singularity interesting, but very off topic for this thread. My long fragile ship would break up if its engines did not everywhere compensate for stresses put on it by gravity sources.
Now, if we find a black hole spinning faster than its allowed " The speed limit is set by the event horizon, eventually, at a high enough spin, reaches the singularity. You can’t have what’s called a naked singularity.
There is no limit to the angular momentum of it, but if it spins that fast, it does become naked, and is no longer a black hole, just a collection of mass being flung away because it collectively has too much angular momentum to ever form a black hole. It seems an interesting way to unblack an existing hole. Just spin it faster, beyond its limits.
You can’t have a singularity exposed to the rest of the Universe. That would mean that the singularity itself could emit energy or light and somebody outside could actually see it. And that can’t happen. " :)
It can happen. It just wouldn't be a singularity anymore. Actually, it probably cannot happen, because as the black hole shrinks, it becomes more and more difficult to apply more angular momentum to it. At the limit, none can be added. So yes, that cannot happen.
Wouldn't that be interesting?
Intersting yes, but there is a spinning black hole thread active right now. Why not post this stuff in there? My topic has nothing to do with them.

If the ship cannot tolerate longitudinal stress, it cannot be accelerated by a finite number of engines since the thrust of each engine must be transmitted to the intervening material by stress.
Maybe it applies force the way a uniform gravitational field accelerates Earth without putting additional stress on it. OK, the sun's field is not totally uniform, so we get tidal stresses.
For the sake of this example, the ship can locally take the stresses from its engines.
Therefore the ship must be modelled as an array of infintesimal elements, each with its own engine and some means of ensuring that they work together in complete synchronism.
Pretty much, yes.
Thus the entire ship must accelerate as a single entity. There being no change in length, there can be no relative velocity or acceleration between the front and the back of the ship and thus no change in perceived clock rates between observers on the ship.
We need to pinpoint those rules.
There can be no change in proper length. But there is very much going to be changes in relativistic length.
For it to have a proper length, it needs to be stationary in its own frame. I fretted a lot about that one since it seems to be difficult to avoid, but decided it was a mandatory requirement, and that the solution to the problem lies exactly in that requirement.
Your last one is unreasonable. There will be a perceived change of clock rates just as there would be in a building on a planet. We’re accelerating after all and barring a window to look out of, the occupants cannot tell the difference between the two situations. Clocks forward of a given observer will appear to run faster, and clock behind a given observer will appear to run slower. The amount they get off depends on the separation, the acceleration rate, and how long we keep it up.
This is quite different from a rigid rod, propelled from one end.
I started out with that as my example, but it cannot be immune to strain, else it would transmit the thrust immediately to the other end, violating the light speed limit on information travel. So I do it as a fragile ship where all the local ‘engines’ know the flight plan. There can be no quick decisions by the pilot, since the new plan must be transmitted to all engines before any of the engines can react.
The propulsive force is transmitted at the speed of sound in the rod which leads to mechanical compression and loss of synchronism way in excess of any relativistic effect, and is the reason that pushrods were abandoned in favour of overhead camshafts in highrevving engines.
My original post talked about speed of sound like that. I abandoned it for the time since I didn’t need the complication. Speed of sound has an upper limit of c. No material can be physically more rigid than that.

If the front and back of the ship are not accelerating at (at least very nearly) the same rate, you are tearing your ship apart.
Not so. See the threadbreaking topic in the newtheories forum. It was that topic that got me thinking about this topic.
There is a tiny gravitational effect due to the mass of the ship which means that the middle of the ship (where the fore and aft masses cancel out) are subject to a smaller field than the ends but that's hardly going to matter.
It would seem to only matter near the ends, and even then, our ship is narrow and not likely to generate a significant local gravitational field. I cannot say it is massless, violating my stipulation about that, but for the purpose of the thought experiment, we can either ignore that or have the engines make that microcompensation for it.

I'm afraid those threads tend to go of in divergent angles Halc, and I admit to being guilty here :). What you were discussing was whether something can hold together being accelerated to the speed of light, or as close as possible at least, if I got that right? That made me think of rotating black holes, and also about the way we see our universe accelerating expanding. A rotating black hole has a 'speed' of sorts, although it also can be seen as forever accelerating although that dot we put upon it never increase its 'speed per distance done' if you get ny drift. And looked at that way they are the 'fastest' objects I know of, 87% of the speed of light if I remember right? They do hold together, and seem to have no problem doing so under their whole evolution. If you think of spinning up a disk to that speed there are two possibilities, either it should crack as the rim will be at a different speed relative its interior, aka Lorentz Fitzgerald contraction, or it doesn't. I find the idea of black holes rotating very interesting. If we now instead look at 'space' then there is no limit to its 'speed' meaning that in a accelerating expanding universe we can use two buoys and define the space between them to expand FTL without us needing any new theory of Relativity. You made me think of a lot of things there Halc :)

My first cut at this was incorrect I think, but I'll describe it here.
I reached an inconsistency if I accelerated the ship hard:
I have a ship that is a light year long. In frame P (parked) it extends from 0 (tail) to 366 (nose) light days.
Now I accelerate it (or at least the tail) to .866c (dilation 50%) in one month as measured by a P clock.
The tail of the ship is now at perhaps location 15 light days, and the ship, if moving at .866c, is dilated to half its length, so only 183 light day long. So the nose is 15+183=198 light days away, much closer than it was when parked. In fact, it would need to move faster than light to get to that spot.
This all seemed quite contradictory, and so I supposed there might be an acceleration limit based on the length of the object.
Where I seemed to go wrong is to consider the state of the ship in frame P as it is accelerating. In no other frame is the entire ship moving at one uniform velocity, but this doesn't mean there is stress or strain on it. In the ship's own accelerating frame, the thing is always stationary, and thus stress free. In that frame, the nose never moves backwards since there is no length contraction. You can accelerate as hard as you like. There seems to be no limit.

I'm not sure about that one Halc, as soon as your ship start to move its structure will contract at the speed of sound, as its 'accelerating motion' carries/pushes its structure. Made out of unobtanium the speed of sound should be regulated by 'c' in which case it will accelerate to that limit. Were it made of steel? Also, and here's one really tricky part, the speed of light is observer dependent. Although we agree on getting the same limit 'c', it doesn't matter from what uniformly moving frame you measure that speed. And uniformly moving 'laboratories' can indeed be found to have different 'speeds' relative each other. So when you define it as shrinking you also will need to define what frame of reference you're using for observing that shrinking. I'm guessing we could use earth for it.
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What I mean by it contracting is that its acceleration won't touch the whole ship simultaneously, unless it's made out of unobtanium. It's the same principle as you moving a very long rod to touch the moon. Your acceleration of the rod travels at the speed of sound, and speed depends on the rigidity of the rods material.

What you were discussing was whether something can hold together being accelerated to the speed of light,
Just accelerated at all. Not to the speed of light, or necessarily particularly close to it. I just use higher accelerations and speed to illustrate where the problems appear.
And looked at that way they are the 'fastest' objects I know of, 87% of the speed of light if I remember right?
There are constructs that fire Jupitersize bullets at well over .99c, so maybe that qualifies more as a faster object. The amount of violence represented in a thing that can do that is fairly unimaginable.

I'm not sure about that one Halc, as soon as your ship start to move its structure will contract at the speed of sound, as its 'accelerating motion' carries/pushes its structure.
My ship has engines the whole length to prevent exactly that speed of sound problem. Read the OP. The ship is fragile (brittle), not made of unobtanium.
Also, and here's one really tricky part, the speed of light is observer dependent.
No it isn't. It is the same for all observers.

Yes, its the same :)
It's 'c'. But you can still define different speeds to different laboratories, with one requirement, no acceleration involved for them. they will all give you the same limit 'c', no matter what 'speed' you define them too.

Also it doesn't help making the whole ship into a engine, as the push effect from it will start at some point instead of being simultaneously pushing at the whole ship. It would be very difficult to create engines that pushes equally/simultaneously at all parts.
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But you made a really good point there. Would that be a principle for how a (rotating) black hole holds together under its evolution? It can't be, can it?

I haven't seen a reply to this yet.
If the front and back of the ship are not accelerating at (at least very nearly) the same rate, you are tearing your ship apart.

http://www.gregegan.net/SCIENCE/Rindler/RindlerHorizon.html

I haven't seen a reply to this yet.
If the front and back of the ship are not accelerating at (at least very nearly) the same rate, you are tearing your ship apart.
I had replied (with a reference) in post 13.
Essentially, if the two ends accelerate at the same rate (same g force applied for the same duration as measured by a local clock), then they'll stay the same distance apart (in the original frame) but the ship breaks up due to length contraction in that original frame.
The same thing can be expressed using accelerating frames, but that's the simplest explanation.

I have a ship that is a light year long. In frame P (parked) it extends from 0 (tail) to 366 (nose) light days.
Now I accelerate it (or at least the tail) to .866c (dilation 50%) in one month as measured by a P clock.
...
You can accelerate as hard as you like. There seems to be no limit.
I thought about this some more and found it unrealistic to accelerate the tail. The pilot is going to want to sit right in the middle where his commands can be carried out in minimal time. So how fast can the middle be accelerated? If the front accelerates less, the rear must accelerate harder. So is there a limit to that?
I think not again, but it gets funny. My ship is two light years long (1 each way from our observer midpoint). I accelerate the pilot to .866c in a month, meaning the tail has to move .54 light years in a month, sort of. The sort of saves us, but since the clock at the tail moves backwards, does it need to reach into a time when the ship was stationary?

I had replied (with a reference) in post 13.
oops.
Sorry, I missed that.
But the problem is that, as I sit on the ship, there's nothing causing it to break. Any hypothetical breakage is at odds with causality.
So I know that the acceleration of the two ends are the same (and the clocks , which are stationary from my PoV, run at the same rate).

http://www.gregegan.net/SCIENCE/Rindler/RindlerHorizon.html
Good reading, yes. Haven't even got into it yet, but it opens with a discussion of fishing from a black hole, and equating that to an accelerating observer trailing something behind, exactly what I brought up in my prior post.
Without reading the article beyond that, I see a problem: This is equivalent to a uniform gravitational field of the same force as my acceleration at the ships midpoint. As I go further back, I'm getting deeper in the gravity well, until the escape velocity back there is light speed, and my ship cannot accelerate without breaking.
That means that a sufficiently long ship cannot accelerate at all. The tail can accelerate, but any arbitrary point above that has a limit, which is near zero for most of the ship.

But the problem is that, as I sit on the ship, there's nothing causing it to break. Any hypothetical breakage is at odds with causality.
Sure there is. Picture it as a series of ships, all accelerating identically and independently. As length contracts in the original frame, the separation between ships does not. So it breaks because gaps form. The ship becomes stretched, and it cannot take that.
That's what the other thread was about, but it is framed as sort of a push for evidence of aether, which it isn't.
So I know that the acceleration of the two ends are the same (and the clocks , which are stationary from my PoV, run at the same rate).
Yes, so the separation between the two clocks is always the same, but the ship length is not, so it breaks.

OK, Let's imagine there are a string of ships each a foot apart, and each pilot carefully keeps a foot long ruler between his ship and the next.
As the string all speed up all the rulers shorten. All the ships shorten and all the gaps between the ships shorten And they all shrink to exactly the same extent.
So the rulers all still fit exactly into the gaps.
Just saying "The ship becomes stretched
does not work.
There needs to be something that I, on my ship, can see causing the break, or it won't happen.
From my PoV, the ship stays the same length.

OK, Let's imagine there are a string of ships each a foot apart, and each pilot carefully keeps a foot long ruler between his ship and the next.
As the string all speed up all the rulers shorten. All the ships shorten and all the gaps between the ships shorten And they all shrink to exactly the same extent.
So the rulers all still fit exactly into the gaps.
No, the gaps do not shorten, else the ship 20 light years ahead would be closer to the rear (in the frame where everyone was stopped) than before he started accelerating.
Really, read the other thread. It totally discusses exactly that issue.
The ship becomes stretched
does not work.
There needs to be something that I, on my ship, can see causing the break, or it won't happen.
Well, if they're a stack of independent ships, you see the gap widen. If it is one brittle object, you see it break due to being stretched. The forces of contraction don't bring the two pieces together like they would do on a real ship of reasonable length because there is an equal force the other way of the next ship pulling the opposite direction. The tension forces might alter the front and back a bit beyond what the engines are doing, but the middle has no choice but to break up.
From my PoV, the ship stays the same length.
If the line of independent ships all behave the same, then from your POV (not on any of them), the line stays the same length, yes. But it is one object, and object contract with the speed it has from your POV, so it cannot stay the same length like the line of independent ships is trying to do.

Clocks forward of a given observer will appear to run faster, and clock behind a given observer will appear to run slower.
No, because you have stipulated that they are all accelerating at the same rate. You can't have your cake and eat it!
The key word here is "relativity". Every observation is made relative to what?

No, the gaps do not shorten, else the ship 20 light years ahead would be closer to the rear (in the frame where everyone was stopped) than before he started accelerating.
Well, yes, and no.
They don't shorten from my PoV and that's exactly why my ship doesn't fall apart. If I use my (accelerating) ruler to measure the (equally accelerating) gap, I get the same measurement. From my PoV nothing is shrinking on my ship. The people I left behind at the launch pad are shrinking.
The gaps do shorten from someone else's perspective. But those people don't see anything fall apart, they just see the ship shrink slightly along its length.

Ok so you have a ship 1 lightyear long moving with inertial motion. As the front passes you the rear sends a light signal towards you. If it takes less than 1 year to reach you then you can say that length contraction is physical. If it takes 1 year then length contraction is only a function of time dilation. An interesting proposition.
EDIT Of course then you have the issue of determining time dilation. Who do you consider to be moving and who is stationary?

Clocks forward of a given observer will appear to run faster, and clock behind a given observer will appear to run slower.
No, because you have stipulated that they are all accelerating at the same rate. You can't have your cake and eat it!
The key word here is "relativity". Every observation is made relative to what?
For one, the different parts of the ship are not accelerating at the same rate, else the ship would break apart. I stipulated that the ship was always stationary in the frame of any point in the ship at any time. There is a term for it that I learned from Janus's link: The ship is 'Born rigid'. Those frames are all different depending on the point in the ship. Anyway, this is needed for the ship to not break apart.
Secondly, perhaps I was not clear. My observer above is on the ship, not in any inertial frame. For such an observer, clocks (accelerating with the observer or not) ahead of the observer in the accelerating reference frame will advance at a pace greater than the observers clock, and clocks behind will lose time, even to the point of running backwards.
This is apparent in the Andromeda paradox where a calendar there might be October in my frame when the Earth spins me towards some planet in Andromeda, but is July there 10 hours later after I've accelerated away from it. Their clock has run backwards from my POV.
That can't happen on my ship. If it did, the ship would break up.

No, the gaps do not shorten, else the ship 20 light years ahead would be closer to the rear (in the frame where everyone was stopped) than before he started accelerating.
Well, yes, and no.
They don't shorten from my PoV and that's exactly why my ship doesn't fall apart.
You ship is no different from a building sitting on a planet with a gravitational field identical to the acceleration of the ship. The upper floors accelerate less (you can tell because you weigh less up there), and they take longer to do the same acceleration (the clocks run faster up there if you compare them to the lower floors). So that's why the ship holds together. The different parts are accelerating at different rates, just like the building.
The gaps do shorten from someone else's perspective. But those people don't see anything fall apart, they just see the ship shrink slightly along its length.
This leads to a direct contradiction. From the perspective (in the frame F) of a stationary observer as the ships depart, ship X and Y both accelerate independently and identically. They are 10 light years apart, at location 0 (X) and 10 (Y), accelerating in the positive direction. They take 1 year to get to .866c relative to F so the ships are both now half their original length. Ship X has moved from 0 to about 0.45, and you say the gap of 10 light years has shortened to 5 light years, so Y is now at location 5.45, a location it could not reach from location 10 in just 1 year. It seems to have moved backwards at 4.5c despite accelerating forwards just like X did.

You ship is no different from a building sitting on a planet with a gravitational field identical to the acceleration of the ship. The upper floors accelerate less (you can tell because you weigh less up there),
It is very plainly different.
I can measure the gravitational field as I go up + down building, and I can work out from those reading how big the planet is.
That measurement the radius of the planet gives me a "scale" for the rate of change of acceleration with distance.
But on a ship, in space there's no planet nearby.
So there's nothing to calculate the change of acceleration with distance.
So there is no such change.
Fundamentally, you are saying that my ship falls apart as I watch , but no matter how hard I look on my ship, I can find no source of the force that causes it to break up.
That's a breach of causation.

Ok so you have a ship 1 lightyear long moving with inertial motion.
OK, so we're considering a different frame F than the ship's frame S. Is the ship a light year of proper length (in S), or 1 light year long in the F? Given context of the question, you apparently assume a one light year proper length, and it is contracted in F. Just making sure. Our observer is O who is stationary in F.
As the front passes you the rear sends a light signal towards you.
This is vague since no frame is specified. Let's call the event of the front passing the observer E1.
I have one signal sent from the rear at an event E2 simultaneous with the E1 in frame F. Another signal is sent at event E3 which is simultaneous with E1 in frame S.
If it takes less than 1 year to reach you then you can say that length contraction is physical. If it takes 1 year then length contraction is only a function of time dilation. An interesting proposition.
O will measure less than a year between E1 and getting the signal from E2 or E3, but the E2 signal gets to him first.
EDIT Of course then you have the issue of determining time dilation. Who do you consider to be moving and who is stationary?
The answers above do not depend on this at all.

You ship is no different from a building sitting on a planet with a gravitational field identical to the acceleration of the ship. The upper floors accelerate less (you can tell because you weigh less up there),
It is very plainly different.
Einstein says they're identical, except that the building would need to be in a uniform gravitational field, and Earth's field is uniform only over limited heights. The exact analogy would be a building in a perfect uniform field.
I can measure the gravitational field as I go up + down building, and I can work out from those reading how big the planet is.
No you cannot. You need more information than that to measure radius. There are 4 planets with gravity pretty much the same as Earth, so the guy measuring his weight change would not know the very different radius of the different planets. Saturn is actually the closest gravity to Earth.
But on a ship, in space there's no planet nearby.
So there's nothing to calculate the change of acceleration with distance.
You can walk up and down the ship with a scale, just like you did with the building.
Fundamentally, you are saying that my ship falls apart as I watch , but no matter how hard I look on my ship, I can find no source of the force that causes it to break up.
The force is the front of the ship pulling too hard, trying to get further ahead of the rear.
Please comment on the contradiction I pointed out in my prior reply to you.

OK, so we have an acceleration limit on our long object.
So let's give an example, and see if we can generalize afterwards.
I have a ship that cannot take stress as I've described. It is 100 light years in length, stopped in Frame F. I want to move it forward by one light hour (about 1.08 billion km) in frame F. How quickly (as measured in F) can I do that? Obviously a tiny object can do it in about an hour at maximum speed.
We can't go at maximum speed. If the tail T accelerates to c in an instant, the nose N requires 100 years to get up to that speed and by that time it has moved far further than a lousy light hour. So it seems we want to instantly accelerate T just enough to get the nose of the ship to our destination (100 LY + 1 light hour) in the frame of T, and then instantly accelerate N by the opposite amount to drag the tail up the same distance. Boom. We've moved the desired distance.
So let's see, there are 876000 hours in a century, so we want to dilate the distance between the target of N and the current position of T by that factor (876000/875999) which happens at about 452 km/sec. So I instantly accelerate T to 452 km/sec, and then slow down at a steady pace until I stop. That's an average of 226 km/sec, so it takes over 55.3 days to move my ship that far. It cannot be done faster. Passengers near either end will die of the G forces if the engines don't accelerate them with the rest of the fragile ship, but the ones in the middle will experience a snaillike acceleration of about 0.68 m/sec every hour.
I will get disagreements of course, but I'm going to defend that answer.

The force is the front of the ship pulling too hard, trying to get further ahead of the rear.
No.
I carefully set the engines to produce the same acceleration.
Each section of the ship has the same mass.
So, they all are subject to the same forces.
All that force (for each section) goes into moving that bit of the ship
So there's none left over to pull my ship apart.
Please comment on the contradiction I pointed out in my prior reply to you.
OK.
Your contradiction is based on claims that you can not justify.
No you cannot.
Yes I can because the change in apparent mass is not linear.
Essentially, if the change with height is slow then the radius is big.
Einstein says they're identical, except that the building would need to be in a uniform gravitational field
So, it's only identical if you have an infinitely large planet.
Since infinite planets don't exist there is a difference.
Thanks for confirming that I'm right.

For one, the different parts of the ship are not accelerating at the same rate, else the ship would break apart.
That is obviously incorrect.

No you cannot. You need more information than that to measure radius. There are 4 planets with gravity pretty much the same as Earth, so the guy measuring his weight change would not know the very different radius of the different planets.
No more information required, if you can solve simultaneous equations (most 12yearolds can).

No more information required, if you can solve simultaneous equations (most 12yearolds can).
I stand corrected on this one, from a nonrelativistic standpoint. A small radius produces a nonuniform gravitational field and the radius is determined by the Newtonian detection of that nonuniformity.
A uniform field is equivalent to infinite radius, and that is what would be experienced in an accelerating ship. You weigh less on the ship due to relativistic reasons: A rock dropped at the bottom of the ship/building might accelerate at 9.8 m/sec, but one higher up (a lot higher up) will fall at 9.7 m/sec, partly because the clock up there runs faster and the rock is measured for a shorter duration, but also because you weigh less up there.

OK.
Your contradiction is based on claims that you can not justify.
They're your claims.
No you cannot.
Yes I can because the change in apparent mass is not linear.
Essentially, if the change with height is slow then the radius is big.
See my comment above. I was wrong on this one. The rocket is equivalent to infinite radius gravitational field.

They're your claims.
Don't be silly. The title of the thread is your claim not mine.

You (Halc, not BC) seem to forget that relativity is just that. There is no relativistic effect within a body subject to uniform acceleration because there is no external comparator for it to be "relative to".

They're your claims.
Don't be silly. The title of the thread is your claim not mine.
The thread title is a question. It implies a potential claim that there are limits that prevent long things from moving as fast as smaller things.
The claims being put out by you and alancalverd seem to fall into two categories of clock synchronization and the fact that all parts of a ship accelerate uniformly.
As for the former:
From post 8:
Therefore the ship must be modelled as an array of infintesimal elements, each with its own engine and some means of ensuring that they work together in complete synchronism. Thus the entire ship must accelerate as a single entity. There being no change in length, there can be no relative velocity or acceleration between the front and the back of the ship and thus no change in perceived clock rates between observers on the ship.
From post 24:
So I know that the acceleration of the two ends are the same (and the clocks , which are stationary from my PoV, run at the same rate).
OK, those quotes had claims about both categories.
From post 29:
Clocks forward of a given observer will appear to run faster, and clock behind a given observer will appear to run slower.
No, because you have stipulated that they are all accelerating at the same rate. You can't have your cake and eat it!
I have stipulated no such thing. If they all accelerate at the same rate, the ship breaks apart. That is the essence of your red claim vs mine. We're dealing with the time thing here.
Post 34:
Fundamentally, you are saying that my ship falls apart as I watch , but no matter how hard I look on my ship, I can find no source of the force that causes it to break up.
Since time moves faster for the front of the ship, if it accelerated at the same rate as the rear, it would do so for a longer time, and pull away from the rear. That is a way of viewing the force that tears apart the ship.

My simple example is this: I have two small ships N and T that accelerate identically to some significant speed. Their clocks are synced as they start, simultaneously in the frame F where they were at rest. They're 1 light year apart initially, with N in the lead. Let's say they accelerate to .5c and then coast at that speed.
Their clocks will still be synced in frame F because both ships have done identical things. Do either of you disagree with that?
In the inertial frame of either ship after both have stopped accelerating, their clocks are not in sync. Different frames order events differently, so when the T clock reads Jan 1, the N clock will read I think Apr 14 or so.
If the two ships were in fact one long ship accelerating like that, the clocks, in the frame of the ship, would get very out of sync.
If their clocks are still in sync as you both seem to claim, then the synchronization of clocks moving at identical velocity can be done in any frame. This is what I'm getting from both of you. Tell me if I am misrepresenting your position.
  
On to your claims that all parts of a ship must accelerate identically.
See the red portions above, but I have plenty more:
Post 9:
If the front and back of the ship are not accelerating at (at least very nearly) the same rate, you are tearing your ship apart.
Post 27:
As the string all speed up all the rulers shorten. All the ships shorten and all the gaps between the ships shorten And they all shrink to exactly the same extent.
So the rulers all still fit exactly into the gaps.
Post 30:
The gaps do shorten from someone else's perspective. But those people don't see anything fall apart, they just see the ship shrink slightly along its length
If a ship moves uniformly at .866c, the people left behind should see it shorten by half, not just 'slightly'. I don't claim that it moves uniformly in frame F since the parts are not accelerating identically. So I don't get this contradiction.
Post 38:
I carefully set the engines to produce the same acceleration.
Each section of the ship has the same mass.
So, they all are subject to the same forces.
All that force (for each section) goes into moving that bit of the ship
So there's none left over to pull my ship apart.
What is left over is the ships pulling apart from each other in their own frames. They remain equally spaced only in the original frame.
Post 39:
For one, the different parts of the ship are not accelerating at the same rate, else the ship would break apart.
That is obviously incorrect.
What is obvious is Newton's rules, and he was wrong (or at least very incomplete) about it. Please comment on my example below that illustrates what follows from what you find obvious.
Post 44:
There is no relativistic effect within a body subject to uniform acceleration because there is no external comparator for it to be "relative to".
I can locally feel acceleration, without consulting any external comparator. Speed is definitely relative, but acceleration and rotation are not, and both have relativistic effects.
OK, that seems to be my list of quotes where one or the other of you seems to claim that the front of a ship accelerates identically (same g force) as the rear. So I put together my little counterexample assuming that claim. Neither of you commented on it except for BC claiming that it was based on my claims, not his. I'll do it again.
= = = =
There is a long ship (20 light years) made up of a lot of small ships bolted together nose to tail. The small ships are all blue except every light year there is a yellow one with a big number on it. Each numbered ship (Y0 through Y20) is parked next to a space dock labeled D0 through D25 spaced every light year, and everything is stationary in frame F. The ship ends at D20, but there are 5 more just so we have a grid extended a little further. All clocks are synchronized in frame F, at least before movement starts.
In addition, just for jollies, we can have 21 independent pacer (P0P20) ships that sit alongside the yellow D ships. They’re identical, just not bolted to the entire mass. Their intent is to keep pace with the big ship.
Flight plan: Each ship is going to accelerate at 1.95g in the 20 direction, for 1.31 years (ship clock) and then coast. All parts of the big ship plus all the little pacing ships do the same thing.
As a passenger with no window to see the space docks go by, there would be no way to tell which of the ships you are on since they all pull the same g for the same amount of time.
After 1.73 years pass in frame F, each ship is moving at .866c, enough for 50% dilation of everything. The acceleration is paced exactly so that this velocity is achieved just when each ship passes the next space Dock:
Y0 and P0 are at D1,
Y1 and P1 are at D2,
….
Y20 and P20 (the nose of the big ship and its pacer) are at D21.
Each space Dock sees these things happen at the same time on their clocks, which is 1.73 years from time 0. The ships also see their first dock go by, but their clocks each show 1.31 years because they’re running slower at that speed. Point is, they all log the same time on their local clocks as they see the first space dock go by. Do you agree with that? All 21 yellow ships and 21 pacer ships have executed the identical flight plan at the same time.
So at time 1.73 years. (as defined by frame F) the entire big ship is going at .866c, it is only 10 light years in length, but its tail is at space dock 1 and the nose is at space dock 21. That’s still 20 light years separation.
I see that as a blatant contradiction. Either the ship hasn’t contracted as relativity says it should, isn’t actually moving at .866c, or it has shattered into a bunch of separated little ships. My vote of course is with the last one.
Please tell me where I went wrong with all that. Don’t assert something else like you’ve been doing. Tell me where the story above is wrong. The whole thing is pretty much as seen in frame F, the only frame in which the ship is expected to contract.
From the ship frame, the space docks are contracted and only half a light year apart, and the ship is the original 20 light years in length. So why is each yellow ship logging a space dock going by? They should be seeing only the even numbered space docks since the odd ones are each halfway between two numbered yellow ships. So another contradiction.
None of this matches my story, where the rear accelerates harder than the front. The passengers very much know which end of the ship they’re in. Clocks do not stay synchronized from front to back. My story is not self contradictory.

What is left over is the ships pulling apart from each other in their own frames. They remain equally spaced only in the original frame.
Because they all move identically, they all experience the same "frame".The clock on my mantelpiece is in the same frame as my head so they agree on time. Both are effectively accelerating (at about 9.8 m/s/s) but that affects both equally.
The clock upstairs reads slightly differently but "upstairs" is only relevant because there's a well defined "up" here because of the variation of the gravity of Earth.
You only get a gradient of time dilation if you have a gradient of acceleration. And I built my ship so that it all accelerates at the same rate.
Sure none of the clocks says the same thing as those on the launchpad but, from the PoV of the ship's crew, "ship time" is well defined.

OK, that seems to be my list of quotes where one or the other of you seems to claim that the front of a ship accelerates identically (same g force) as the rear.
Your initial condition, that the ship is fragile, demands it. There is nothing to discuss, otherwise.

Your initial condition, that the ship is fragile, demands it. There is nothing to discuss, otherwise.
So discuss it. I took exactly that premise and drove it to inconsistency in the example in the end. I asked that you find the flaw in the example, else your assertion is worthless.
I asked explicitly for you to take apart my example, showing me where it went wrong.
All I get is more assertions.
Maybe argument from google search will help.
I found a similar situation at https://www.av8n.com/physics/hyperbolicmotion.htm (https://www.av8n.com/physics/hyperbolicmotion.htm)
Section 2.1 shows a cluster of 5 unconnected ships spaced every 0.2 LY, (very much like my pacer ships) accelerating at 1g for half a year.
1) the ships spacing in the original frame (which they call the terrestrial lab frame) remain the same: No length contraction of the space between them, just like I said.
2) The red dashed lines are lines of constant time in the inertial frame comoving with the cluster. The black dots are constant time as measured on the ships. The red dashed lines are not parallel with the dots, so the clocks are not in sync, in contradiction with your assertions.
A few quotes from the bullets below the diagram:
Relative to the clock in the middle, the clock at the back of the cluster racks up less elapsed proper time.
By the same token, relative to the clock in the middle, the clock at the front of the cluster racks up more elapsed proper time.
This is just as I had worked out earlier in the thread. The engine at the front runs longer, but at lower power (less g). In the end, all ships are going the same speed after they shut down.
Another quote, directly to the point:
What’s far more serious is that at the end of the maneuver, the cluster is not the same shape as when it started out! The length between subrockets has increased.
This is of course what tears the ship apart if it is one big ship instead of a cluster of little ones.
Hey, the problem has a name!
This was pointed out by Dewan and Beran (reference 6) and eventually became known as Bell’s Spaceship Paradox.
The references are not links, so I just googled that.
Wiki has a page on it:
https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox (https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox)
The original problem seems to be a pair of ships connected by a string as they accelerate identically.
Both spaceships start accelerating simultaneously and equally as measured in the inertial frame S, thus having the same velocity at all times in S. Therefore, they are all subject to the same Lorentz contraction, so the entire assembly seems to be equally contracted in the S frame with respect to the length at the start. Therefore, at first sight, it might appear that the thread will not break during acceleration.
This argument, however, is incorrect as shown by Dewan and Beran and Bell.[1][2] The distance between the spaceships does not undergo Lorentz contraction with respect to the distance at the start, because in S, it is effectively defined to remain the same, due to the equal and simultaneous acceleration of both spaceships in S. It also turns out that the rest length between the two has increased in the frames in which they are momentarily at rest (S′), because the accelerations of the spaceships are not simultaneous here due to relativity of simultaneity. The thread, on the other hand, being a physical object held together by electrostatic forces, maintains the same rest length. Thus, in frame S, it must be Lorentz contracted, which result can also be derived when the electromagnetic fields of bodies in motion are considered. So, calculations made in both frames show that the thread will break; in S′ due to the nonsimultaneous acceleration and the increasing distance between the spaceships, and in S due to length contraction of the thread.
Proof by wiki, Q.E.D.

BC
It's seldom I don't agree with you
But this, ahem, I don't agree to :)
" As the string all speed up all the rulers shorten. All the ships shorten and all the gaps between the ships shorten And they all shrink to exactly the same extent. So the rulers all still fit exactly into the gaps. "
I don't see how that is possible. We're talking a acceleration here, and in any acceleration there has to be a point of 'force' initiating it, and keep on doing so each time something needs to pushed to a higher speed. To spread it out you will need uniform motion as I think.
=
spelling sux

The only way we can create a engine that pushes equally at all points is imaginary. It would have to be 'dragged' in all points to do it. Which then means you need to create a 'extrinsic force' acting on each point of that engine equally. Now that would be a cool idea if someone knew how to create such a force acting on our spaceship

So discuss it. I took exactly that premise and drove it to inconsistency in the example in the end. I asked that you find the flaw in the example, else your assertion is worthless.
The flaw is in the notion that you can accelerate different parts of an object at different rates without distorting the object. That is too obvious to merit further discussion.

So discuss it. I took exactly that premise and drove it to inconsistency in the example in the end. I asked that you find the flaw in the example, else your assertion is worthless.
The flaw is in the notion that you can accelerate different parts of an object at different rates without distorting the object. That is too obvious to merit further discussion.
My example did not do that. All parts were accelerated at the same rate. Did you even read it??? Your comments suggest that you have not.
Did you read the various articles I found on the web? None of them support your view. You are so sure that you are right that you will not read examples that show otherwise.

We're talking a acceleration here, and in any acceleration there has to be a point of 'force' initiating it, and keep on doing so each time something needs to pushed to a higher speed.
The only way we can create a engine that pushes equally at all points is imaginary.
The sun accelerates Pluto in this way, so it is neither impossible nor imaginary.
You are posting about the engineering challenges of a thought experiment, which detracts from the points I'm trying to make. I have no intention of actually needing to build this, so the engineering is of no concern.

My example did not do that. All parts were accelerated at the same rate.
Where is that example? I'm too lazy to search.
If all parts are accelerated at the same rate, then the accelerated thing breaks, right?
We must 'manually' Lorentz contract our long and fragile object. Short and sturdy rods contract 'automatically'.

My example did not do that. All parts were accelerated at the same rate.
Where is that example? I'm too lazy to search.
If all parts are accelerated at the same rate, then the accelerated thing breaks, right?
Bottom of post 45, after the = = =
Yes, I accelerate every part at the same rate, and bad things happen.
We must 'manually' Lorentz contract our long and fragile object. Short and sturdy rods contract 'automatically'.
Nothing sturdy involved. The idea is to put no significant stress on the ship. That means accelerating each piece differently. If you accept this, then the main post on the table actually addresses the subject matter of the topic: A limit to how quickly a large thing can be moved.
See post 37 for that, where I show that a 100 LY object needs a minimum of 55 days to be moved (stopped, accelerate, and slow to a stop again) a distance of one light hour. A short object can do it in about an hour of course.

Not really Halc, a gravitational acceleration is still a geodesic as far as I know, that means that Pluto still is in a uniform motion. Then again, I missed the article you referred to in where the string breaks between the two ships so you already seen one definition. But, thinking of it this way it becomes slightly trickier.
Depending on acceleration rate, shouldn't there be a threshold for where that string breaks, meaning that if one just accelerate slow enough you might come up to a very high speed relative some distant suns blue shift without breaking that string. If that would be true then there would be two thresholds, one due to ones rate of acceleration, the other due to the impossibility for matter (proper mass) to get to 'c'?
After all, we all 'accelerate' as we move around in our daily life

In which case I will agree on BC:s definition existing as a possibility too.

If that would be true then there would be two thresholds, one due to ones rate of acceleration, the other due to the impossibility for matter (proper mass) to get to 'c'?
Neither.
Perhaps I misunderstood what is being described here.
Completely ontopic, I don't see either of these two factors limiting how long it takes for an object to get from A to B, stopped at both ends.
I am assuming infinite acceleration, meaning any part of the ship can accelerate to the velocity of choice in zero time. If it takes time to do it, then you can add that time to the total trip time I guess.
As for speed, moving at c will move us too far. We will overshoot our target (B). A pointobject like a photon can do that, but a ship with nonzero dimensions cannot without overshooting. So none of the ships are requested to move at c, but if you're going a long way, you probably get pretty close to it.
My method of moving the ship is quite simple. You have a length L that is the distance between the starting point of the tail of the ship and the destination point of the nose of the ship. Accelerate the tail as quickly as possible (instantly?) to whatever speed is required to contract L down to the length of the ship. That brings the nose to its destination (or actually brings the destination to the nose). Now we instantly stop the nose, which springs L back to its original length, bringing the tail to its final destination. We're done. The time it takes to do that is the same as the amount the clocks get out of sync between the nose and the tail.
So if I have a ship that is a lightmonth in length and I want to get the nose of the ship to a planet that is a lightyear away from the tail, L is one light year. I need to compress L to a 12th its size in ship's frame, which happens at .9965c, so we accelerate the tail to that speed. At that time (in the frame of the tail) we instantly stop the nose, and we're done. The trip takes 364 days in inertial time, and about 97 days ship time.
That was a ship that was quite a bit shorter than the distance we wanted to move, so we were able to get it up to an impressive speed. If the ship were much shorter, it would take almost the same inertial time, but almost no ship time.
I find it interesting that having a ship that is already a 12th of the way there (due to its length) to make almost no difference in the time required to get there. Have to play with that more.

It's not possible Halc. No way you can accelerate at such a rate without the ship breaking into pieces due to LortentzFitzgerald contractions, as well as tensile material stress. That ship will need unobtanium to work I'm afraid.
=
you need to find a solution in where every point of that ship is in a same frame of reference relative the push of what engine you imagine, I don't see how that can be done myself.

you need to find a solution in where every point of that ship is in a same frame of reference relative the push of what engine you imagine, I don't see how that can be done myself.
That was my solution. The entire ship is always stationary in its own frame at all times.
If you feel a need to limit acceleration, fine, but it will add to your minimum trip time.

Can someone help me out here please?
I'm meant to be leading this "ship" it's actually a flotilla of little ships.
All the pilots know that they can accelerate their craft at well defined rates and they all move at the same speed WRT the launch pad (which they left long enough ago that its local gravity isn't a factor)
I know that I can hold the fleet together simply by making sure all the little bits of my ship accelerate at the same rate.
But someone is now saying that , in spite of being deliberately held together, it will fall apart.
He refuses to give a mechanism, but my crew are still starting to get jumpy.
What should I tell them?
Do I tell them to rely on common sense, or do I tell them that magic gremlins are pulling the ship apart?
(These are experienced spaceship pilots. they consider relativity to be common sense)

My method of moving the ship is quite simple. You have a length L that is the distance between the starting point of the tail of the ship and the destination point of the nose of the ship. Accelerate the tail as quickly as possible (instantly?) to whatever speed is required to contract L down to the length of the ship. That brings the nose to its destination (or actually brings the destination to the nose). Now we instantly stop the nose, which springs L back to its original length, bringing the tail to its final destination. We're done. The time it takes to do that is the same as the amount the clocks get out of sync between the nose and the tail.
What stops you accelerating it faster than that? If you can individually accelerate each atom to a tiny fraction below c and get the timing right, all of them can then move at that speed with a delay until the front of the ship is moving too, and then when you stop, the rear ones stop first, being decelerated to a speed that makes them fully happy to sit next to the atoms stopped around them  the length of the trip shouldn't limit you to slower speeds than that on shorter trips. With the right kind of launch and catch system, this could be done in such a way that nothing breaks despite the astronomical acceleration force because the arrangement of atoms isn't broken in any way  they are just momentarily the wrong distance apart, but that's put right again at a rate that propagates along the ship at a fraction below the speed of light.

Can someone help me out here please?
I'm meant to be leading this "ship" it's actually a flotilla of little ships.
All the pilots know that they can accelerate their craft at well defined rates and they all move at the same speed WRT the launch pad (which they left long enough ago that its local gravity isn't a factor)
I know that I can hold the fleet together simply by making sure all the little bits of my ship accelerate at the same rate.
But someone is now saying that , in spite of being deliberately held together, it will fall apart.
He refuses to give a mechanism, but my crew are still starting to get jumpy.
What should I tell them?
Do I tell them to rely on common sense, or do I tell them that magic gremlins are pulling the ship apart?
(These are experienced spaceship pilots. they consider relativity to be common sense)
This is launchpad personnel's view:
If the readings of the accelerometers of the ships are the same, then the increasing time delay of light signals traveling towards the front causes a pilot to see a ship at the rear becoming increasingly retarded. Said pilot should see an elastic band connecting the ships stretching, otherwise there is a inconsistency: Pilot sees other ship falling behind, but does not see the connecting elastic band getting longer.
If on the other hand the observed accelerations observed by the pilots are the same, then the readings of the accelerometers are not the same.
Oh yes, it was the pilots' view that was requested. Well it's that everything happens slower on ships closer to the rear. Whatever happens inside a rocket motor happens slower, whatever happens inside an accelerometer happens slower. Slowed down accelerometer measures slowed down motor to accelerate the ship 'normally'.

What stops you accelerating it faster than that?
I need to stop when I get there. I accelerate the tail just enough to contract the distance I need to travel to be exactly even with the nose of the ship. If it goes any faster, the nose overshoots the place where it needs to stop.
Keep in mind that during the acceleration phase, the tail of the ship never moves. If I accelerate over finite time, then yes, the tail moves.
If you can individually accelerate each atom to a tiny fraction below c and get the timing right, all of them can then move at that speed with a delay until the front of the ship is moving too,
That makes parts of the ship not stationary, and other parts stationary. It can't take that (right ?!). Perhaps it is a mathematical stipulation that the ship always be stationary in its own frame.
I think I see what you're envisioning, sort of compressing the ship at light speed like a slinky. Any two parts of the ship going a different velocity are always separated in a spacelike manner, never a timelike manner, so the discrepancy cannot cause breakage. It violates my mathematical stipulation, but can a brittle ship take that? I cannot identify what would break. What the tail is doing at event X is of no concern to parts of the ship outside X's light cone.

If on the other hand the observed accelerations observed by the pilots are the same, then the readings of the accelerometers are not the same.
What are the pilots reading if not the accelerometers? How do they otherwise decide that they're the same?
Second note is, same as what? Identical to the value measured on other ships, or just identical from moment to moment? Nobody seems to be proposing that a particular ship vary its acceleration during the process (except David just now), but it isn't off the table either.
An accelerometer on a ship will measure proper acceleration. Not sure what meter the lauchpad guy is reading, but that one will read acceleration in his frame, not the ship's proper acceleration. The former falls off as speed grows, while proper acceleration should be constant for the duration.

With the right kind of launch and catch system, this could be done in such a way that nothing breaks despite the astronomical acceleration force because the arrangement of atoms isn't broken in any way  they are just momentarily the wrong distance apart, but that's put right again at a rate that propagates along the ship at a fraction below the speed of light.
This is actually a cool idea. The example of my 100 LY ship moving only one light hour would have the tail start and stop long before the nose ever moves. The wave of movement would propagate up to the front (at what rate?).
The thing would move exactly like a caterpillar.
Would that be faster? My ship took 55 days (see post 37), but a 100 LY ship would seem to need more time than that for the 'wave' to reach the front.
It seems not to violate the brittleship thing. There is a point in the ship where all the matter to the rear is moving nearly at c, but the stuff in the other direction is stopped. If that persisted for even a moment, it would shatter, but it doesn't. The wave passes before any stress/strain can build up. Still, the wave would seem to propagate at 2c at best. It would take 50 years to move my big ship that way, not just 55 days.
For slower speeds (well under c), the wave propagates faster than 2c. We need to find a sweet spot that balances wave speed with physical speed. It would depend on the ratio of ship length to trip length it seems. My method I suspect is independent of trip length, at least for short trips. I think it takes 55 days to go any short distance. The figure is not specific to travel of one light hour.

Still, the wave would seem to propagate at 2c at best.
That was wrong. If we accelerate the tail to light speed, the wave propagates at light speed, but the wave seems to move faster with slower ship speeds, so for instance if we accelerate the tail to .866c, the wave moves at about 1.732c (sqrt(3)), if I did that correctly. The caterpillar gets there faster if it moves slower. Whodathunkit?

What are the pilots reading if not the accelerometers? How do they otherwise decide that they're the same?
Second note is, same as what? Identical to the value measured on other ships, or just identical from moment to moment? Nobody seems to be proposing that a particular ship vary its acceleration during the process (except David just now), but it isn't off the table either.
An accelerometer on a ship will measure proper acceleration. Not sure what meter the lauchpad guy is reading, but that one will read acceleration in his frame, not the ship's proper acceleration. The former falls off as speed grows, while proper acceleration should be constant for the duration.
Bell's spaceships are seen to accelerate at the same rate by the launchpad ... and clocks in the ships are seen to tick at the same rate. And accelerometers screwed on the ships and observed by a telescope from the launchpad are seen to read the same value.
A pilot of a normal spaceship sees all parts of his ship to accelerate at the same rate.

Bell's spaceships are seen to accelerate at the same rate by the launchpad ... and clocks in the ships are seen to tick at the same rate. And accelerometers screwed on the ships and observed by a telescope from the launchpad are seen to read the same value.
A pilot of a normal spaceship sees all parts of his ship to accelerate at the same rate.
Agree to all but the last one. Our pilot would need an accelerometer bolted to either end of his ship, and if he looked at them, they'd read a different value. If the ship is short as most are, they'd not read very different, but it gets quite apparent with longer ships. They're getting shorter in launchpad frame, so the front isn't getting up to the same velocity in that frame. In ship frame, the front clock is running faster, so it takes more time to do the same acceleration. In both frames that spells different reading on the accelerometers at either end of the ship.

I think I might be able to see what you are on about.
Imagine I assemble my crew of pilots + ships in space then set them off at 1 second intervals.
As they leave the launch point they are quite close together.
At their destination, they also arrive at 1 second intervals. And now they are doing 100,000 miles a second
But they are now travelling at high speed so 1 second is long enough to travel 100,000 miles
So the flotilla has "stretched" in transit.
But the problem there is that you can't say at what time I launched the flotilla. Was it when I set off the first ship, the last one, tee one in the middle or what?
If there wasn't a flotilla at the start, how can you say it stretched?
(Obviously, this isn't a relativistic effect)

I think I might be able to see what you are on about.
...
But the problem there is that you can't say at what time I launched the flotilla
...
(Obviously, this isn't a relativistic effect)
That is not at all what anybody is on about. The long ship, or the flotilla that paces it, are all launched at the same time in the initial rest frame of everything.
It is very much a relativistic effect that I'm talking about. The thing you mention there is indeed not a relativistic effect.

If an array of particles all launch at the same time, with the same acceleration vector, their mutual relative velocities will remain zero so they will remain at the same separation relative to one another. No relative motion = no relativistic effects.
If the initial array was a straight line, then an observer at the launch point will see the line contract in the radial direction, but not in the tangential direction, as they approach c relative to the launch point. Relative motion = relativistic effects.

Agree to all but the last one. Our pilot would need an accelerometer bolted to either end of his ship, and if he looked at them, they'd read a different value. If the ship is short as most are, they'd not read very different, but it gets quite apparent with longer ships. They're getting shorter in launchpad frame, so the front isn't getting up to the same velocity in that frame. In ship frame, the front clock is running faster, so it takes more time to do the same acceleration. In both frames that spells different reading on the accelerometers at either end of the ship.
Yes, the accelerometers show different readings, and from that we know that I did not say or mean that the accelerometers show the same readings.
I meant the eyes of the pilot tell him that the accelerations are the same, the same way as the eyes of drag racers tell the guys in the cars what the difference of accelerations is.

If an array of particles all launch at the same time, with the same acceleration vector, their mutual relative velocities will remain zero so they will remain at the same separation relative to one another. No relative motion = no relativistic effects.
This is all from the inertial frame perspective. Their mutual relative velocities will remain zero in the original stopped inertial frame, yes. There will be relativistic effect: time will pass for the particles more slowly but identically because they're moving.
If the initial array was a straight line, then an observer at the launch point will see the line contract in the radial direction, but not in the tangential direction, as they approach c relative to the launch point. Relative motion = relativistic effects.
No. They're all accelerating identically, so no contraction. See my very carefully worded example at the bottom of post 45 which describes exactly this kind of uniformly accelerating array. For contraction to happen, the tail needs to accelerate more than does the front, bringing it closer to the front in the original inertial frame.
I encourage you to reword that example with the same acceleration to give the coordinates of the various parts of the ship after the acceleration completes. Each piece accelerated identically for 1.3 years (ship time) or about 1.7 years in the inertial frame. They all move exactly one light year (which is why those numbers were chosen), and that makes them all still the same distance apart. No contraction of the space between them. If you contract that space, some of the ships need to move far faster than light to get the ship length down in time.
Read and comment on the example (bottom of post 45) and stop waving it off because you know a different answer. All I get is you holding your ears going "Lalala" when the contradiction is pointed out, or when I find several articles on the web (post 48) that support what I've been trying to say.
Describing in the frame of the array cannot be done because there is no one such frame. Each of the elements is moving at a different speed because the ones at the front have been accelerating for a longer time than the ones in the rear. Their clocks were in sync in the inertial frame, so they cannot be synced in any other (except you appear to also deny relativity of simultaneity). That means they've accelerated for different amounts of time, and that's why they pull apart from each other in the frame of any of the pieces.
My thread isn't even about this. I assumed one knows that different parts of the ship accelerate differently, and the question was if this limits a long ship from going places anytime quickly.

I meant the eyes of the pilot tell him that the accelerations are the same, the same way as the eyes of drag racers tell the guys in the cars what the difference of accelerations is.
The drag racers are side by side, not end to end, and not moving at relativistic speeds, and are doing a nonlocal observation.
I don't think eyes can detect acceleration. If I put a camera in a car pointing down at the back seat (not out the window), and somewhere in a minute of footage the car accelerates, I could not tell from watching the camera footage when that acceleration starts. Acceleration is felt, and possibly visually detected by seeing something bend to the side or some other accelerometer, and it will be felt very different at one end of the ship than the other.
In my example of a long ship moving a short way (post 37), the people at either end of the ship die the strawberry jam death, and the ones in the middle die of boredom. That would be something the pilot could see except the trip is shorter than the time needed for the image of the dead people at either end to reach the pilot in the middle.

The drag racers are side by side, not end to end, and not moving at relativistic speeds, and are doing a nonlocal observation.
I don't think eyes can detect acceleration. If I put a camera in a car pointing down at the back seat (not out the window), and somewhere in a minute of footage the car accelerates, I could not tell from watching the camera footage when that acceleration starts. Acceleration is felt, and possibly visually detected by seeing something bend to the side or some other accelerometer, and it will be felt very different at one end of the ship than the other.
In my example of a long ship moving a short way (post 37), the people at either end of the ship die the strawberry jam death, and the ones in the middle die of boredom. That would be something the pilot could see except the trip is shorter than the time needed for the image of the dead people at either end to reach the pilot in the middle.
Do I really need to explain that one drag racer gets ahead of the other one when the accelerations are not the same
:) ::)

Do I really need to explain that one drag racer gets ahead of the other one when the accelerations are not the same
Apparently, to some folk here, yes. You need to explain it.
You also need to explain that drag racers actually look out of the window.

Thus the entire ship must accelerate as a single entity. There being no change in length, there can be no relative velocity or acceleration between the front and the back of the ship and thus no change in perceived clock rates between observers on the ship.
We need to pinpoint those rules.
There can be no change in proper length. But there is very much going to be changes in relativistic length.
For it to have a proper length, it needs to be stationary in its own frame. I fretted a lot about that one since it seems to be difficult to avoid, but decided it was a mandatory requirement, and that the solution to the problem lies exactly in that requirement.
Clearly my assessment of the rules was wrong. It seems a brittle ship doesn't need to be stationary in any frame, and thus its proper length is only defined as the collective proper length of the parts.
In particular, a ship that is accelerating has parts that are necessarily moving at different velocities in other frames (like the original 'stopped' frame), and my description kept the ship stationary only in its own frame. If it can move at different speeds in that frame, it can do it in its own, and that means it might not even have a frame that is its own.
So David's post clued me into that. You can have the bottom half of the ship going at .9c and the top half stopped. That doesn't break the brittle ship unless any time is allowed to pass without moving the line between the fast stuff and the slow stuff.
So picture a causal diagram for the exact point/event E in the ship where this velocity difference exists. Draw a big X with the event in the middle.
The stuff at the bottom is the past light cone, and nothing is moving in that cone. As far as E has measured, the ship is stationary and has no reason to feel stress or strain.
The region above the X is the future light cone, and everything moves at .9c there. As far as E will measure, the ship will always be uniformly fast and has no reason to feel stress or strain. The stuff to the left and right are very different, but out of the causal cone. The ship at E will need to accelerate to .9 instantly as the wave passes by. It does not see the wave coming since it travels at faster than light, so the computer needs to know the plan, but we always said that.
Interestingly, the wave travels at just over light speed if the velocity change is near c, but far faster than light if the velocity change is low. Because of this, the fastest way to get from A to B is to go slow. I think my original plan is still the optimal one. I could not think of a way to get the ship from A to B faster by allowing parts to move at different velocities like that.
I moved my ship one light hour in 55 days by keeping the speed down, but if we go at .999c and let the wave move up the ship, it takes 50 years (plus an hour). I need to run the numbers for a wave resulting from an abrupt acceleration to 452 km/sec, which was the winning speed before.

Can you combine the two methods? Your way produces a faster time for the front of the ship (by setting it moving sooner), while mine produces a faster trip time for the back of the ship. Apply your method first to set a wave of acceleration through it much faster than the speed of light, then apply my method afterwards to increase the speed of the back end to nearly c with this wave running through the ship at a slower speed. The next thing to look at would be whether the trip time for the middle of the ship can be improved too.

Can you combine the two methods? Your way produces a faster time for the front of the ship (by setting it moving sooner), while mine produces a faster trip time for the back of the ship.
Did you run the numbers? I don't think any part of the ship gets anywhere faster by your way. It opened my eyes to an unnecessary condition I had been putting on the ship, but I don't think it helps win the race. Not sure.
I admit that I have not yet run the numbers for a pure caterpillar movement at say 300 km/sec. Mine moves at an average pace of 226 km/sec, with the middle achieving twice that halfway through the trip. 300 might be too slow, since it needs to add travel time (many days) to the wave propagate time (also days?). Faster one is, the slower the other one is. There must be an optimal point, but I've not plugged the numbers yet.
Would a hybrid plan like you suggest help? Maybe so.

To drive the points home, my objects will be large and fast, but never with impossible properties like being massless, infinite rigidity, or with instantaneous acceleration
The ship at E will need to to accelerate to .9c instantly...
Hmmm... A few premises being violated there...
I don't think eyes can detect acceleration.
But eyes and ears can. And butts certainly can.
Have you ever been in an aeroplane, stationary at the end of a runway? The aisle looks perfectly level.
Then the plane accelerates down the runway. The aisle looks like it is tilting up towards the front of the plane. But looking out the window, you see that the plane has not rotated yet (ie it hasn't lifted the front wheel off the runway). Your ears can detect the acceleration, and they tell your brain that the direction of "up and down" has shifted, so your brain interprets the aisle as being tilted.
Even with your eyes closed, your butt feels the acceleration in your seat. It doesn't take much brains to detect acceleration.
But it does take external inputs to distinguish acceleration from the effects of gravity.

Halc: try reading about relativity (Einstein's book https://www.penguinrandomhouse.com/books/297702/relativitybyalberteinstein/9780143039822 is probably the easiest to read because it was written by a genius rather than someone trying to bask in reflected glory) instead of making it up and getting it wrong.

Halc: try reading about relativity (Einstein's book https://www.penguinrandomhouse.com/books/297702/relativitybyalberteinstein/9780143039822 is probably the easiest to read because it was written by a genius rather than someone trying to bask in reflected glory) instead of making it up and getting it wrong.
I don't think you should be making such a recommendation to someone who understands relativity much better than you do. Halc knows what he's talking about, but you keep repeating the same mistake.
If an array of particles all launch at the same time, with the same acceleration vector, their mutual relative velocities will remain zero so they will remain at the same separation relative to one another. No relative motion = no relativistic effects.
They will indeed maintain the same separation as measured by the frame in which they were at rest to begin with, but they will also be seen to contract in length, so the gaps between them will open up and they would, if they were capable of seeing and thinking, see themselves moving further apart and imagine themselves to be accelerating at different rates with the leading ones accelerating more strongly than the ones following them.

Have you ever been in an aeroplane, stationary at the end of a runway? The aisle looks perfectly level.
Then the plane accelerates down the runway. The aisle looks like it is tilting up towards the front of the plane. But looking out the window, you see that the plane has not rotated yet (ie it hasn't lifted the front wheel off the runway). Your ears can detect the acceleration, and they tell your brain that the direction of "up and down" has shifted, so your brain interprets the aisle as being tilted.
Unusually, I beg to differ from my learned friend. We use a combination of tilt and optical illusion to create the sensation of linear acceleration in a simulator, but a real plane on a runway really does start to tilt very early in its trajectory. The semicircular canals are sensitive to rotation but not to linear acceleration, and the body's initial response to backwards rotation is to try to maintain the head horizontal, so you will see the aisle rotate even without an external reference, because your head will rend to rotate forwards to compensate. Baroreceptors respond to pressure caused by linear acceleration, and horizontal acceleration is no different in a plane, bus or train  you don't notice the aisle of a train rotating upwards as it leaves the station,do you? The reason the simulator "works" is because a strong visual input (the projected horizon doesn't move up or down the "windscreen") plus baroreceptor sensation overrides a weak rotation signal if the sim tilts slowly.
The initial sensation of takeoff can be very confusing. The front seat of a high performance training glider is supine when on the ground. Initial acceleration from a winch is very rapid, so you are being accelerated feetfirst, which we normally interpret as falling, which is alarming. Next phase is to rotate forwards to get the tailwheel off the ground, so for a second or so you are "falling" and actually rotating towards a facedown position  very unpleasant! Problem is that the instructor sits in the back seat, almost upright, and just feels the expected pressure in his back, so can't understand why the passenger/student is confused.

The ship at E will need to to accelerate to .9c instantly...
Hmmm... A few premises being violated there...
Fair enough. As fast as we can then, and I gave my ships very powerful engines. If instant acceleration can demonstrate some inconsistency, then it cannot be allowed. Infinite rigid rods for instance can be used to signal distant places faster than light. Unobtanium can be used to extract objects from black holes.
I don't think eyes can detect acceleration.
But eyes and ears can. And butts certainly can.
The ship is quiet of course. If it accelerates everything perfectly, there's no vibration. If it accelerates everything but the butts, the brittle chairs would probably shatter. Think of it like the Enterprise hitting warp speed and not splatting everybody against the far wall, unless of course the director tells them all to pitch themselves to the right on his signal.
It's a thought experiment, not an exercise in engineering. I can give the ship all the power I want and kill its occupants if that is convenient, but I can't violate rules like breaking light speed.
Have you ever been in an aeroplane, stationary at the end of a runway? The aisle looks perfectly level.
Then the plane accelerates down the runway. The aisle looks like it is tilting up towards the front of the plane.
That's how it feels, not looks. Somebody watching a camera in the plane would not detect that tilt (and wouldn't detect it when the rotation actually happens), and would only notice Betty there getting pressed into her seat as she's playing the role of the accelerometer.
But looking out the window, you see that the plane has not rotated yet (ie it hasn't lifted the front wheel off the runway). Your ears can detect the acceleration, and they tell your brain that the direction of "up and down" has shifted, so your brain interprets the aisle as being tilted.
Yup. Inertial cues, not visual ones, except for the window, which is a nonlocal measurement.
Even with your eyes closed, your butt feels the acceleration in your seat. It doesn't take much brains to detect acceleration.
But it does take external inputs to distinguish acceleration from the effects of gravity.
Agree.
Do any of these points detract from the main topic? Can my big ship get to its destination quicker because the engines fail to accelerate the occupants along with every other particle?

Can my big ship get to its destination quicker because the engines fail to accelerate the occupants along with every other particle?
A frog has been levitated in the lab. It may be possible to levitate all the passengers with sufficient force to prevent acceleration forces flattening them. Probably better to develop technology to freeze them in a nonlethal manner though, but even then you need to guard against them snapping.

I have a ship that cannot take stress as I've described. It is 100 light years in length, stopped in Frame F. I want to move it forward by one light hour (about 1.08 billion km) in frame F. How quickly (as measured in F) can I do that? Obviously a tiny object can do it in about an hour at maximum speed.
We can't go at maximum speed. If the tail T accelerates to c in an instant, the nose N requires 100 years to get up to that speed and by that time it has moved far further than a lousy light hour. So it seems we want to instantly accelerate T just enough to get the nose of the ship to our destination (100 LY + 1 light hour) in the frame of T, and then instantly accelerate N by the opposite amount to drag the tail up the same distance. Boom. We've moved the desired distance.
So let's see, there are 876000 hours in a century, so we want to dilate the distance between the target of N and the current position of T by that factor (876000/875999) which happens at about 452 km/sec. So I instantly accelerate T to 452 km/sec, and then slow down at a steady pace until I stop. That's an average of 226 km/sec, so it takes over 55.3 days to move my ship that far. It cannot be done faster.
I am going to redo this experiment with moving the same ship one light minute instead of a light hour. That's about 18 million km.
Dilation factor needed is 1.000000019 which you get at 58.5 km/sec, or average speed half that. The trip takes 7 days 3 hours. I was wondering if it would take the same time, but no, it is apparently also a function of distance.
Next I will attempt using the caterpillar method to move that ship one light hour, the original scenario. Using a hybrid method will be more complicated.

Can you combine the two methods? Your way produces a faster time for the front of the ship (by setting it moving sooner), while mine produces a faster trip time for the back of the ship.
Did you run the numbers? I don't think any part of the ship gets anywhere faster by your way. It opened my eyes to an unnecessary condition I had been putting on the ship, but I don't think it helps win the race. Not sure.
I admit that I have not yet run the numbers for a pure caterpillar movement at say 300 km/sec. Mine moves at an average pace of 226 km/sec, with the middle achieving twice that halfway through the trip. 300 might be too slow, since it needs to add travel time (many days) to the wave propagate time (also days?). Faster one is, the slower the other one is. There must be an optimal point, but I've not plugged the numbers yet.
I ran the numbers on the simple case. Had to write a program to do it:
#include <stdio.h>
#include <math.h>
#define SpD 86400. // seconds per day
#define kmLH 1080000000. // km in a Light hour
int main(int ac, char **av)
{
double factorD, // lorentz factor (down)
speedC, // speed as fraction of c
speedK, // speed in km/sec
speedK10, step, // range limit km/sec
tDmov, tDwav; // time in days
sscanf(*++av, "%lf", &speedK);
sscanf(*++av, "%lf", &speedK10);
step = (speedK10speedK)/10.0;
speedK10 += step/3;
while (speedK < speedK10)
{
speedC = speedK / 300000.; // Compute speed as fraction of c
factorD = sqrt(1  speedC * speedC); // Lorentz contraction
tDmov = kmLH / speedK / SpD; // Time to move 1 LH at that speed
tDwav = 36500 * (1.  factorD); // Wave time: 36500 light day ship len
printf("S %.2f T %.14f W %.14f = %.14f \n",
speedK, tDmov, tDwav, tDmov+tDwav);
speedK += step;
}
return 0;
}
One inputs the low and high range of speed to test in km/sec, and it gives travel time T for one light hour at that speed plus wave time W to get the caterpillar wave to traverse the length of the 100 light year ship.
Output is in days.
This first run gave me a general sense of where the sweet spot is:
> caterpillar 100 5100
S 100.00 T 125.00000000000000 W 0.00202777783209 = 125.00202777783210
S 600.00 T 20.83333333333333 W 0.07300007300048 = 20.90633340633381 < Close to my prior solution of 452 km/sec
S 1100.00 T 11.36363636363636 W 0.24536193580077 = 11.60899829943713
S 1600.00 T 7.81250000000000 W 0.51911480262024 = 8.33161480262024
S 2100.00 T 5.95238095238095 W 0.89426095483064 = 6.84664190721159
S 2600.00 T 4.80769230769231 W 1.37080351890573 = 6.17849582659804
S 3100.00 T 4.03225806451613 W 1.94874646653875 = 5.98100453105488
S 3600.00 T 3.47222222222222 W 2.62809461481267 = 6.10031683703489
S 4100.00 T 3.04878048780488 W 3.40885362640275 = 6.45763411420763
S 4600.00 T 2.71739130434783 W 4.29103000981162 = 7.00842131415945
S 5100.00 T 2.45098039215686 W 5.27463111963672 = 7.72561151179358
After narrowing it down, I got this final run:
> caterpillar 3135.26 3135.36
S 3135.26 T 3.98691017650849 W 1.99333063672691 = 5.98024081323540
S 3135.27 T 3.98689746018684 W 1.99334335266144 = 5.98024081284828
S 3135.28 T 3.98688474394631 W 1.99335606864054 = 5.98024081258685
S 3135.29 T 3.98687202778690 W 1.99336878465611 = 5.98024081244302
S 3135.30 T 3.98685931170861 W 1.99338150071221 = 5.98024081242082 <<< Sweet spot
S 3135.31 T 3.98684659571143 W 1.99339421680883 = 5.98024081252026
S 3135.32 T 3.98683387979536 W 1.99340693295003 = 5.98024081274539
S 3135.33 T 3.98682116396041 W 1.99341964912769 = 5.98024081308810
S 3135.34 T 3.98680844820657 W 1.99343236534588 = 5.98024081355245
S 3135.35 T 3.98679573253385 W 1.99344508160865 = 5.98024081414249
S 3135.36 T 3.98678301694223 W 1.99345779791194 = 5.98024081485416
It seems the caterpillar method can get the ship up to 3135 km/sec and do the trip in under 6 days, doing the movement in under 4 days and the wave taking just under 2 days to move up the 100 lightyear ship. That's like 11% of the 55 days I got via the other method.
Did I get all the math right? In particular, I got a wave propagation speed of 1/LC where LC is the lorentz contraction factor of the speed of movement. That speed is just over light speed if ship speed is close to c, but is far greater than c for slow speeds. The first printout really shows this.
It works. The hybrid method should probably shave something off that 4 day T figure, so we can play with that. Complicated....

Are you moving a 100 lightyear long ship one lighthour? If so, the back end can in principle move one lighthour in a fraction over an hour (with astronomical energy costs). You want to get the front end moving as soon as possible, so you need a wave that propagates much more quickly than the speed of light through the length of the ship. I'm assuming you've found a way to find the ideal speed for that, but due to pressing work I haven't put the effort into trying to follow the maths to check it. Every other part of the ship should be able to make the trip faster than the front end does, and I'm envisaging sending out multiple waves from the back end to achieve that (an infinite number of them), each one taking particles to a higher speed than the previous one but taking longer to propagate. As soon as they reach their required destination, they stop. The nearer a particle is to the front of the ship, the lower the speed it will be doing when it reaches its destination and has to stop.

Are you moving a 100 lightyear long ship one lighthour? If so, the back end can in principle move one lighthour in a fraction over an hour (with astronomical energy costs).
Yes, 100 LY ship moved 1 LH. Being energy efficient is not a goal of this topic.
That I can move part of it in an hour doesn't help me. That data point is on my chart, and it takes a century to move the ship that way.
The rule is the entire ship must move, and come to a stop, in minimal time. By stopping, there is less ambiguity over how long the procedure takes, but time in the inertial frame is the one I'm counting. The ship in this scenario doesn't move fast enough to make much difference in what the ships clocks will read when we're done.
You want to get the front end moving as soon as possible, so you need a wave that propagates much more quickly than the speed of light through the length of the ship.
That's the hybrid approach, and the problem is hardly trivial. Yes, get the front moving ASAP (I can do that instantly), and by symmetry, keep the back end moving until the end. The optimum solution probably has no pointdiscontinuity of speed like the simple example I just ran. I suspect an ugly curve and plenty of integration to do.
Every other part of the ship should be able to make the trip faster than the front end does,
By symmetry, this cannot be so. The back end moves just like the front, but in reverse: The back goes fastest at first, but slows until the end, just like in my post 37 example. The front gathers speed the whole time and slows much more quickly at the end.
and I'm envisaging sending out multiple waves from the back end to achieve that (an infinite number of them), each one taking particles to a higher speed than the previous one but taking longer to propagate.
Yes, a continuous curve, with no distinct 'waves'.
What we need is a formula for each section of the ship: Accelerate exactly like this. Only the exact middle of the ship will have a symmetrical waveform to its speed profile.
As soon as they reach their required destination, they stop.
That should be all at the same time. The entire ship moves the entire duration, which is not what the scenario above depicts, where all parts move for 4 days, and are stationary for 2 days (partly on either side of the moving period).
The nearer a particle is to the front of the ship, the lower the speed it will be doing when it reaches its destination and has to stop.
I came to the opposite conclusion: The front of the ship is moving the fastest at the end, same speed as the tail goes at the beginning.
Our bottleneck seems to be the middle. I can yank the back up to speed fast, and the front can slow very fast, but the middle has to accelerate steady and carefully for both halves. As far as the wave speed goes, the ends are the bottlenecks. So I don't have an intuitive feel as for what our winning plan will look like, or how to go about proving there's no better plan.

The back end can go straight up to (an infinitesimal fraction less than) c, but the front end has to accelerate slowly to avoid breaking off the part behind it  you can accelerate a long chunk of ship behind it too at the same time, but length contraction will break it if the front end isn't the slowest in that acceleration, and if that long chunk of ship doesn't include the back end, it will break somewhere. The back end can slow from nearly c to zero in an instant, and the front can slow from whatever speed it's doing to zero in an instant too. If you want the fastest journey time for the ship, the back end will cover the distance in the shortest time and the front end will take the longest. You appear to want the back end to be as slow as the front end overall, but that's a slower average journey time. The distance travelled will limit the top speed of the front part of the ship, while its rate of acceleration is determined by the length of the ship. If you can work out that relationship, you then have a way to work out how quickly any inbetween part of the ship can accelerate because any such point is equivalent to the front end of a shorter ship.

If you want the fastest journey time for the ship, the back end will cover the distance in the shortest time and the front end will take the longest. You appear to want the back end to be as slow as the front end overall, but that's a slower average journey time.
It may be that it doesn't matter, but if it matters, the solution will be symmetrical, meaning the front accelerates in a pattern that is the reverse of the rear of the ship. If you play the video in reverse, it should look the same. All scenarios attempted so far have been symmetrical. If it is important to begin moving the nose ASAP (I think it is), then it is important to keep the tail moving right until the end. I'm certain of this.
The limit is probably due to the endpoints, but not sure. I'm thinking of a slow acceleration of the tail at first to get the 'wave' moving to midships much quicker than the uniform acceleration that was done in the output above.
The distance travelled will limit the top speed of the front part of the ship, while its rate of acceleration is determined by the length of the ship. If you can work out that relationship, you then have a way to work out how quickly any inbetween part of the ship can accelerate because any such point is equivalent to the front end of a shorter ship.
As I said, 55 days if you do it that way. That's exactly what was done in post 37.
Edit: That is not exactly what was done. I only got each end up to 452 km/sec, not near lightspeed.
I think I see what you're saying. Floor it from the tail, but stop the nose once it gets far enough, which is well before it is simultaneous with its tail. The solution is asymmetrical, meaning the final speed of the tail doesn't matter.

Calculating the max acceleration of the nose of my ship turns out to be straightforward. From the opening comments of the Rindler article:
whenever we talk about an inverse acceleration being equal to a distance, or vice versa, their product will equal c^{2} in conventional units.
So c^{2} is 9e16 (units of meters and seconds), and my ship is 100 light years long, or 9.46e17 meters giving us an acceleration of 0.09513 m/sec^{2} which takes 78 days to move that light hour.
Did I do that correctly?? That's 320 km/sec at the end, slower than my 452, which I limited for contraction reasons. Did I exceed some limit in post 37?
Why is the simple caterpillar method so much faster?

I realise now that my method can't combine with yours. If I accelerate the back end straight up to a fraction under c, it has to catch the particle ahead of it quickly in order for it to maintain connection with it at that speed, so the particle ahead can't accelerate until it's practically been caught as any earlier movement will open up a gap far greater than the length contraction requires for the two of them. That means a very long wait before the front end can start moving. To move the front end in the minimum amount of time, the back end has to accelerate more gently, though it can always accelerate more aggressively than any particle further forward. One limit on how quickly it can accelerate depends on how long it can "feel" stretched before it detaches from the particle ahead, and I don't know how that would be calculated.

From post 93, it takes me about 100 days to find my stupid error
Calculating the max acceleration of the nose of my ship turns out to be straightforward. From the opening comments of the Rindler article:
whenever we talk about an inverse acceleration being equal to a distance, or vice versa, their product will equal c^{2} in conventional units.
So c^{2} is 9e16 (units of meters and seconds), and my ship is 100 light years long, or 9.46e17 meters giving us an acceleration of 0.09513 m/sec² which takes 78 days to move that light hour.
Did I do that correctly?? That's 320 km/sec at the end, slower than my 452, which I limited for contraction reasons. Did I exceed some limit in post 37?
I did not do that calcuation right. Somehow I thought the 55 day figure was wrong, but no, this one is. It takes just over 55 days to go one light hour at .09513 m/sec²
This is in agreement with the very different method of arriving at this figure from post 37

Off topic sort of, butt...
I don't think eyes can detect acceleration.
But eyes and ears can. And butts certainly can.
The ship is quiet of course. If it accelerates everything perfectly, there's no vibration.
Clearly I read the full comment incorrectly. It isn't about noise. Can inner ear detect actual acceleration? Butt's do it the same way, but if it is detectable, then a lot of it will be unhealthy. I'm thinking of the perfect acceleration couch like in SciFi where the occupant is immersed in liquid including the lungs like they do with preemie babies. How much yanking around can you then take without noticing, or without injury?
As I said, this is a thought experiment, and my very capable ship can accelerate each part of itself (including the occupants) as hard as it wants. They'll feel nothing, else it wasn't engineered right. I'm going to further explore scenarios with the ship and occupants staying intact (no stress or strain) despite the head moving at a vastly different speed than the feet. I ran with David's idea and it showed that the ship can get to its destination a helluva lot faster than 55 days. I want to improve on the 6 day trip time before I move on to pure stationary objects.

To drive the points home, my objects will be large and fast, but never with impossible properties like being massless, infinite rigidity, or with instantaneous acceleration
The ship at E will need to to accelerate to .9c instantly...
Hmmm... A few premises being violated there...
This comment prompted me to edit the OP with this:
Edit: There seems to be nothing impossible about near instantaneous acceleration. Many of my examples assume as a limit an acceleration to a desired speed in negligible time. If this is found to violate finite light speed or some other law, kindly post details since it will effect my answers for minimum time to get a big thing somewhere.
Nobody has posted any blatant violations of physics resulting from instantaneous acceleration as opposed to arbitrarily high acceleration. Since nobody seems up to the task, I will attempt to do it myself, and in the process, sink the caterpillar method of moving the ship. Sorry David.
The post is rather long, so bear with me, since I think it is all relevant.
Summary so far:
We have a bornrigid ship that is 100 light years long, and we wish to move that ship a distance of 1 lighthour (north let's say), with it stopped at either end of the trip. No solution that involves strain on the ship is allowed.
I presumed the ship had to be always stationary in its own frame along its entire length during the whole trip. From this presumption, I computed a trip time of about 55 days in post 37.
David Cooper suggested what has become known as the caterpillar method of moving the ship. The idea is to accelerate the tail quickly to some speed and propagate that acceleration to the front of the ship as the relativistic contraction allows. The faster the speed chosen, the greater the contraction and the slower the 'wave' of acceleration moves to the front of the ship. The wave always moves faster than light. I found the optimal speed at 3135 km/sec which gives 4 days to move the lighthour and 2 days for the wave to propagate 100 light years for a total trip time of 6 days. I intend to demonstrate that the method only works with infinite acceleration, and thus is a violation of my initial premise. It is effectively like suggesting unobtanium.
Seeming inconsistencies with the method which are not in fact problematic:
The solution seems asymmetric. The ship is stopped and to get it going, you must accelerate it from the tail at first and let the wave propagate to the front. This allows the tail to move first and is consistent with the ship contracting in length as it moves at 3135 km/sec. But then we accelerate it the other way and again this must be initiated at the tail, not the nose, allowing the ship to expand to its original length as it stops. That's the asymmetry. Acceleration in both directions requires the wave to move from south to north. If I try to stop the ship by stopping the nose first, then the north end of the ship moves for much less time than the south end, and the ship stops much shorter than its original length, and it breaks.
So I tried to visualize the trip in the frame of the moving ship where it is stationary (and has undilated length) at the middle of the trip. Surprise! In that frame, the ship is moving south at first, and the acceleration starts at the north end (nose) of the ship and takes 2 days to reach the south end. The wave moves the other way in that frame. The solution is symmetrical after all. This is not intuitive at first, but an interesting side effect of relativity of simultaneity.
The fatal discovery:
So what if I consider the situation in the frame halfway between the two frames described above? Which way does the wave move then?? Turns out it doesn't. The ship is partially contracted when 'parked', but moving south with the space station, and identically contracted when moving north at the same speed but opposite direction. The solution only works because the ship instantaneously (in that frame) changes direction without ever changing speed. If it took a millisecond to do this, then for that millisecond, it would be longer that it is before and after, and it would shatter.
Infinite acceleration cannot be allowed.
But why can't I accelerate over a minute to 3135 km/sec, still using the wave method?
This was the obvious solution for a while. OK, so the trip takes a minute longer. No problem. But it doesn't work.
I tried to optimize the trip by doing several smaller waves. Accelerate to 500 km/sec. The smaller speed difference lets the wave move at a larger speed, and it takes less than 2 days to get to the front. Then, a few minutes later, initiate another wave like that. Send about 20 waves like that, each getting to the front in less than a day, and the ship now gets a total speed of 10000 km/sec and the time to move is reduced to 1.3 days. Total less than 2 days, right? Wrong! It is not obvious until you look at it in the other frames and realize the same waves move the opposite way and are thus arranged in the opposite order. Any gradual acceleration results in compression of that acceleration until singularities occur.
Since finite acceleration can be integrated as a series of small step speedchanges, that finite acceleration would become infinite at some point along the line, so the limit of the acceleration is one where that singularity occurs forward of the front of the ship, and that's the solution posted in post 37.

We have a bornrigid ship that is 100 light years long, and we wish to move that ship a distance of 1 lighthour (north let's say), with it stopped at either end of the trip. No solution that involves strain on the ship is allowed.
You have to allow some strain on it to accelerate it because of length contraction  there's no possible way to accelerate it at all without strain. What we have to avoid though is any move that leaves atoms sitting the wrong distance apart such that they are free to cause crumples or rips, but we are allowed to move an atom in such a way that the forces are very strong while we're accelerating it just so long as when we stop accelerating it it will be able to sit comfortably where we put it at the speed we've set it to. With the caterpillar method, we take the atom at the tail end and accelerate it towards the atom ahead of it, but we don't let it go until we've accelerated the next atom to the same speed, by which time the forces between them are back to comfortable levels (such that they will sit that distance apart naturally), and we delay the start of that second atom's acceleration so that they end up the right distance apart when we've let go of them both. The practicality of doing this is close to zero, but we're interested in an extreme case where the "ship" might just be a very long chain of carbon atoms with hydrogen's stuck along the sides  this molecule could be held sufficiently flat that all our external machinery for accelerating it can access every single atom and precisely control its acceleration. This will not work for any human passengers which can't be flattened to match, but perhaps we can invent some way of beaming forces through to individual atoms within complex structures where they're hidden deep beneath layers of many others  if we're allowed to do this, then we're still discussing the extreme limit of the potentiallytheoreticallypossible even if there are live humans on board.
I presumed the ship had to be always stationary in its own frame along its entire length during the whole trip. From this presumption, I computed a trip time of about 55 days in post 37.
By the way, I never understood the full details of your method, so I just assumed that you know what you're doing with the maths (and continue to make that assumption). I wouldn't be surprised if you're the only person here who understands it. Perhaps it could be made easier to understand and discuss if the lightyears aspect was removed to cut it down to a better size. If we just work in units of d (distance), then the length of the ship can be 100d and the move can be d. We can then imagine a ship of 100 atoms in length all ending up one atom further along from where they started. Or we could imagine a ship of 10 atoms in length all ending up 1/10 of an atom further on by the finish. That would make it easier to discuss what happens in a way that can be visualised easily, and which could be simulated too with JavaScript to provide a moving diagram of the action governed by the relevant maths. The number of atoms used may affect the result, but we'll be able to see the relationship between different versions of the experiment as we go from 10 to 100 to 1000 atoms, and then we can calculate how it would work with a 100 lightyear ship with its atoms at normal atom spacing, but everyone would be able to gain a good understanding first from the simpler cases. (Time should be in units of t based on t=1 for light travelling the distance d.)
David Cooper suggested what has become known as the caterpillar method of moving the ship. The idea is to accelerate the tail quickly to some speed and propagate that acceleration to the front of the ship as the relativistic contraction allows. The faster the speed chosen, the greater the contraction and the slower the 'wave' of acceleration moves to the front of the ship.
That's right, because you can accelerate the particle ahead sooner as the space between them will be bigger at the target speed than for a higher speed, but you can then follow it up with another wave of acceleration to take the atoms to a higher speed, and you can do that for all possible speeds with a different wave for each. The wave with the slowest target speed will lead to the front atom being accelerated almost immediately, but it's so small a change in speed that it won't look as if that atom is moving at all.
The wave always moves faster than light. I found the optimal speed at 3135 km/sec which gives 4 days to move the lighthour and 2 days for the wave to propagate 100 light years for a total trip time of 6 days. I intend to demonstrate that the method only works with infinite acceleration, and thus is a violation of my initial premise. It is effectively like suggesting unobtanium.
So long as you aren't accelerating any particles to c, the acceleration will be finite.
The fatal discovery:
So what if I consider the situation in the frame halfway between the two frames described above? Which way does the wave move then?? Turns out it doesn't. The ship is partially contracted when 'parked', but moving south with the space station, and identically contracted when moving north at the same speed but opposite direction. The solution only works because the ship instantaneously (in that frame) changes direction without ever changing speed. If it took a millisecond to do this, then for that millisecond, it would be longer that it is before and after, and it would shatter.
If you pick the frame half way in between, you start with the whole ship moving south and end up with the whole ship moving south at the end, but it will have spent some of its time moving north, and in this frame the whole ship will suddenly be moving north at the same time, then it will suddenly be moving south again some time later. The contraction will be the same for both directions of travel through this frame, so it's easy for the whole ship to make these accelerations simultaneously in this frame. The ship has changed direction twice, and it's also changed speed twice (if you consider the southward movement to be at v and the northward movement to be at +v). If you're going to make the change in speed from one direction to the other take a millisecond, then you will have extreme forces applying during that moment trying to extend the ship, but these are no different from the forces that you have to handle on an atombyatom basis when looking at it from the other frames, because when you accelerate the end atom towards the one ahead of it, you are sending it towards an atom which is for most of that time applying a force to try to stop the accelerated atom from moving that way, and that opposing force will strengthen as they get closer together. That opposition of forces is only removed when you start accelerate the second atom up to the right speed for the two to sit comfortably together at their new separation distance. Clearly, if we're very precise in how we apply the acceleration to the first atom, it won't be pushed off course, and we can amplify our acceleration force too as it gets closer to the atom ahead of it. Some of the energy we're putting into the first atom will be transferred to the second atom, so that will affect the amount of force we have to apply directly to that atom later, but if we're accelerating the first atom to a speed close to c, the second atom doesn't have much time to respond to this before we start to move it anyway, so this becomes more of an issue the lower our target speed is. The cure for it is accuracy so that when high opposing forces exist, they are acting directly along the direction in which the ship is aligned  damage would only be done if the atoms get slightly out of alignment, because that would lead to strong sideways accelerations which would blow the ship apart, but we're already handling that in the original frame in the way we control the acceleration of our atoms (making sure they aren't going out of line and being deflected sideways), so we must be handling that in all other frames too.
But why can't I accelerate over a minute to 3135 km/sec, still using the wave method?
This was the obvious solution for a while. OK, so the trip takes a minute longer. No problem. But it doesn't work.
I tried to optimize the trip by doing several smaller waves. Accelerate to 500 km/sec. The smaller speed difference lets the wave move at a larger speed, and it takes less than 2 days to get to the front. Then, a few minutes later, initiate another wave like that. Send about 20 waves like that, each getting to the front in less than a day, and the ship now gets a total speed of 10000 km/sec and the time to move is reduced to 1.3 days. Total less than 2 days, right? Wrong! It is not obvious until you look at it in the other frames and realize the same waves move the opposite way and are thus arranged in the opposite order. Any gradual acceleration results in compression of that acceleration until singularities occur.
If something works in one frame, it has to be compatible with all other frames. If that wasn't the case, relativity would break. Consider just two waves. We have one where we accelerate atoms nearly to c, but we have a second wave where we accelerate them to 0.5c. The latter acceleration will propagate from atom to atom at a higher speed than the former, with both propagating at speeds higher than c, but these things are fully possible in the frame of reference in which the starting speed is zero. This must be compatible with the other frames that you're considering. In the frame moving at nearly c, we see what looks like a deceleration of the atoms from nearly c to zero, and because we're uncontracting the ship from the point of view of this frame, we see the wave move from the front of the ship to the back. There' no problem there. Let's add our second wave in.This wave starts at the same time as the other and from the same location, but it reaches the other end first and then stops, so we have to wait for the first wave (the one described first) to reach the same finish line. When we view this from the other frame, the first wave really is the first wave in that it's seen to leave first, and the second wave is sent a little later. They both reach the finish (the tail of the ship) at the same time as each other), the first wave not quite stopping the atoms, but the second wave finishes that job.
Since finite acceleration can be integrated as a series of small step speedchanges, that finite acceleration would become infinite at some point along the line, so the limit of the acceleration is one where that singularity occurs forward of the front of the ship, and that's the solution posted in post 37.
I still think that the fastest way to move the front of the ship to its destination will involve the caterpillar method with an infinite number of waves moving at different speeds so as to maximise the acceleration of the leading atom, but I don't know how to handle the maths for combining all those waves.

It depends on what one look at Halc.
'Light' has no acceleration
It has a 'release' and a 'absorption' sort of, but there is no acceleration involved in this.
Only conservation laws.

And no, a engine that 'pushes' in all directions won't 'move'. You need to create a 'chamber' in where the 'action' acts in one direction to make it work.

Fear not David, I am working on a reply, but it is taking a while.
Meanwhile:
It depends on what one look at Halc.
'Light' has no acceleration
It has a 'release' and a 'absorption' sort of, but there is no acceleration involved in this.
Only conservation laws.
There is no light in my scenario. Nobody is sending signals anywhere. We're accelerating a long object, not accelerating light, and we're not even moving it quickly unless that yields a better answer.
And no, a engine that 'pushes' in all directions won't 'move'. You need to create a 'chamber' in where the 'action' acts in one direction to make it work.
If you're worried about these irrelevant implementation issues, the long object is probably a rod with measurement markings on it, and nothing else. It is pushed from forces from the outside just like a rail gun. There are no engines or chambers.

Ok, something being accelerated without a intrinsic engine? " Is there a stressfree way of accelerating a long object? "
Yeah.

Thanks for looking at this David.
I'm arguing against your post not because it is wrong, but more as a critical review. You have some strong points. I feel like I'm on thin ice with some of my replies.
We have a bornrigid ship that is 100 light years long, and we wish to move that ship a distance of 1 lighthour (north let's say), with it stopped at either end of the trip. No solution that involves strain on the ship is allowed.
You have to allow some strain on it to accelerate it because of length contraction  there's no possible way to accelerate it at all without strain.
I don't understand your point at all. Of course its possible, at least mathematically, and this is a mathematical exercise after all, not an engineering one. I'm not really concerned about accelerating individual atoms. I consider the object to be a homogeneous rod, perhaps with length marks along it.
Nearest way to implement such a thing is the rod completely enclosed in a 100 lightyear rail gun that can accelerate each portion at the appropriate rate.
What we have to avoid though is any move that leaves atoms sitting the wrong distance apart such that they are free to cause crumples or rips, but we are allowed to move an atom in such a way that the forces are very strong while we're accelerating it just so long as when we stop accelerating it it will be able to sit comfortably where we put it at the speed we've set it to.
'When we stop accelerating' is a frame dependent thing. In my standard description (no wave), the object is stationary in its own frame for its entire length, but not so in any other frame, where different parts are moving at different speeds. One cannot ever suddenly stop accelerating it 'simultaneously' in one of those other frames.
So for instance, the caterpillar method had the object moving at different speeds in any frame, as long as the wave existed. Until the wave reaches the other end, the acceleration process cannot stop without shattering the object.
With the caterpillar method, we take the atom at the tail end and accelerate it towards the atom ahead of it, but we don't let it go until we've accelerated the next atom to the same speed, by which time the forces between them are back to comfortable levels
There never should be force between those two atoms. No need to hold them until they're moving identically. Well sort of... If they're not moving identically, they obviously are being accelerated. There is thus a force on each one, and that counts as being 'held' I suppose.
Two atoms can move at different speeds and not result in strain between them. It takes time to build up strain, and we don't give it that time.
I sort of ran the proof of that in post 78. There is zero strain on the object between any two points. No strain means no stress. The fault in the description was that it posited zero time for the acceleration, and that is unreasonable. It can be done over a finite time to give finite acceleration, but the interval of time to do it shortens as the wave moves forward, and it shortens to zero before it gets to the other end of the object. That forced singularity is why the method doesn't work. You can make the acceleration gradual enough that the singularity doesn't happen before the other end of the object, but then you're back to a 55 day trip.
(such that they will sit that distance apart naturally), and we delay the start of that second atom's acceleration so that they end up the right distance apart when we've let go of them both.
Yes, we stop accelerating them once this is achieved. But at no point is there stress between the two of them, even though one may be moving and the other not. We're holding on not to keep them at an unnatural separation, but to apply the force needed for acceleration.
Interestingly, in the instantacceleration scenario, that requires neither infinite force nor infinite power. Both work out to finite numbers, at least in most frames of reference. That wasn't obvious at first.
The practicality of doing this is close to zero,
As I said, this is a mathematical exercise and I'm not worried about practical issues. My disproof is a mathematical one, not a demonstration that humans could not be kept alive if onboard.
I presumed the ship had to be always stationary in its own frame along its entire length during the whole trip. From this presumption, I computed a trip time of about 55 days in post 37.
By the way, I never understood the full details of your method, so I just assumed that you know what you're doing with the maths (and continue to make that assumption).
The 55 day thing required 2 steps.
Step 1: Compute the exact speed of the ship. There are two ways to do this.
1A: Use a lorentz conversion to compute the speed the universe would need to go to get it the 100 LY distance to contract by a light hour. That gives me the speed the object needs to go (~452 km/sec).
1B: To confirm that, I did it a very different way in post 93, and made an arithmetic mistake, corrected in post 95. Just compute c²/100 LY to get the maximum acceleration possible at the nose of the ship, and punch that number into a trip calculator with destination of 1 lighthour. That latter part is what I get wrong since my trip calculator assumed I wanted to decelerate the 2nd half of the trip, but no, I want to accelerate the whole way.
Both methods yielded the same 452 km/sec
Step 2:
In post 37, I realize that the nose of the ship will accelerate at a constant rate (and the tail decelerate similarly), and hence move at an average speed of half the 452, so 226 km/sec. So 55 days of that speed gets you one light hour. Simple multiplication.
I wouldn't be surprised if you're the only person here who understands it.
There are a few who know their stuff better, but they've not posted much in this thread. All I get are the ones that have a deathgrip on their Newtonian assumptions, and it turns out that we've been making some of them ourselves. I had to find my own errors since nobody else was pointing them out.
Perhaps it could be made easier to understand and discuss if the lightyears aspect was removed to cut it down to a better size. If we just work in units of d (distance), then the length of the ship can be 100d and the move can be d.
Well then I don't get a concrete answer. It takes a long time to move my object 1 lightyear, and yet I can move my meterstick a centimeter in a moment. I need real units, not abstract ones, and I need a long object so the relativity aspect is obvious.
I can move it a lightyear if that makes it simpler for you. The max speed would be 42082 km/sec. so half that is 21041, at which speed it takes 14¼ years to do the move.
We can then imagine a ship of 100 atoms in length all ending up one atom further along from where they started.
Yea, but who can relate to the bazillionth of a second it takes to do that? The relativity isn't going to be apparent.
That would make it easier to discuss what happens in a way that can be visualised easily, and which could be simulated too with JavaScript to provide a moving diagram of the action governed by the relevant maths.
I find it easier to visualize on a large scale, where there are hours or days difference in times depending on frame of choice. I can have lengthmarks on my object, which seems to serve the same purpose as your discreet atoms, but I found no need to refer to them to compute the times required by the various methods, or to demonstrate that the caterpillar method doesn't work at all.
David Cooper suggested what has become known as the caterpillar method of moving the ship. The idea is to accelerate the tail quickly to some speed and propagate that acceleration to the front of the ship as the relativistic contraction allows. The faster the speed chosen, the greater the contraction and the slower the 'wave' of acceleration moves to the front of the ship.
That's right, because you can accelerate the particle ahead sooner as the space between them will be bigger at the target speed than for a higher speed, but you can then follow it up with another wave of acceleration to take the atoms to a higher speed, and you can do that for all possible speeds with a different wave for each.
I twas trying to do that, finding a faster way by using multiple waves. It doesn't work. The waves catch up to each other, which wasn't at all obvious at first.
The fatal discovery:
So what if I consider the situation in the frame halfway between the two frames described above? Which way does the wave move then?? Turns out it doesn't. The ship is partially contracted when 'parked', but moving south with the space station, and identically contracted when moving north at the same speed but opposite direction. The solution only works because the ship instantaneously (in that frame) changes direction without ever changing speed. If it took a millisecond to do this, then for that millisecond, it would be longer that it is before and after, and it would shatter.
If you pick the frame half way in between, you start with the whole ship moving south and end up with the whole ship moving south at the end, but it will have spent some of its time moving north, and in this frame the whole ship will suddenly be moving north at the same time, then it will suddenly be moving south again some time later. The contraction will be the same for both directions of travel through this frame, so it's easy for the whole ship to make these accelerations simultaneously in this frame.
Here we differ. In all other cases, the 'instant acceleration' was simply the limit of things as acceleration reached an arbitrary value, but in this case, the value with which we're concerned (length contraction) does not approach zero change as the time to make the acceleration decreases. So I find it unreasonable to say that since it happens in zero time that one can get from one speed to another speed without hitting the speeds in between.
Avoiding the length contraction by doing the acceleration 'while God blinks' so to speak seems a cheat. I'd accept the method if it worked with a finite (fraction of a second) acceleration that still propagated up the length in a wave. I was trying to get the mathematics right on that scenario and was wondering why it didn't work. Considering it in this middleframe shows me why it doesn't work.
If you're going to make the change in speed from one direction to the other take a millisecond, then you will have extreme forces applying during that moment trying to extend the ship, but these are no different from the forces that you have to handle on an atombyatom basis when looking at it from the other frames
Again we differ. These forces do not exist when doing it over a millisecond, atom by atom. At no point are two atoms in a stressful arrangement. The argument would indeed have merit if this temporary force existed, but it doesn't. I showed that it doesn't. Two atoms cannot exert a force during a pair of event separated in a spacelike manner.
By the same argument, that force (stress/strain) admittedly cannot exist during an instantaneous directionchange. I agree that far, but I find it to be cheating to use this singularity to get a value that is not approached by arbitrarily high acceleration. 5n/n is 5 for all values of n except zero, and it is valid to assign an arbitrary value (like 13) to the undefined value at n=0, but contradictions can be reached if you allow such mathematics at the singularities. I can prove that 1=2 if you allow that.
because when you accelerate the end atom towards the one ahead of it, you are sending it towards an atom which is for most of that time applying a force to try to stop the accelerated atom from moving that way, and that opposing force will strengthen as they get closer together. That opposition of forces is only removed when you start accelerate the second atom up to the right speed for the two to sit comfortably together at their new separation distance.
Well, no. It sort of works exactly because this doesn't happen. Acceleration of an atom doesn't result in any force against its unaccelerated neighbor. What does this is displacement, and displacement takes time. For it to put a force on the neighbor would be to have a causal effect at greater than light speed, which cannot happen.
My argument against this method is not that there would be stress, but that it isn't a solution that is approached by arbitrarily high acceleration. Only at the singularity does it work, and therein lies my protest. The lack of approached limit is what I find unacceptable.
Your approach is also on the discreet atomic level rather than the homogeneous mathemeatical level, but if we model the 'ship' as a series of discreet points that are accelerated individually, then there really is no length of the object, just spacings between the atoms which are to be ignored for the duration that a force is applied to them. If we allow that, even for a shorter duration than the speed of light between adjacent atoms, then the length of the object seems meaningless. The rules are to be ignored while we briefly take tongs to each atom in turn and change its velocity.
How does QM handle this? I swat the sun away, and its gravity still pulls Earth from where it used to be for 9 minutes. Eventually the corrections are made by gravity waves that make the necessary adjustments to keeps the conservation laws happy. Something similar must happen when we accelerate an atom to a new frame all outside the light cone of its neighbors. That must emit some sort of EM equivalent of graviton that is going to apply the stress and strain that the immediate speed of light prevented. I'm no expert here. I was approaching this mathematically, not from a quantum physics standpoint.
Some of the energy we're putting into the first atom will be transferred to the second atom
Due to QM effects perhaps, but otherwise no. The EM field will aways consider adjacent atoms to be stationary relative to each other, but speedoflight particles will be emitted by the acceleration, and I suppose those would put stress on our object. There isn't supposed to be any, but at a QM level (as opposed to mathematically), I suppose it happens.
but if we're accelerating the first atom to a speed close to c, the second atom doesn't have much time to respond to this before we start to move it anyway
It will be accelerated itself long before the acceleration of its neighbor can possibly be noticed. We're not doing it anywhere near c. A few hundred or thousand km/sec. 1% of c at best.
But why can't I accelerate over a minute to 3135 km/sec, still using the wave method?
This was the obvious solution for a while. OK, so the trip takes a minute longer. No problem. But it doesn't work.
I tried to optimize the trip by doing several smaller waves. Accelerate to 500 km/sec. The smaller speed difference lets the wave move at a larger speed, and it takes less than 2 days to get to the front. Then, a few minutes later, initiate another wave like that. Send about 20 waves like that, each getting to the front in less than a day, and the ship now gets a total speed of 10000 km/sec and the time to move is reduced to 1.3 days. Total less than 2 days, right? Wrong! It is not obvious until you look at it in the other frames and realize the same waves move the opposite way and are thus arranged in the opposite order. Any gradual acceleration results in compression of that acceleration until singularities occur.
If something works in one frame, it has to be compatible with all other frames. If that wasn't the case, relativity would break.
It apparently doesn't work in any frame, but it isn't so intuitive in say the initial rest frame. The one (middle) frame just made it real obvious why it didn't work, and yes, per relativity, the other frame thus must also not work.
Consider just two waves. We have one where we accelerate atoms nearly to c, but we have a second wave where we accelerate them to 0.5c. The latter acceleration will propagate from atom to atom at a higher speed than the former, with both propagating at speeds higher than c, but these things are fully possible in the frame of reference in which the starting speed is zero.
No, they're not possible in that (or any) frame. It just wasn't initially obvious to either of us. It became more apparent when I started to attempt optimizations and was running into so much trouble.
This must be compatible with the other frames that you're considering. In the frame moving at nearly c, we see what looks like a deceleration of the atoms from nearly c to zero, and because we're uncontracting the ship from the point of view of this frame, we see the wave move from the front of the ship to the back. There's no problem there.
There is a problem there.
I think it stems mostly from the difference between acceleration and proper acceleration. We have to assume constant proper acceleration else the motion will not be symmetric from one reference frame to the next. But the actual acceleration (in a given frame) needs to be constant in order for the wave to progress at a uniform speed. It works only with infinite acceleration because there is no difference between actual and proper acceleration, both being infinite and without duration.
I still think that the fastest way to move the front of the ship to its destination will involve the caterpillar method with an infinite number of waves moving at different speeds so as to maximise the acceleration of the leading atom, but I don't know how to handle the maths for combining all those waves.
Yes, that's one of the ideas I was trying and not getting to work.

In the frame moving at nearly c, we see what looks like a deceleration of the atoms from nearly c to zero, and because we're uncontracting the ship from the point of view of this frame, we see the wave move from the front of the ship to the back. There' no problem there.
Let me describe the contradiction a different way. Suppose we create a wave not instantly, but over a short period like a minute or an hour. It doesn't matter if it is in a frame that considers it an increase or decrease in speed. The point is that it is uniform acceleration for the duration of that minute or hour, and all points on the object will experience that uniform acceleration for that time. But this cannot be since an accelerating object must accelerate harder at the tail than at the head, as we worked out in the beginning of this thread and in that other thread in New Theories you were involved in. The ship will compress or pull apart if it has uniform acceleration, and a moving wave must produce that uniform acceleration, or the wave must change shape (lengthen or contract at least) as it moves, which violates the way we are envisioning it as just a contracted object leaving a normal length object behind it as it decelerates. No such wave can traverse the object except a superlow acceleration one that changes slowly as it moves, slowly enough that the distortion of the wave doesn't result in a singularity before reaching the other end of the object. It takes 55 days to do this.

I don't understand your point at all. Of course its possible, at least mathematically, and this is a mathematical exercise after all, not an engineering one. I'm not really concerned about accelerating individual atoms. I consider the object to be a homogeneous rod, perhaps with length marks along it.
If you have a "ship" made of only two atoms and you accelerate them (in any direction), the amount of force each receives from the other will vary momentarily and will only settle down when you stop accelerating them. That is stress on a twoatom "ship"  it's unavoidable. If you want to avoid all stress, you can't accelerate it. The two atoms are both applying forces to each other, and if you move them a little, those forces are momentarily being applied in the wrong direction.
This creates a problem for us though, because if we are allowed to have some stress, how can we limit it? We could just have the whole ship accelerate to a fraction under c and maintain that speed for a fraction over one hour, then stop the whole ship in an instant, and all we need to do is hold each atom in place so that the ship can't contract in length. It's only if we let go of them at any point during that year that the ship will be able to contract and will rip itself into fragments, although by moving it at nearly c, that hour gets converted into such a short time that no contraction may occur, meaning that by the time we've stopped it again, the whole ship is completely undamaged. This lets us move every part of it a whole lighthour in a time just a fraction over one hour, and the accelerations all take place in a greaterthanzero length of time.
'When we stop accelerating' is a frame dependent thing.
I was talking about stopping an individual atom, and there's no need to worry about trying to stop accelerating any two atoms simultaneously  you would just stop accelerating them once they are in places where they will sit comfortably without further inputs of force.
The fault in the description was that it posited zero time for the acceleration, and that is unreasonable. It can be done over a finite time to give finite acceleration, but the interval of time to do it shortens as the wave moves forward, and it shortens to zero before it gets to the other end of the object.
How can it shorten to zero? Why can't you just start accelerating each particle sooner than the one behind it and have the propagation of the wave accelerate to accommodate this?
I presumed the ship had to be always stationary in its own frame along its entire length during the whole trip.
I don't see how it would be possible for it to be stationary in its own frame when it has parts moving at different speeds, other than by being stationary on average in one frame (which will always be the case no matter what you do).
The 55 day thing required 2 steps.
Step 1: Compute the exact speed of the ship. There are two ways to do this.
1A: Use a lorentz conversion to compute the speed the universe would need to go to get it the 100 LY distance to contract by a light hour. That gives me the speed the object needs to go (~452 km/sec).
I don't understand why this should be the speed of the ship. If you have a constant acceleration for the front end of the ship, what's the back end doing? What are the speeds of the front and back ends of the ship at 0, 5, 10, ... 45, 50, 55 years into the trip (or use some other time gap if you've already got a similar set of numbers). This would make it possible for other people to visualise how your ship is moving.
We can then imagine a ship of 100 atoms in length all ending up one atom further along from where they started.
Yea, but who can relate to the bazillionth of a second it takes to do that? The relativity isn't going to be apparent.
You can contain all the action on the top of a desk. Light only moves about 30cm in the tick of a 1 gigahertz processor, and an object 30cm long moving at 0.866c will be contracted to 15cm in length. there's no need to go big to illustrate relativity. But if you want to, you can spread the 100 atoms out over a hundred lightyears and have them sit comfortably a lightyear apart. What matters is that you find ways to provide an illustration of what different parts of the ship are doing  what speeds they're moving at and when. In the absence of diagrams, that needs a table.
I can have lengthmarks on my object, which seems to serve the same purpose as your discreet atoms, but I found no need to refer to them to compute the times required by the various methods, or to demonstrate that the caterpillar method doesn't work at all.
You may think there's no need to refer to them, but I can't follow what different parts of the ship are doing in your 55 day version.
I twas trying to do that, finding a faster way by using multiple waves. It doesn't work. The waves catch up to each other, which wasn't at all obvious at first.
With each wave propagating at a lower speed than the one that set out before it, that can't be possible.
So I find it unreasonable to say that since it happens in zero time that one can get from one speed to another speed without hitting the speeds in between.
Avoiding the length contraction by doing the acceleration 'while God blinks' so to speak seems a cheat.
It isn't cheating  we can make the acceleration take a finite time longer than zero and still not have to worry about the length contraction because it's so quick that the particles have no chance to respond to the momentary contraction forces. Objects are not required to be the length that the length contraction formula says they would settle to if they're left long enough to settle.
These forces do not exist when doing it over a millisecond, atom by atom. At no point are two atoms in a stressful arrangement. The argument would indeed have merit if this temporary force existed, but it doesn't. I showed that it doesn't. Two atoms cannot exert a force during a pair of event separated in a spacelike manner.
As soon as you move one atom towards another, you run it into a strengthening force from the other atom, but you also sent ahead a strengthening force toward the other atom which will propagate towards it at c, and that may start to accelerate the next atom before we start trying to accelerate it directly. Even if it doesn't though, it will still add force and lead us to need to put less direct acceleration force into it (although we aren't saving energy as we had to put extra energy into the first atom due to the increasing force it was running into from the second atom).
Well, no. It sort of works exactly because this doesn't happen. Acceleration of an atom doesn't result in any force against its unaccelerated neighbor. What does this is displacement, and displacement takes time. For it to put a force on the neighbor would be to have a causal effect at greater than light speed, which cannot happen.
The change in force form the moving atom will reach the other atom at c. The change in force from the stationary atom upon the atom moving towards it will apply instantly because the moving atom is running into that strengthening force.
Your approach is also on the discreet atomic level rather than the homogeneous mathemeatical level, but if we model the 'ship' as a series of discreet points that are accelerated individually, then there really is no length of the object, just spacings between the atoms which are to be ignored for the duration that a force is applied to them. If we allow that, even for a shorter duration than the speed of light between adjacent atoms, then the length of the object seems meaningless. The rules are to be ignored while we briefly take tongs to each atom in turn and change its velocity.
If you accelerate a ship and the length changes, you necessarily have different parts of it moving at different speeds and different length contractions applying to it in different places, so how are you going to stop that reaching the level of individual pairs of atoms? You can't do it on a wholeship basis, and any other basis in between uses arbitrary divides.
It apparently doesn't work in any frame, but it isn't so intuitive in say the initial rest frame. The one (middle) frame just made it real obvious why it didn't work, and yes, per relativity, the other frame thus must also not work.
I see it working in all frames.
Consider just two waves. We have one where we accelerate atoms nearly to c, but we have a second wave where we accelerate them to 0.5c. The latter acceleration will propagate from atom to atom at a higher speed than the former, with both propagating at speeds higher than c, but these things are fully possible in the frame of reference in which the starting speed is zero.
No, they're not possible in that (or any) frame. It just wasn't initially obvious to either of us. It became more apparent when I started to attempt optimizations and was running into so much trouble.
The front end is moving slowest, so any problem caused by a wave not propagating fast enough must be possible to solve by increasing its propagation speed as it goes along. I can't see any way for this to fail to work. We only need it to work in one frame to know that it must work in all frames, and so long as we aren't moving anything faster than the speed of light (or even just reaching it), it should be fine. Instant accelerations (from one speed to another) are possible for individual particles, so they should also be possible for atoms, but even if you want to make them take a longerthanzero time for each acceleration, that can still be achieved by starting the accelerations sooner. The back end of the ship moves fastest and the front end moves slowest, so if the front end isn't starting any acceleration soon enough, we start that acceleration sooner.

You can accelerate something without 'stress', ideally at least. You just need a geodesic ending into a 'infinity' avoiding 'tidal forces'. That is also called a 'gravitational acceleration'. Locally measured there shouldn't be any 'stress' applied anywhere in such a 'ship'. What you can't avoid though should be a 'length contraction', but just as with the 'gravitational acceleration' this 'length contraction' you find another object to have is a result of frames of reference interacting. Locally defined you still live in proper time finding a proper length.
=
This is if you go by local experiments.
If you have another opinion you also need to show how you will measure that 'stress' in a 'non local' manner.
a non gravitational acceleration is quite another thing. It will be local, locally measurable bringing with it a 'stress' on the 'ship'. That should hold for a 'atom' too I think. When it comes to 'point particles' I'm not as sure, you need length, width and height, as well as 'time' to define a SpaceTime. But mathematically with 'point particles'?
Is light length contracted? If you think of it in a 'real acceleration' then light will blue respectively red shift depending on where in the ship you measure it from. Ideally those two should even themselves out, leaving the intrinsic properties of light unchanged. That's the only properties I can think of when it comes to light. A 'length contraction' doesn't make sense for it. Ok :) forget the momentum for this. Actually, thinking of light this way makes a 'time dilation' unnecessary too, possibly? Now, that is weird, isn't it? Or maybe not, depending on views :)

I don't understand your point at all. Of course its possible, at least mathematically, and this is a mathematical exercise after all, not an engineering one. I'm not really concerned about accelerating individual atoms. I consider the object to be a homogeneous rod, perhaps with length marks along it.
If you have a "ship" made of only two atoms and you accelerate them (in any direction), the amount of force each receives from the other will vary momentarily and will only settle down when you stop accelerating them.
The other atom will not notice the acceleration of the first before it too is accelerated. I suppose the first one can feel the force from the 2nd as it moves through the essentially static EM field generated by that 2nd atom. But all this action takes place outside each other's light cone. I posted that the discrepancy between the field of the distant atom and what the atom over there is actually doing outside our light code is counterbalanced by photon or something equivalent to a graviton that corrects for the discrepancy. Thinking about such things is how GR needed to posit such particles.
So there are these photons or whatever that result from acceleration, and those exert force. I can accept that, but at not point can two particles be allowed to exist at an unnatural distance from each other for the duration that light takes to travel between them.
That alone admittedly doesn't preclude infinite acceleration. It doesn't even have to be infinite since it just has to take less time than light takes to allow the particles to notice the new velocity of its neighbors.
My protest against the method is that the solution cannot be approached by increasing acceleration to an arbitrary value. Using a singularity is a cheat because it is taking advantage of the fact that the length of the object is undefined at that singularity, and in particular, that length is not something that is approached by increasing acceleration.
That is stress on a twoatom "ship"  it's unavoidable. If you want to avoid all stress, you can't accelerate it. The two atoms are both applying forces to each other, and if you move them a little, those forces are momentarily being applied in the wrong direction.
It seems that slow and steady acceleration seems quite stable. The acceleration varies from one end to the other, but the object is mathematically Bornrigid the entire way. The entire length of the accelerating region is stationary and unvarying in length in its own frame. Yes, limited light speed puts some stress on the atoms as you describe, but only because the various atoms have no way of detecting what the other ones are doing, only what they have done some time ago.
This creates a problem for us though, because if we are allowed to have some stress, how can we limit it? We could just have the whole ship accelerate to a fraction under c and maintain that speed for a fraction over one hour, then stop the whole ship in an instant, and all we need to do is hold each atom in place so that the ship can't contract in length.
That violates Born rigidity. The wave thing does not, but a finite wave much change form as it moves, which wasn't apparent to either of us at first. Holding each atom at an unnatural separation from its neighbor for an hour (using the unlimited force with which we've endowed our propulsion) would work, but it would be stress. The whole thing would be under massive tension stress, balanced mostly except near the ends. No force applied in any direction will relieve that tension stress. Force is OK but stress isn't a force since it doesn't cause acceleration (except again at the ends, which are for the most part not in the light cone of the vast majority of the object).
It's only if we let go of them at any point during that year that the ship will be able to contract and will rip itself into fragments
It was already ripped to fragments when the acceleration was done. I suppose it can always be reassembled by using force to put each atom back in its rest frame and then letting go.
although by moving it at nearly c, that hour gets converted into such a short time that no contraction may occur, meaning that by the time we've stopped it again, the whole ship is completely undamaged.
It takes time in frames other that the one of the moving object. I agree that it comes out undamaged since we've put every fragment back in place. A broken egg doesn't stay broken if every atom is put back exactly where it used to be. The problem is trivial if we allow such things.
The fault in the description was that it posited zero time for the acceleration, and that is unreasonable. It can be done over a finite time to give finite acceleration, but the interval of time to do it shortens as the wave moves forward, and it shortens to zero before it gets to the other end of the object.
How can it shorten to zero?
I think I was mistaken when I said that. A wave initiated over a finite time is a bunch of small discreet accelerations, and since they are small, their waves propagate at more speed than the aggregate. So while acceleration to almost c creates a wave that supposedly moves at just over c, in fact the little waves move much faster, approaching infinitely fast. It gets to the front of the object right away, but also at a much smaller accleration rate. Anyway, the wave doesn't shorten to zero size. Rather the opposite. Any noninfinite acceleration propagates at a rate that approaches infinite speed since it is made up of acceleration quanta that approach infinitely small speed changes, and yet the aggregate speed of the wave must be much less, a contradiction.
Why can't you just start accelerating each particle sooner than the one behind it and have the propagation of the wave accelerate to accommodate this?
That's exactly what happens naturally. There is no wave then since the whole thing starts to move at once, and the entire object is stationary in its own frame at all times. Funny thing is that it is not all moving at the same speed in any other frame. Only its own frame.
So this begs a different problem: How long does it take to accelerate a 100 light year object to say 1%c? Answer: depends where the clock is.
I presumed the ship had to be always stationary in its own frame along its entire length during the whole trip.
I don't see how it would be possible for it to be stationary in its own frame when it has parts moving at different speeds, other than by being stationary on average in one frame (which will always be the case no matter what you do).
But it is. In its own frame, no part is moving at a different speed than any other part. They're all stopped in fact. Not true of the infiniteacceleration wave, but that involves discontinuities.
The 55 day thing required 2 steps.
Step 1: Compute the exact speed of the ship. There are two ways to do this.
1A: Use a lorentz conversion to compute the speed the universe would need to go to get it the 100 LY distance to contract by a light hour. That gives me the speed the object needs to go (~452 km/sec).
I don't understand why this should be the speed of the ship. If you have a constant acceleration for the front end of the ship, what's the back end doing?
Constant acceleration to the same speed as the front. It takes less time for the back to do this since it accelerates harder.
What are the speeds of the front and back ends of the ship at 0, 5, 10, ... 45, 50, 55 years into the trip (or use some other time gap if you've already got a similar set of numbers). This would make it possible for other people to visualise how your ship is moving.
Speed of the rear (km/sec) is 452, 411, 370 ... 82, 41, 0. Speed of the front is those same numbers, but in reverse. The 452 figure is just after the high acceleration finishes after say one minute, and one minute before the front decelerates hard to 0.
For points other than the front or the rear, the peak speed is reached at a proportional time relative to the distance from the rear. So a point an 11th of the way forward will reach peak speed in 5 days and ramp evenly down from there. The midpoint will accelerate constantly for half the time and decelerate constantly for the other half.
You can contain all the action on the top of a desk. Light only moves about 30cm in the tick of a 1 gigahertz processor, and an object 30cm long moving at 0.866c will be contracted to 15cm in length. there's no need to go big to illustrate relativity. But if you want to, you can spread the 100 atoms out over a hundred lightyears and have them sit comfortably a lightyear apart.
Or just put marks each lighthour on the object. I'm moving my big object a lot less than 1% of its length, and the relativistic effects are a lot more than just contraction. The other effects are not readily apparent to me when working with a ruler and femptoseconds. Maybe its just me.
What matters is that you find ways to provide an illustration of what different parts of the ship are doing  what speeds they're moving at and when. In the absence of diagrams, that needs a table.
OK, I gave an initial 'table' with crude figures (for speed) above. A computer printout would be more accurate, especially when illustrating an attempt at a wave, showing where it fails.
So I find it unreasonable to say that since it happens in zero time that one can get from one speed to another speed without hitting the speeds in between.
Avoiding the length contraction by doing the acceleration 'while God blinks' so to speak seems a cheat.
It isn't cheating  we can make the acceleration take a finite time longer than zero and still not have to worry about the length contraction because it's so quick that the particles have no chance to respond to the momentary contraction forces.
I would accept that if the solution could be approached by arbitrarily high acceleration, but it isn't, and that makes it a trivial cheating answer to a real question posed in the OP. I accept the instant speed thing on the ground where they work: Sure, the stress is unnoticed in the sufficiently short time since light cannot travel to the next atom in that time.
As soon as you move one atom towards another, you run it into a strengthening force from the other atom, but you also sent ahead a strengthening force toward the other atom which will propagate towards it at c, and that may start to accelerate the next atom before we start trying to accelerate it directly.
Of course not. Our waves move faster than light. We'll be accelerating it directly before the motion of the first atom is noticed by the 2nd. We'd violate rigidity if that were not so. Still, argument from the atomic level is probably still a physical violation since there is no way to apply that sort of force to a single atom without affecting any of its neighbors. That's why I've been going for idea mathematical solutions, not practical 'quantum' ones.
If you accelerate a ship and the length changes, you necessarily have different parts of it moving at different speeds and different length contractions applying to it in different places
Agree, this is true whether we're doing a wave or not. This does not itself cause stress since the parts of the object moving at a different speed are outside of the causal cone.
so how are you going to stop that reaching the level of individual pairs of atoms? You can't do it on a wholeship basis, and any other basis in between uses arbitrary divides.
If it is a continuous curve (such as it is in the 'rest frame' moving the ship as a whole), then you need to integrate the contraction over the length of the object moving at varying speeds. I didn't bother to do that since it was much simpler to use the frame of the object.
No integration is needed for the wave method since there are only two discreet chunks of objects, one at each speed.
[The finiteacceleration wave method] apparently doesn't work in any frame, but it isn't so intuitive in say the initial rest frame. The one (middle) frame just made it real obvious why it didn't work, and yes, per relativity, the other frame thus must also not work.
I see it working in all frames.
Then you're not thinking it through. You don't show how you arrive at this conclusion, so I have a hard time pointing out where it fails.

I don't understand your point at all. Of course its possible, at least mathematically, and this is a mathematical exercise after all, not an engineering one. I'm not really concerned about accelerating individual atoms. I consider the object to be a homogeneous rod, perhaps with length marks along it.
It makes a difference whether you take into account an objects stress when its accelerating. The answer depends on it.
Saying this is just a math question is wrong. Math is the description of nature, not the other way around. I could say that an object is moving at 3 times the speed of light "mathematically" but physically its wrong.

I don't understand your point at all. Of course its possible, at least mathematically, and this is a mathematical exercise after all, not an engineering one. I'm not really concerned about accelerating individual atoms. I consider the object to be a homogeneous rod, perhaps with length marks along it.
It makes a difference whether you take into account an objects stress when its accelerating. The answer depends on it.
Saying this is just a math question is wrong. Math is the description of nature, not the other way around. I could say that an object is moving at 3 times the speed of light "mathematically" but physically its wrong.
So where is the stress? I'm applying force to all of the object at once, not just one part and letting the stress transfer that force to other parts at the speed of sound.
The best way to do that is something like a (stationary) rail gun that runs the entire length of the object so I can locally apply whatever force is necessary. That should be able to do the job without any significant stress. My forces should cause acceleration, but no strain, which is defined as deformation of the object. If there is no strain, there is no stress.

The other atom will not notice the acceleration of the first before it too is accelerated.
You're right  I was forgetting that the acceleration wave is propagating faster than light.
We could just have the whole ship accelerate to a fraction under c and maintain that speed for a fraction over one hour, then stop the whole ship in an instant, and all we need to do is hold each atom in place so that the ship can't contract in length.
That violates Born rigidity. The wave thing does not, but a finite wave much change form as it moves, which wasn't apparent to either of us at first. Holding each atom at an unnatural separation from its neighbor for an hour (using the unlimited force with which we've endowed our propulsion) would work, but it would be stress. The whole thing would be under massive tension stress, balanced mostly except near the ends.
With the ship travelling at just a fraction under c, the time of one hour for us would to that ship appear to be an infinitesimal moment, not giving it enough time to shorten  we don't need to support each atom at all during that hour but can just let them all drift, and while they will pull together a beyondmicroscopic amount during that hour, we will decelerate the whole thing to a halt before it does any damage, at which point it will push back out the same amount tiny amount. This allows any ship to be moved anywhere at nearly c with all parts moving at practically the same speed. There is no significant contraction of the object because its functionality is as good as halted for the entire trip.
Anyway, the wave doesn't shorten to zero size. Rather the opposite. Any noninfinite acceleration propagates at a rate that approaches infinite speed since it is made up of acceleration quanta that approach infinitely small speed changes, and yet the aggregate speed of the wave must be much less, a contradiction.
I'm not managing to convert that into anything that I can visualise, so I can't see the contradiction (which I'm not saying isn't there). I probably won't get it without a diagram (and one that shows things moving).
Why can't you just start accelerating each particle sooner than the one behind it and have the propagation of the wave accelerate to accommodate this?
That's exactly what happens naturally. There is no wave then since the whole thing starts to move at once, and the entire object is stationary in its own frame at all times. Funny thing is that it is not all moving at the same speed in any other frame. Only its own frame.[/quote]
It may be that trying to describe it as waves is limiting the ability to represent what can actually be done.
I presumed the ship had to be always stationary in its own frame along its entire length during the whole trip.
I don't see how it would be possible for it to be stationary in its own frame when it has parts moving at different speeds, other than by being stationary on average in one frame (which will always be the case no matter what you do).
But it is. In its own frame, no part is moving at a different speed than any other part. They're all stopped in fact. Not true of the infiniteacceleration wave, but that involves discontinuities.
That doesn't work  you have the back end moving at a different speed from the front end, so the material at different places along your ship are contracted to different extents and you don't have a single frame for the whole ship to be stationary in, unless you're using some weird kind of frame which pretends that they're all moving at the same speed by being a mixture of a long series of real frames. If you're doing that, then you're going to get into horrific mathematical complications which will make it very hard to work out what's going on, not least because the speed of light relative to each part (in the direction of travel) is different in real frames.
I don't understand why this should be the speed of the ship. If you have a constant acceleration for the front end of the ship, what's the back end doing?
Constant acceleration to the same speed as the front. It takes less time for the back to do this since it accelerates harder.
If you have the back end accelerating harder, it must be moving faster than the front end. It's only when you stop the acceleration that the two ends of the ship can settle to moving at the same speed (after a bit of compression while the extra momentum form the tail end is shared out with the front).
What are the speeds of the front and back ends of the ship at 0, 5, 10, ... 45, 50, 55 years into the trip (or use some other time gap if you've already got a similar set of numbers). This would make it possible for other people to visualise how your ship is moving.
Speed of the rear (km/sec) is 452, 411, 370 ... 82, 41, 0. Speed of the front is those same numbers, but in reverse. The 452 figure is just after the high acceleration finishes after say one minute, and one minute before the front decelerates hard to 0.
So, you start the process by instantly having the rear part move at 452, but you immediately begin to decelerate it while you accelerate the front part gradually. By the half way point, the whole ship will be moving at the same speed, but at all other times, different parts are moving at different speeds and will be differently contracted. Have I understood that correctly?
For points other than the front or the rear, the peak speed is reached at a proportional time relative to the distance from the rear. So a point an 11th of the way forward will reach peak speed in 5 days and ramp evenly down from there. The midpoint will accelerate constantly for half the time and decelerate constantly for the other half.
What happens to the length of your ship through the course of this process? The initial acceleration of the rear part will lead it to want to be contracted, while the contraction required for the rest goes down for each section all the way to the front. By the end of the process, the opposite occurs, so the length is the same at the end as it was at the start, except that when it started, the sudden acceleration of the tail from 0 to 452 made it the wrong length for a moment (so it was too long for the atomtoatom separation distances to be comfortable). Half way through the process, I'm imagining the whole ship moving at the same speed (226). The ship should be at its shortest length at this point because the speed of the front has caught up with the speed of the rear, and from now on it will lengthen out again. I don't know how to apply maths to this to test whether the length of the ship is always right for the sum of all the differentlycontracted parts at every moment in the process, so I don't know if the numbers match up, but the whole methodology looks a bit suspect.
I see it working in all frames.
Then you're not thinking it through. You don't show how you arrive at this conclusion, so I have a hard time pointing out where it fails.
I arrive at that conclusion because I can see the back end being able to accelerate up to a fraction under c where it can all concertina up into almost a 2D object, and I can see the potential for everything ahead of the 2D compression zone to move forward a little before that 2D compression zone catches up with it, and this delays the formation of the 2D compression zone a bit because the second last atom will move forwards a bit while the rearmost atom closes in on it. I realise now that the limit of this though ends up being the case where the rearmost atom doesn't actually close in on the one ahead of it at all because the one in front is moving at the same speed, as is the one ahead of that, and all the way to the front, so we end up with the whole thing moving at next to c, and it's stable in transit because its functionality is slowed to a halt. This works at the highest speed, and it works at the lowest speed, but there may be some speeds in between where it breaks.

With the ship travelling at just a fraction under c, the time of one hour for us would to that ship appear to be an infinitesimal moment
Not sure why you're considering this case since at that speed, it takes the wave almost 100 years to get to the other end. Hardly an optimal solution.
It may be that trying to describe it as waves is limiting the ability to represent what can actually be done.
Indeed, it isn't a wave anymore. The only way to do a wave is with infinite acceleration (abrupt change in velocity to something else), and it only works because the singularity makes certain values (notably length of the object) undefined.
In its own frame, no part is moving at a different speed than any other part. They're all stopped in fact. Not true of the infiniteacceleration wave, but that involves discontinuities.
That doesn't work  you have the back end moving at a different speed from the front end, so the material at different places along your ship are contracted to different extents and you don't have a single frame for the whole ship to be stationary in.[/quote]How is stopped a different speed than the stopped at the other end? That single frame is for the whole object. I don't call it a ship since it is easier to visualize the forces needed being applied by the rail gun outside the object.
Yes, different parts of the object are moving at different speeds in other frames where they are not stationary, and hence the contraction factor isn't constant over the length of the object in those other frames. There is no contraction in the object frame since it is everywhere stationary in it.
unless you're using some weird kind of frame which pretends that they're all moving at the same speed by being a mixture of a long series of real frames.
It is a standard accelerating reference frame. Different stationary points in space accelerate at different rates in such a frame, and the reference frame is bounded by an event horizon to the rear, beyond which events are not part of the frame at all. The object cannot extend beyond that event horizon, at least not while remaining Born rigid.
I learned a bit about general relativity when researching this topic.
If you're doing that, then you're going to get into horrific mathematical complications which will make it very hard to work out what's going on, not least because the speed of light relative to each part (in the direction of travel) is different in real frames.
Speed of light isn't really a meaningful thing in an accelerating reference frame. I suppose I can shine a light to a mirror further forward and time the return of that signal, and the observer up there can similarly do such a measurement via a mirror by me. We won't measure the same duration. I will measure a longer elapsed time.
If you have the back end accelerating harder, it must be moving faster than the front end.
In an inertial frame, yes. The frame of the object is not an inertial frame.
It's only when you stop the acceleration that the two ends of the ship can settle to moving at the same speed (after a bit of compression while the extra momentum form the tail end is shared out with the front).
If we stop the acceleration all at once in the object's frame, then there is nothing to settle and no extra compression or momentum to deal with. The object is already stopped in its own frame (and always has been), so nothing needs to be fixed.
So, you start the process by instantly having the rear part move at 452
Quickly at least. Instantly isn't necessary. We do it in an arbitrarily short time.
but you immediately begin to decelerate it while you accelerate the front part gradually. By the half way point, the whole ship will be moving at the same speed.
In the initial inertial frame, the object is moving at top speed at the half way point, and the ends are moving at half speed.
but at all other times, different parts are moving at different speeds and will be differently contracted. Have I understood that correctly?
At all times the different parts are moving at different speeds. This is true of any accelerating object . I just made it more obvious by making the object stupidly large. When it stops accelerating, it needs to do it along its length simultaneously in its own frame, not simultaneously in the original frame, which wouldn't work since it is moving at different speeds in that frame.
In our 55 day trip, we immediately start decelerating, and don't stop at all until we're stationary back in the original frame.
For points other than the front or the rear, the peak speed is reached at a proportional time relative to the distance from the rear. So a point an 11th of the way forward will reach peak speed in 5 days and ramp evenly down from there. The midpoint will accelerate constantly for half the time and decelerate constantly for the other half.
What happens to the length of your ship through the course of this process?
Frame dependent question. In the original inertial frame, the object contracts at first, and expands again towards the end, as you would expect of an object that moves at relativistic speed. We're only going a lousy 452 km/sec max in the middle when the object as a whole achieves maximum average speed, but it is never going all the same speed in the original frame except at the endpoints.
The initial acceleration of the rear part will lead it to want to be contracted, while the contraction required for the rest goes down for each section all the way to the front. By the end of the process, the opposite occurs, so the length is the same at the end as it was at the start, except that when it started, the sudden acceleration of the tail from 0 to 452 made it the wrong length for a moment (so it was too long for the atomtoatom separation distances to be comfortable).
Did not. The material nearby is also going nearly that speed, so it all contracts exactly the amount it needs to. It is always the correct length. No strain.
Half way through the process, I'm imagining the whole ship moving at the same speed (226).
No, the middle reaches peak speed at that point. All points need to average 226 the whole way, so the middle is no exception, accelerating cleanly from 0 to 452 and back down again. So at 27.6 years, the ends are moving at 226 but the middle is moving at 452.
The ship should be at its shortest length at this point because the speed of the front has caught up with the speed of the rear, and from now on it will lengthen out again.
Correct.
I arrive at that conclusion because I can see the back end being able to accelerate up to a fraction under c where it can all concertina up into almost a 2D object,
Well, the rear of the ship does that quickly as you say, but it takes well over 100 years for the whole thing to compress to a 2D object like that. The front is accelerating at about 0.3 m/sec per hour, so it takes a wicked long time to get the front up to enough speed to consider the object compressed to negligible length. The front cannot accelerate faster. It is a function of the proper length of the object and has nothing to do with the power we're applying to the thrust.
and I can see the potential for everything ahead of the 2D compression zone to move forward a little before that 2D compression zone catches up with it, and this delays the formation of the 2D compression zone a bit because the second last atom will move forwards a bit while the rearmost atom closes in on it.
Like that, yes.
I realise now that the limit of this though ends up being the case where the rearmost atom doesn't actually close in on the one ahead of it at all because the one in front is moving at the same speed, as is the one ahead of that, and all the way to the front,
During accleration, the atoms behind are always faster than the ones ahead of them since they are accelerating harder. From some inertial frame where things are speeding up, the object always keeps compressing.
so we end up with the whole thing moving at next to c, and it's stable in transit because its functionality is slowed to a halt. This works at the highest speed, and it works at the lowest speed, but there may be some speeds in between where it breaks.
It is stable and retains its proper length the whole way, so it doesn't break. That was the initial condition, not a conclusion. I accelerate each piece enough so the accelerating rearmost piece stays the same proper distance from it at all times.

Speed of the rear (km/sec) is 452, 411, 370 ... 82, 41, 0. Speed of the front is those same numbers, but in reverse. The 452 figure is just after the high acceleration finishes after say one minute, and one minute before the front decelerates hard to 0.
The numbers above are a bit misleading because they're so small. If we keep accelerating the front to significant speeds, the numbers drop off in a curve, not a linear rate as is suggested above. We're assuming not constant acceleration (which cannot be kept up indefinitely), but rather constant proper acceleration (which can), so from some inertial frame, the acceleration is greatest at first, but drops off per unit of time as the mass of the object goes up. At 452 km/sec, the mass of the object hasn't really changed much and the numbers still appear linear.

If you're only considering the 'stress' created by a length contraction, ignoring compression waves/stresses, then it doesn't matter. Everything should break just before 'c', doesn't matter if it's a spinning disk or a 'rod'. It's mass will reach infinity at whatever 'edge' you define, be it a rod or a plate. Presuming that you can accelerate a object equally over its whole mass/density, which to me seems pretty impossible in itself ( I would really like to see how that is thought to work btw ) the idea seems to be that everything becomes this 'edge'? In that case we might think of it as every 'atom' having a equivalent acceleration. Well, seems to me you're setting up a 'black hole scenario' if so :) For this it doesn't matter if you constantly accelerate at one gravity to then, some years later, close in to 'c'. The rods mass must reach infinity as it nears the speed of light in a vacuum.

If you're only considering the 'stress' created by a length contraction
There is none. In frames where the object contracts, the parts move at different speeds in the exact manner to prevent any stress at all. So the rear moves faster at first in accordance with the contracting length of the thing.
Everything should break just before 'c', doesn't matter if it's a spinning disk or a 'rod'.
Relativity says no such thing, and I'm only going about 1/700th of c max with my object, hardly close to light speed. Do you even read the posts?
If I spin a Bornrigid disk, it will break at any any rotation rate, far before any part of it has significant speed.
Presuming that you can accelerate a object equally over its whole mass/density
I'm not accelerating it equally over its length. It would break if I did that.

Hmm, would you mind explaining how you think writing that the rod would break if every atom in it had a equal acceleration? If you on the other hand presume slightly different accelerations inside the material you must include stress. A equal acceleration of every atom should give a equal length contraction at every point of this rod. It's a weird idea :) though that seems to go against the lack of simultaneity relativity discuss. You could treat the atoms as related to each other relative both time dilation's and LorentzFitzGerald contractions.
=
Actually, presuming identical atoms in a identical space having a identical acceleration, seems to me to state that they also must share a exact same frame of reference. That would be turning accelerations upside down sort of :) Doesn't mean it has to be wrong, but it's funny :)
You could argue that this is what a perfect non spinning sphere, of a perfectly distributed density of one gravity, actually have. And as that could be seen as the equivalence to a uniform acceleration of one gravity? Not sure though. Accelerations always seem to come in 'steps', even with a planet. Mass invariant, with gravity's potential changing inside the planet.

With the ship travelling at just a fraction under c, the time of one hour for us would to that ship appear to be an infinitesimal moment
Not sure why you're considering this case since at that speed, it takes the wave almost 100 years to get to the other end. Hardly an optimal solution.
I wasn't doing it with a wave, but with the whole ship being accelerated to a fraction under c at the same time. The whole thing can then travel for an hour and it won't have time to contract significantly because it's functionality is practically halted by its high speed of travel, so when you halt it an hour later, it is still almost the same length as when it started and will make an infinitesimal correction in an infinitesimal amount of time to get back to full length. No damage done. This is the fastest way in principle to move objects, including long ones, and it's a lot less interesting than what I was hoping to find.
unless you're using some weird kind of frame which pretends that they're all moving at the same speed by being a mixture of a long series of real frames.
It is a standard accelerating reference frame.
That is why I had trouble working out what you were doing  I assumed you would be using real frames rather than contrived ones in which the speed is claimed to be the same relative to each part of the ship while in the real universe it varies. If you're allowed to use such contrived frames, you can design some really warped ones to cover all the action in any caterpillar solution too and assert that the entire ship is stationary in the ship's frame at all times, though clearly you want to stick to the particular contrived frames used that are accepted in GR, so that's fair enough as an exercise.
Different stationary points in space accelerate at different rates in such a frame, and the reference frame is bounded by an event horizon to the rear, beyond which events are not part of the frame at all. The object cannot extend beyond that event horizon, at least not while remaining Born rigid.
I learned a bit about general relativity when researching this topic.
Well, now I can see why you're aiming for that specific kind of solution, and if your requirement is to have the whole ship stationary in an officially recognised GR frame, then you likely do have the best solution of that kind.
If we stop the acceleration all at once in the object's frame, then there is nothing to settle and no extra compression or momentum to deal with. The object is already stopped in its own frame (and always has been), so nothing needs to be fixed.
Except that you have the back end instantly moving at 452 without any time for it to contract to a comfortable length (as observed from the inertial frame in which the journey begins with the whole ship at rest).
I arrive at that conclusion because I can see the back end being able to accelerate up to a fraction under c where it can all concertina up into almost a 2D object,
Well, the rear of the ship does that quickly as you say, but it takes well over 100 years for the whole thing to compress to a 2D object like that.
We aren't worried about compressing the whole ship. The point of the caterpillar method is that we should be able to move the entire ship using your method as a starting point, but add in the caterpillar compression to the rear to reduce journey time for the rear while still delivering the front end to its destination in 55 days. This must produce a viable method of moving the ship without leaving the atoms at uncomfortable separations for any extended length of time, but merely fails to comply with any GRapproved frame for the whole ship to be stationary in at all times.
The front is accelerating at about 0.3 m/sec per hour, so it takes a wicked long time to get the front up to enough speed to consider the object compressed to negligible length. The front cannot accelerate faster. It is a function of the proper length of the object and has nothing to do with the power we're applying to the thrust.
I can see that there will be a limit to the speed you can get the front end up to under this rule (of not leaving the atoms at uncomfortable separations for any extended length of time), and your method may well have identified that limit for the caterpillar method too, but I wouldn't want to bet on that. Because I can get the back end moving faster, the length is shortening faster and the limit may be shifted by that.
I realise now that the limit of this though ends up being the case where the rearmost atom doesn't actually close in on the one ahead of it at all because the one in front is moving at the same speed, as is the one ahead of that, and all the way to the front,
During accleration, the atoms behind are always faster than the ones ahead of them since they are accelerating harder.
Not in the case I was thinking about there where I was referring to the limit under rules that allow you to have atoms sit at uncomfortable separations for extended periods so long as their functionality is practically halted (such that they won't contract or extend). There are three different sets of rules here, so we're tripping up over category boundaries.
I accelerate each piece enough so the accelerating rearmost piece stays the same proper distance from it at all times.
Fair enough, but you can certainly move the rear faster than that while still following that rule, so the only thing stopping you doing that is your desire to stick to a GRapproved frame in which the whole ship is stationary. We have three categories with different rules applying, and you have identified the fastest method for the category with the greatest constraints on what's allowed (although you may have to adjust the way you start the back end moving, because for shorter ships you're going to have trouble with an instant acceleration to high speed where the lack of contraction on it is wrong), while I've identified the fastest method for the category with the least constraints. The remaining category is the one in between in which the tail compresses to nearly 2D while the front end may move at the same speed as in your accelerated frame method, so the main remaining interest for me is whether that limit should apply to the front end or if it can accelerate faster due to the compression of the back end. The back end needn't immediately compress to nearly 2D though, because the particle ahead can accelerate early to enable the one ahead of it to accelerate early, and this chain of early accelerations will propagate all the way along the ship, potentially allowing the front end to move a bit faster than in your case.

I wasn't doing it with a wave, but with the whole ship being accelerated to a fraction under c at the same time. The whole thing can then travel for an hour and it won't have time to contract significantly because it's functionality is practically halted by its high speed of travel, so when you halt it an hour later, it is still almost the same length as when it started and will make an infinitesimal correction in an infinitesimal amount of time to get back to full length. No damage done.
In the original frame, it is held at its full length for an hour while it should have contracted to say a 1000th that length. Damage is very much done.
In its own frame, it's like I spread your body all over Earth in tiny pieces, which is OK since I promise to put the pieces back in 3 seconds. It breaks. Such solutions are not even close to following the premise.
This is the fastest way in principle to move objects, including long ones, and it's a lot less interesting than what I was hoping to find.
Fastest way to move a lengthy load of sand perhaps, but not my rigid object.
It is a standard accelerating reference frame.
That is why I had trouble working out what you were doing  I assumed you would be using real frames rather than contrived ones in which the speed is claimed to be the same relative to each part of the ship while in the real universe it varies.
Are you claiming that accelerated reference frames are less real? Sure, they have different properties than inertial or rotating frames, but they're all equally natural. Per the equivalence principle, you live in such a frame, and there is no avoiding it. Everything the object is doing in my descriptions also happens to you and more rigid things like buildings and such.
If you're allowed to use such contrived frames, you can design some really warped ones to cover all the action in any caterpillar solution too and assert that the entire ship is stationary in the ship's frame at all times, though clearly you want to stick to the particular contrived frames used that are accepted in GR, so that's fair enough as an exercise.
Suit yourself. You are welcome to compute all the locations, speeds, lengths and stresses in say the one (unspecified) absolute frame, but the stresses will work out to exactly zero or you've done it wrong. The mathematics of that is beyond me.
As for contrived frames, I think we used a composite frame to work through the wave method, but I eventually found that it was much simpler to use the inertial 226 km/sec frame. That wasn't obvious at first.
Well, now I can see why you're aiming for that specific kind of solution, and if your requirement is to have the whole ship stationary in an officially recognised GR frame
I never had that requirement. I just haven't found any better solutions that don't involve singularities.
If we stop the acceleration all at once in the object's frame, then there is nothing to settle and no extra compression or momentum to deal with. The object is already stopped in its own frame (and always has been), so nothing needs to be fixed.
Except that you have the back end instantly moving at 452 without any time for it to contract to a comfortable length (as observed from the inertial frame in which the journey begins with the whole ship at rest).
The back end is stopped in the ship's frame, as is all the rest of it. It is perhaps moving at 452 after the first moment in the initial frame, but that isn't the object's frame. No, you cannot simultaneously cease acceleration of all of the object's parts in that frame. It would indeed break.
We aren't worried about compressing the whole ship. The point of the caterpillar method is that we should be able to move the entire ship using your method as a starting point, but add in the caterpillar compression to the rear to reduce journey time for the rear while still delivering the front end to its destination in 55 days.
I was looking for such a solution. It seems that it doesn't exist. I invite you to make a description of how that would work, or in particular, how you would get the speed of any part of the object over 452 km/sec without overshooting your destination. I found the 452 figure right away (working backwards from a target Lorentz contraction) and only later computed how long it would take to move a light hour averaging exactly half that speed.
Later on I computed the same number using A= c²/length : c2 is 9e16 (units of meters and seconds) / 9.46e17 meters (100 LY) giving us a max acceleration of 0.09513 m/sec2. That is the max acceleration of the front and the max deceleration at the rear, and it takes 55.3 days at that acceleration to go a light hour, topping out at 452 km/sec after those 55.3 days. Go any faster and it takes longer that 55 days to get that fast and you can't stop it in time.
I can see that there will be a limit to the speed you can get the front end up to under this rule (of not leaving the atoms at uncomfortable separations for any extended length of time), and your method may well have identified that limit for the caterpillar method too
The caterpillar method used a singularity to make contraction computation undefined, thus allowing it to use a higher speed.
Fair enough, but you can certainly move the rear faster than that while still following that rule, so the only thing stopping you doing that is your desire to stick to a GRapproved frame in which the whole ship is stationary.
Nope. I invite other solutions, but the singularity was too much. Acceleration needs to be finite.
Clearly it is allowed for different parts of the object to be moving at different speeds in other frames. No reason why other parts of the object need to be stationary in the frames any given parts. So maybe there is a better solution, and we just haven't identified it yet. I suppose I need a proof that my 55.3 day thing is optimal, but I don't have that proof yet.
We have three categories with different rules applying, and you have identified the fastest method for the category with the greatest constraints on what's allowed (although you may have to adjust the way you start the back end moving, because for shorter ships you're going to have trouble with an instant acceleration to high speed where the lack of contraction on it is wrong), while I've identified the fastest method for the category with the least constraints. The remaining category is the one in between in which the tail compresses to nearly 2D while the front end may move at the same speed as in your accelerated frame method.
How are you going to stop the rear if you get it up to such a speed? That was the part I couldn't solve.
so the main remaining interest for me is whether that limit should apply to the front end or if it can accelerate faster due to the compression of the back end. The back end needn't immediately compress to nearly 2D though, because the particle ahead can accelerate early to enable the one ahead of it to accelerate early, and this chain of early accelerations will propagate all the way along the ship, potentially allowing the front end to move a bit faster than in your case.
I encourage investigation of such a solution. The wave thing worked best at around 3150 km/sec, hardly a speed worthy of massive contraction, but it sure got the job done a lot faster than 55 days. But it only worked with that singularity, not if you approached it.

In the original frame, it is held at its full length for an hour while it should have contracted to say a 1000th that length. Damage is very much done.
In the original frame, that hour isn't enough to contract the object by 1000th, never mind to 1000th of the initial length. The functionality of the ship is practically halted. Think about a planet orbiting a star. If the star is stationary, you could watch the planet take a year to go round it once. Now have the star and planet move past you at 0.866c while you are stationary and you will see the planet take two years to go round the star instead of one. Increase the speed to 0.969c and you will see it take four years to orbit once. The faster we move the star and planet past you, the more we slow those orbits, and as we get near to c, the orbiting (and all other functionality) practically stops. In the same way, a ship of any length that's accelerated to a speed that practically stops functionality will not contract significantly  we can pick a theoretically achievable speed that will keep the amount of actual contraction so low that no damage will be done by the time we've stopped the ship again, even if the journey lasts a billion years. This solution works.
Are you claiming that accelerated reference frames are less real?
Of course they're less real. Take a rotating frame as an example of a fake frame. Imagine that you're in a space station made of a rotating ring designed to produce artificial gravity. You have a series of clocks round the ring which you want to synchronise, so you synchronise the first pair, then the next (meaning one of the first pair plus the next clock round from there), then the next, and so on all the way round to the start. Have you got a frame for the whole ring in which there's a single unified moment? No  you can see it break catastrophically between the first and last clock. It breaks because the speed of light across each clock is different relative to that clock in opposite directions round the ring. Rotating frames are bogus. We know from such rings that the actual speed of light relative to objects varies in different directions, and that's a crucial piece of knowledge which must be applied to everything else. In an accelerated frame where an object is actually accelerating through space, we know that the speed of light relative to different parts is not the same, so the frame provides a distorted representation of reality. With inertial frames too, we know that one of them must be a true representation of reality (because it provides the correct speeds for light relative to an object in every direction) while all the rest must be false. However, because we can't tell which one is true, we have to treat all inertial frames as potentially true. We shouldn't do that with an accelerated frame though because it's guaranteed not to be true.
Sure, they have different properties than inertial or rotating frames, but they're all equally natural. Per the equivalence principle, you live in such a frame, and there is no avoiding it. Everything the object is doing in my descriptions also happens to you and more rigid things like buildings and such.
When an accelerated frame is actually stationary and the difference in the speed of light across objects relative to them in different directions is caused by gravity, again that frame is a misrepresentation of reality. A clock higher up is ticking more quickly because the speed of light across it is either higher or more even, but the true frame has its time running faster still, and it runs at that higher speed at all depths in the gravity well.
However, all of that is predicated on the idea that light can travel at speeds approaching c in the first place. In 4D models, light must actually travel at zero speed because it has no option other than to reduce all the paths it follows to zero length. These 4D models provide the only semireasonable excuse to declare frames that I label as fake to be valid, but they don't stand up to scrutiny when you push them into a corner to see if they actually work as claimed (due to eventmeshing failures in dynamic versions and fake causality in static versions where nothing ever had the opportunity to cause anything). That's a discussion for elsewhere though as some proofs are not welcome outside of the backwaters.
The back end is stopped in the ship's frame, as is all the rest of it. It is perhaps moving at 452 after the first moment in the initial frame, but that isn't the object's frame. No, you cannot simultaneously cease acceleration of all of the object's parts in that frame. It would indeed break.
If the object is stationary in the initial frame, you can't instantly have it with the back end moving at 452km/s without the contraction being wrong when the trip begins. The error may be small and trivial at this speed, but when you apply the method to shorter ships, the scale of the error will grow and cause damage.
I was looking for such a solution. It seems that it doesn't exist. I invite you to make a description of how that would work, or in particular, how you would get the speed of any part of the object over 452 km/sec without overshooting your destination.
As soon as any part gets to the place where you want it to stop, you stop it there and it will sit there comfortably, so the speed it moves at to get there can be as high as you like. You have a solution which you consider viable, and I say you can get the tail end to its destination faster by using the caterpillar method. I haven't said that you can get the front end to its destination faster than your method (other than through the recently found method where the whole thing moves at a fraction under c and holds together for an hour unsupported due to it's practicallyhalted functionality), but it is not yet clear to me that the front end will be unable to go a bit faster than with your method if the back end is moving at much higher speed (given that that frees up the bit ahead of the back end to go a bit faster too, and so on, potentially all the way up to the front). I'm not going to spend time trying to do the maths for it though when it's a better use of time to focus on building tools that will make that maths easier to apply, so I'm going to put this on the shelf for later. I know it could be done with a relatively simple simulation, but I've got thousands of other simple simulations that I'd like to run too, and each one takes a long time to build  even if it's only a few hours work (which is never guaranteed  a simple bug can take a week to find sometimes) , it all adds up to lost years, and life's too short for that. I need better tools to automate all the tedious fiddling involved in these builds, so writing those tools up front is the fast route forward.
The caterpillar method used a singularity to make contraction computation undefined, thus allowing it to use a higher speed.
Not quite. Each atom is accelerated to a fraction under c and the "2D" part is never quite 2D, so I don't see any singularity there.
How are you going to stop the rear if you get it up to such a speed? That was the part I couldn't solve.
But we resolved that months ago  you stop each atom where it's supposed to end up, so the last atom stops before the one ahead of it stops and it all lengthens back out. That isn't the tough part. The tough part is visualising the limit on how the faster movement of the tail allows faster movement further forward and whether it leads to the front end being able to move faster than it does with your method. A simulation could resolve that, but it could also provide misinformation if there's an unrecognised bug in it. A top mathematician might notice a way to work through this on the back of an envelope at breakfast, but I haven't spent my life collecting the right algorithms to do that.
I encourage investigation of such a solution. The wave thing worked best at around 3150 km/sec, hardly a speed worthy of massive contraction, but it sure got the job done a lot faster than 55 days. But it only worked with that singularity, not if you approached it.
Well, I'd recommend parking that for now and returning to it later with the right tools so that it can all be resolved at a fraction of the time cost.

Halc;
I think you overlooked simultaneity. (If the graphic is correct)
As F, I would just time the interval from front to back.
Knowing the speed, length=vt.

As for your fantasy physics idea:
NASA has explained the need for an AI program that enables the space probes like those for Mars, to be autonomous. In the landing phase, the machines have to make adjustments in seconds, not minutes. Remote operations are not capable of precise control for material structures, even if they could be built.
You wouldn't know this by watching reruns of Star Truk. (not a typo!)
Another problem area, if the fragile ‘long stick’ passes near a significant mass, the gforce will not be uniform for its length, resulting in deformation.
May the Farce be with you.
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In the original frame, that hour isn't enough to contract the object by 1000th, never mind to 1000th of the initial length. The functionality of the ship is practically halted.
So what? I smash an egg with a hammer, and the egg is very much broken, even in a frame like you describe where the 'functionality is slowed' a thousand fold. Observing the destruction in such a frame doesn't change what happened to the egg, and what you're proposing doing to our object will blow it into considerably more smithereens than detonating a series of nuclear bombs along its length. If you hit even higher acceleration, it will eventually produce enough tidal stress to pull the nucleus of each atom apart. The faster you go, the more violence you're doing to it. I don't know why you're pursuing this proposal since it clearly violates the rigidity conditions.
Are you claiming that accelerated reference frames are less real?
Of course they're less real. Take a rotating frame as an example of a fake frame.
Rotating frame are quite real as well. You live in a rotating accelerating frame. The only sort of frame that doesn't exist anywhere is the kind described by SR, which is a pure inertial frame.
Imagine that you're in a space station made of a rotating ring designed to produce artificial gravity. You have a series of clocks round the ring which you want to synchronise, so you synchronise the first pair, then the next (meaning one of the first pair plus the next clock round from there), then the next, and so on all the way round to the start. Have you got a frame for the whole ring in which there's a single unified moment?
Even with inertial (SR) frames, the synchronization of clocks not in each other's presence is frame dependent: Not real.
A rotating frame is more real in this sense since it is absolute. You put out a signal from the center of rotation and all clocks will zero themselves when they get the signal. You have just objectively synced the clocks in that frame, and you didn't even have to know the angular rate to do it. Of course if the clocks are not moving in that frame, the rate at which they run is a function of the angular rate and distance from said center, so only clocks at the same radius (like the situation you describe) will stay in sync.
No  you can see it break catastrophically between the first and last clock. It breaks because the speed of light across each clock is different relative to that clock in opposite directions round the ring.
You seem to be attempting to sync clocks in a rotating frame using some sort of (Newtonian?) reference frame rules. Use rotating rules when using a rotating frame.
Rotating frames are bogus. We know from such rings that the actual speed of light relative to objects varies in different directions, and that's a crucial piece of knowledge which must be applied to everything else.
That's why you use rotating rules. Speed of light is anything but constant in a rotating frame, so you can't try to use some method that assumes a constant speed of light like you sort of describe above. Its properties being different doesn't make the frame bogus.
In an accelerated frame where an object is actually accelerating through space, we know that the speed of light relative to different parts is not the same, so the frame provides a distorted representation of reality.
Not distorted. Just not inertial.
You are free to label accelerating frames to be contrived if you like and only consider things from the perspective of inertial frames. What appears to various observers and happens to various objects is exactly the same, but the mathematics is far more complicated. You're not seeing problems that are obvious in accelerating frames. The work for such frames has been done. Might as well take advantage of it.
With inertial frames too, we know that one of them must be a true representation of reality (because it provides the correct speeds for light relative to an object in every direction)
You are also free to consider things in only that frame, which is going to be difficult since I did not specify what the absolute velocity of the object is before we start to move it that lighthour. Yet another needless complication.
Are you claiming that these 'more real' frames change the answer to the question posed by this topic? I have no idea why you're going on about any of these things.
In 4D models, light must actually travel at zero speed because it has no option other than to reduce all the paths it follows to zero length.
Light travels at c in the spacetime model, which is a 4D model. Paths are not zero length. Perhaps you're thinking of a different model, but '4D' doesn't ring any other bells.
At this point the post actually seems to get back on topic:
The back end is stopped in the ship's frame, as is all the rest of it. It is perhaps moving at 452 after the first moment in the initial frame, but that isn't the object's frame. No, you cannot simultaneously cease acceleration of all of the object's parts in that frame. It would indeed break.
If the object is stationary in the initial frame, you can't instantly have it with the back end moving at 452km/s without the contraction being wrong when the trip begins.
I had it accelerate in a small amount of time, not instantly. The contraction is exactly correct the whole way. That contraction is how I compute the required acceleration of all the other parts, so if there is any stress, it is because I computed the needed acceleration wrong, not because I cannot accelerate the rear of the object as hard I as I like.
The error may be small and trivial at this speed, but when you apply the method to shorter ships, the scale of the error will grow and cause damage.
Kindly illustrate with an example, because the motion of a shorter object (say one meter) is exactly the same as the motion of the trailing meter of the object. So there you have your shorter object where the scale of the error becomes obvious. Show me where it breaks.
I was looking for such a solution. It seems that it doesn't exist. I invite you to make a description of how that would work, or in particular, how you would get the speed of any part of the object over 452 km/sec without overshooting your destination.
As soon as any part gets to the place where you want it to stop, you stop it there and it will sit there comfortably, so the speed it moves at to get there can be as high as you like.
That would entail decelerating the front of the object while the rear is still accelerating. It will break under compression.
You have a solution which you consider viable, and I say you can get the tail end to its destination faster by using the caterpillar method.
Only by using a singularity. The method doesn't work with finite acceleration. Solutions that approach a singularity are acceptable, but ones that require a singularity are using it to hide things.
I know it could be done with a relatively simple simulation, but I've got thousands of other simple simulations that I'd like to run too, and each one takes a long time to build  even if it's only a few hours work (which is never guaranteed  a simple bug can take a week to find sometimes) , it all adds up to lost years, and life's too short for that. I need better tools to automate all the tedious fiddling involved in these builds, so writing those tools up front is the fast route forward.
My caluculation didn't involve any simulation, and was really trivial. I accelerated the rest of the universe (at least the parts in that 100 LY) to 452, which contracted the universe just enough to get the front of the stationary object even with the finish line. Then I decelerated the universe to expand it back to normal again. Doing it that way takes zero time, but entails a 55.3 year difference in relativity of simultaneity of the events before and after either of those accelerations. Why write a simulation when the problem is that trivial?
The caterpillar method used a singularity to make contraction computation undefined, thus allowing it to use a higher speed.
Not quite. Each atom is accelerated to a fraction under c and the "2D" part is never quite 2D, so I don't see any singularity there.
The slow caterpillar method used a slow speed of about 3150 km/sec. Your fast method indeed has no singularity, just a huge bomb of tidal force tearing it to pieces instantly. Playing that destruction in slow motion over an hour doesn't change the fact that it happens.
How are you going to stop the rear if you get it up to such a speed? That was the part I couldn't solve.
But we resolved that months ago  you stop each atom where it's supposed to end up, so the last atom stops before the one ahead of it stops and it all lengthens back out.
That only works using the singularity to hide the contraction as an undefined value.
That isn't the tough part. The tough part is visualising the limit on how the faster movement of the tail allows faster movement further forward and whether it leads to the front end being able to move faster than it does with your method.
I have less trouble visualizing it. You just have to find a frame that makes what is going on obvious.
It also takes more than 55 days using this method since it takes longer than that for the tail end of the acceleration wave to get to the front. Sure, we stop the rear using the singularity that explodes the object, but if the wave moves that slow, what's the point?
Well, I'd recommend parking that for now and returning to it later with the right tools so that it can all be resolved at a fraction of the time cost.
I will perhaps move on to even longer objects then. You're the only one contributing in a useful way to this topic.

Halc;
I think you overlooked simultaneity. (If the graphic is correct)
You identified few of the items in the graph, so I'm not sure I know what you intend to convey with it.
F seems to be the points simultaneous in some frame, but that frame isn't identified.
S is perhaps the object, but it depicts inertial motion, and my object is never inertial.
What I presume to be events E1, E2, and E3 are also not identified, nor the Sx line.
The blue lines look like light signals sent from E2 and E3 for some reason, but my topic doesn't involve signals being sent anywhere.
I suspect you have not familiarized yourself with the topic. Read the OP.
As for your fantasy physics idea:
NASA has explained the need for an AI program that enables the space probes like those for Mars, to be autonomous. In the landing phase, the machines have to make adjustments in seconds, not minutes. Remote operations are not capable of precise control for material structures, even if they could be built.
I never suggested sending live remote commands to any distant places. The sequence of accelerations would have to be preprogrammed in advance, at least 50 years in advance given the separation of the various events involved.
Another problem area, if the fragile ‘long stick’ passes near a significant mass, the gforce will not be uniform for its length, resulting in deformation.
I did not posit any masses nearby in this hypothetical scenario. It just wasn't the point of the topic. We're assuming flat space just like in SR.

In the original frame, that hour isn't enough to contract the object by 1000th, never mind to 1000th of the initial length. The functionality of the ship is practically halted.
So what? I smash an egg with a hammer, and the egg is very much broken, even in a frame like you describe where the 'functionality is slowed' a thousand fold.
Why are you smashing it with a hammer? All we're doing is accelerating every atom of it up to a fraction under c simultaneously.
If you hit even higher acceleration, it will eventually produce enough tidal stress to pull the nucleus of each atom apart. The faster you go, the more violence you're doing to it. I don't know why you're pursuing this proposal since it clearly violates the rigidity conditions.
Why object to that now rather than in the caterpillar method which has an equally severe acceleration being applied to the atoms at the back end?
Rotating frame are quite real as well. You live in a rotating accelerating frame. The only sort of frame that doesn't exist anywhere is the kind described by SR, which is a pure inertial frame.
Rotating frames are contrived and broken, as shown when you try to synchronise clocks round the whole ring (or equator)  you can only synchronise them for the equivalent nonrotating frame. Pure inertial frames exist in LET.
Even with inertial (SR) frames, the synchronization of clocks not in each other's presence is frame dependent: Not real.
You can synchronise them all for a specific frame. You can't do that with a rotating frame.
You seem to be attempting to sync clocks in a rotating frame using some sort of (Newtonian?) reference frame rules. Use rotating rules when using a rotating frame.
If they weren't fake frames, you'd be able to stand between two clocks and synchronise them, then stand between the next pair and synchronise them too, and so on all the way round, ending up with the last and first being found to be in sync when you stand between them, but they aren't.
That's why you use rotating rules. Speed of light is anything but constant in a rotating frame, so you can't try to use some method that assumes a constant speed of light like you sort of describe above. Its properties being different doesn't make the frame bogus.
If you're agreeing that the speed of light isn't constant relative to the frame in different parts of the frame, then it's a fake frame. A true frame has the same speed of light relative to any objects in it which are stationary in that frame (after you've corrected for it being slowed by gravity). Accelerated and rotating frames are both contrived abstractions.
Are you claiming that these 'more real' frames change the answer to the question posed by this topic? I have no idea why you're going on about any of these things.
It came up because you said the whole ship was stationary within its frame at all times with your method, but in reality the back and front ends are moving through space at different speeds and have different contractions acting on them. That was why I had such difficulty visualising how your method worked before, because I hadn't taken in that you were playing such tricks with accelerated frames. Since you made that clear though, I understand what you're doing, and if you're happy to use such a frame and to limit how you move the ship on the basis of applying the rules of that frame, that's fine.
Light travels at c in the spacetime model, which is a 4D model. Paths are not zero length. Perhaps you're thinking of a different model, but '4D' doesn't ring any other bells.
If you move a ship at 0.866c between points A and B, you shorten the distance between A and B to half. Move the ship at 0.968c and you shorten the distance to a quarter. These shorter lengths are the physical path lengths through the 4D structure. Higher and higher speeds reduce the distance ever more, tending towards zero. Light is not going to take a longer path from A to B than the fastest moving particle, so it must reduce the distance to zero. In 4D models, the speed of light is zero while it is merely the apparent speed of light that is c. If you want the actual speed of light to be greater than zero, you need to switch to a 3D model (and avoid mixing two incompatible types of model).
At this point the post actually seems to get back on topic:
It was all on topic, every part of it being generated from what came before.
Kindly illustrate with an example, because the motion of a shorter object (say one meter) is exactly the same as the motion of the trailing meter of the object. So there you have your shorter object where the scale of the error becomes obvious. Show me where it breaks.
Tell me how fast you have the back end of a metrelong ship move at the start. I assume it will be close to c, while the front end will be stationary. If so, how do you get the back end up to such a high speed and get it to contract to the appropriate length for that speed in an instant?
As soon as any part gets to the place where you want it to stop, you stop it there and it will sit there comfortably, so the speed it moves at to get there can be as high as you like.
That would entail decelerating the front of the object while the rear is still accelerating. It will break under compression.[/quote]
Why would you need to decelerate the front of the ship? The movement of the back end is independent of it, free to move at a fraction under c to travel a lighthour and then stop in exactly the place you want it to stop. The entire back end of the ship can complete its journey before the front end has even started moving. Indeed, 98% of the ship can have completed its journey before the front end has started moving. But because we want to move the front end as soon as we can, we will start moving it sooner than that.
The method doesn't work with finite acceleration. Solutions that approach a singularity are acceptable, but ones that require a singularity are using it to hide things.
At no point does it involve a singularity  there is never complete compression of anything to 2D, none of the speeds reach c, and the accelerations can all be spread out over finite lengths of time which are nearly but not quite zero.
My caluculation didn't involve any simulation, and was really trivial. I accelerated the rest of the universe (at least the parts in that 100 LY) to 452, which contracted the universe just enough to get the front of the stationary object even with the finish line. Then I decelerated the universe to expand it back to normal again. Doing it that way takes zero time, but entails a 55.3 year difference in relativity of simultaneity of the events before and after either of those accelerations. Why write a simulation when the problem is that trivial?
Because the maths gets more complicated when you start trying to move the ship faster by taking advantage of the caterpillar method to move the back faster and potentially allow the front to move faster too. We're back to the business of combining an infinite number of waves, and that makes the maths hard to do (unless you know a way to make it simple, but I don't).
The slow caterpillar method used a slow speed of about 3150 km/sec. Your fast method indeed has no singularity, just a huge bomb of tidal force tearing it to pieces instantly. Playing that destruction in slow motion over an hour doesn't change the fact that it happens.
There is no such destruction  every atom is accelerated to a fraction under c with this timed for each atom such that when they're moving at full speed they're the right distance apart to sit comfortably. (It's only since this thread was revived that you don't need them to sit the right distance apart as the functionality of the material is practically halted, so no damage will occur if you just move all the atoms simultaneously, but in the original idea, I had them all compress up together into something nearly 2D, and I never used a slow caterpillar method.)
How are you going to stop the rear if you get it up to such a speed? That was the part I couldn't solve.
But we resolved that months ago  you stop each atom where it's supposed to end up, so the last atom stops before the one ahead of it stops and it all lengthens back out.
That only works using the singularity to hide the contraction as an undefined value.
There's no undefined value. The contracted part might be a meter thick, or a micron, but it's never zero, but I realise now that there would be a major problem trying to decelerate an atom from the rear of the compressed zone without affecting the ones ahead of it too, so that isn't practical, but then we've never been looking for what's practical  we were looking for a fundamental limit ignoring such practical limitations.
That isn't the tough part. The tough part is visualising the limit on how the faster movement of the tail allows faster movement further forward and whether it leads to the front end being able to move faster than it does with your method.
I have less trouble visualizing it. You just have to find a frame that makes what is going on obvious.
You haven't managed to visualise it and you don't have any frame that makes it obvious. This moves beyond your idea into one that might allow the front end to move faster than in your solution by allowing the back end to move faster than in your solution.
It also takes more than 55 days using this method since it takes longer than that for the tail end of the acceleration wave to get to the front. Sure, we stop the rear using the singularity that explodes the object, but if the wave moves that slow, what's the point?
We have a series of waves of acceleration propagating at different speeds which allow the front end to move right from the gun, although it will initially move next to zero distance. Any speed that you imagine the ship can have under your method, I can have with mine, but I can improve on the speed at the back, and by doing so, I think the speed of the front can be improved too.

Why are you smashing it with a hammer? All we're doing is accelerating every atom of it up to a fraction under c simultaneously.
I was being gentle to it. You are applying vastly more violence to the object, which is more fragile than the egg. The egg will be some shell and goo, but almost all of the atoms will likely still be intact. Not so with what you're doing. We both promise to put all the pieces back together again, but the egg looks like an easier job.
Why object to that now rather than in the caterpillar method which has an equally severe acceleration being applied to the atoms at the back end?
There were no tidal stresses in the standard (55 day) method that has very high acceleration of each end of the object.
The caterpillar method on the other hand has a singularity used to hide the stresses (in the middle more than at the ends). I rejected that method once that became clear.
Even with inertial (SR) frames, the synchronization of clocks not in each other's presence is frame dependent: Not real.
You can synchronise them all for a specific frame.
As I said, frame dependent.
You can't do that with a rotating frame.
I said how to do it in my prior post. You were going about it wrong is all.
If they weren't fake frames, you'd be able to stand between two clocks and synchronise them, then stand between the next pair and synchronise them too
That technique relies on properties of inertial frames.
If you're agreeing that the speed of light isn't constant relative to the frame in different parts of the frame, then it's a fake frame.
OK. Glad to know your terminology. You can describe events in your frame of choice of course, but I tend to look for one that best simplifies the description of what is going on.
Are you claiming that these 'more real' frames change the answer to the question posed by this topic? I have no idea why you're going on about any of these things.
It came up because you said the whole ship was stationary within its frame at all times with your method
I did. You can translate that, if you will to an inertial statement:
At any event at point in the object, in the inertial frame of the object at that event, the other parts of the object are also stationary. There it is in inertial terms.
This is assuming that there is no infinite acceleration. It is very high at either end, but if it were infinite, the object would have multiple speeds at that event, and hence no defined speed and thus no defined frame. So perhaps my object is short of its own event horizon by one meter, which keeps the numbers finite, and adds a millisecond or two to our trip. I think 3 digits of precision is plenty.
The caterpillar method has a singularity for speed along its entire length at once in an inertial frame, and hence hides the contraction calculation as an undefined value. Calculus shows that the value does not approach zero as the time of acceleration approaches zero.
but in reality the back and front ends are moving through space at different speeds and have different contractions acting on them.
Only in different inertial frames. In the object's inertial frame, there is no contraction at all. This doesn't seem to be a requirement. It just turned out that way. Clearly, in other frames, the object moves at different speeds along its length, but no stress has been identified. The contraction, if you integrate it along its length, is exactly in proportion to the distance between its parts. The mathematics is considerably more complex to verify this.
Light travels at c in the spacetime model, which is a 4D model. Paths are not zero length. Perhaps you're thinking of a different model, but '4D' doesn't ring any other bells.
If you move a ship at 0.866c between points A and B, you shorten the distance between A and B to half. Move the ship at 0.968c and you shorten the distance to a quarter.
First of all, you're thinking of points in space, not event in 4D spacetime. Move the ship faster and the endpoints of the path are different events. A and B are not the same two things in these two scenarios.
That said, the two points in space (worldlines in frame X) are unchanged by sending a fast (relative to X) or slow object between them. From the perspective of the object moving relative to X, different events along those two worldlines are now simultaneous, reducing the spatial separation of the heavily inclined worldlines.
These shorter lengths are the physical path lengths through the 4D structure.
No they're not. Physical path lengths in a 4D structure are called intervals, and they are frame invariant. Two events have the same interval between them regardless of the inertial frame chosen. Any path between them, if straight, will have the same physical path length. A path between them can be longer if not straight.
At this point the post actually seems to get back on topic:
It was all on topic, every part of it being generated from what came before.
I found suggestions of moving an object faster than it can contract to be off topic. Using brute force to hold atoms at unnatural separations temporarily is not the sort of solution I'm looking for.
Kindly illustrate with an example, because the motion of a shorter object (say one meter) is exactly the same as the motion of the trailing meter of the object. So there you have your shorter object where the scale of the error becomes obvious. Show me where it breaks.
Tell me how fast you have the back end of a metrelong ship move at the start. I assume it will be close to c, while the front end will be stationary.
Well, we accelerated the rear to 452 km/sec in our example, and took say a microsecond to do that. Less if it helps you illustrate your issue. I decelerated the object much more slowly (over 55 days) to compensate for the very far end needing to slow down, but you're right, if our object is only a meter long, we don't need to do that. So if the object is only a meter long, and we're moving it a lighthour, we're going to go a hecka lot faster than 452.
The maximum speed needed is enough to contract the length of something by a factor of 1.079e12, which is the number of meters in a lighthour. The meterstick is going to get there in an hour, ± something in the 12th digit or more. That hardly tells us anything.
One thing to note is that it doesn't take an hour to get the front up to near light speed. The front end of the object, just like the 100 light year one, is going to approach proper acceleration at c²/length which is 9e16 m/sec² as the tail proper acceleration approaches an arbitrarily high value. So while proper acceleration is constant over that hour, the actual acceleration is nearly a step function. The same applies to my superlong object, but the difference between actual and proper acceleration was negligible at 452 km/sec.
If so, how do you get the back end up to such a high speed and get it to contract to the appropriate length for that speed in an instant?
Don't understand this question. The contraction happens over the course of acceleration, not in an instant. We're doing it nearly as fast as we can, but it still takes time for light to travel that one meter, so that's a minimum time for the rear to mostly catch up with the front, and after a halfhour, the front an rear match speeds and it starts to expand again back to its original 1meter length.
The method doesn't work with finite acceleration. Solutions that approach a singularity are acceptable, but ones that require a singularity are using it to hide things.
At no point does it involve a singularity  there is never complete compression of anything to 2D, none of the speeds reach c
The speed of the object is undefined at two points, and hence the proper length of the object at that moment (in the inertial frame of half the max speed of the object). That's the singularity. I didn't say anything was moving at c.
Because the maths gets more complicated when you start trying to move the ship faster by taking advantage of the caterpillar method to move the back faster and potentially allow the front to move faster too.
I simplified that case by using the halfway inertial frame. Both are pretty trivial cases. You'll notice the code I produced to compute the optimal wave in post 88 did no actual simulation. For any given speed bump, the time to move the long object is the sum of two simple values: the days needed for the wave to go 100 LY (tDwav), and the days needed to go a light hour at the selected speed (tDmov).
We're back to the business of combining an infinite number of waves, and that makes the maths hard to do (unless you know a way to make it simple, but I don't).
If only the mathematics of those contrived accelerated reference frames worked. Sorry, you're on your own if you want to do it the hard way.
There is no such destruction  every atom is accelerated to a fraction under c with this timed for each atom such that when they're moving at full speed they're the right distance apart to sit comfortably.
Oh, I thought you were doing it to all of them at once.
Doing it in a wave still has that undefined speed singularity, and not sure why you'd want to do it so fast since it takes nearly 100 years for that wave to make it it the other end of the object.
There's no undefined value. The contracted part might be a meter thick, or a micron, but it's never zero,
In the halfway inertial frame, it is the entire object that has a completely undefined speed, all at once. That's a singularity. The thing has no defined proper length. If you do it as a finite small wave that moves, there is no singularity, and the contracted length of certain parts of the object are always different than actual separation of them, so it breaks. Again, considering it from that middle frame makes this clear.
but then we've never been looking for what's practical  we were looking for a fundamental limit ignoring such practical limitations.
Indeed. Not caring about practical. Einstein never worried about how the wheels on his train going at .6c held together. That seems to be one of the largest practical limits to making the fastest car: It takes lot of engineering to make a wheel that can turn fast enough to go supersonic speeds. If it doesn't have wheels, it isn't really a car.
You haven't managed to visualise it and you don't have any frame that makes it obvious.
I've shown you the frames (all inertial) that I used. I used no calculus so far.
This moves beyond your idea into one that might allow the front end to move faster than in your solution by allowing the back end to move faster than in your solution.
The front has a limit (c²/length) on acceleration. Faster tail speeds don't help if the front needs too much time to get to those speeds. Likewise, the tail has that same limit on deceleration, so I begin doing that right away after I get it up to top speed.
We have a series of waves of acceleration propagating at different speeds
If they involve infinite acceleration, then you have that singularity. If they don't, the wave propagates immediately to the front. So not sure what you mean by 'different speeds'.
which allow the front end to move right from the gun, although it will initially move next to zero distance.
Yes and yes. If I jump out of a building, I initially move next to zero distance, but can decelerate abruptly when I hit the street. The ride at the front is just like that, except less G and drawn out over 55 days.
Any speed that you imagine the ship can have under your method, I can have with mine, but I can improve on the speed at the back, and by doing so, I think the speed of the front can be improved too.
That would be great if it worked.

Halc;
Thought you understood spacetime graphics.
Maybe I didn't understand all the details as you defined them.
I agree with Pmb.
Can't imagine the ISS built without engineers!
"All things imaginable are not realizable.'

Thought you understood spacetime graphics.
I do, or at least the ones that bother to label the items in the graph.
The picture you posted does not in any way depict what I am describing.

You can translate that, if you will to an inertial statement:
At any event at point in the object, in the inertial frame of the object at that event, the other parts of the object are also stationary. There it is in inertial terms.
At any point in the object, the inertial frame in which that point is stationary has other parts of the ship moving through it rather than stationary (except for half way through the journey when the whole thing might be moving at the same speed).
The caterpillar method has a singularity for speed along its entire length at once in an inertial frame, and hence hides the contraction calculation as an undefined value.
There is nothing hidden or undefined about it. The compression is to a specific separation between atoms at which they sit comfortably, all dictated by the speed of movement through space.
but in reality the back and front ends are moving through space at different speeds and have different contractions acting on them.
Only in different inertial frames.[/quote]
In a single inertial frame they are moving at different speeds.
First of all, you're thinking of points in space, not event in 4D spacetime. Move the ship faster and the endpoints of the path are different events. A and B are not the same two things in these two scenarios.
I'm talking about 4D Spacetime locations, but to spell things out more precisely than I did last time, we've got three of them. We have two of them at great distance apart, but if we move something at great speed from each of them towards the other, they meet at a third Spacetime location. The faster they travel, the shorter the paths they follow to that meeting point. If they move at a fraction less than c, the distance each one travels is a fraction over zero and the time taken to cover that distance is a fraction over zero too. For light, the distance is zero and the time is zero, and that means there are two paths of zero length connecting our original two Spacetime locations via the third location. They are all therefore zero distance apart. This shows that all[i] Spacetime locations are zero distance apart.
These shorter lengths are the physical path lengths through the 4D structure.
No they're not.
Yes they are. If X and Z are the starting points for the light and Y is the meeting point, we know that the path from X to Y has zero length and that the path from Z to Y has zero length, so there is a physical path of zero length between X and Z. This is a consequence of having 4D geometry which people may want to hush up, but it is the mathematical reality of it.
I found suggestions of moving an object faster than it can contract to be off topic. Using brute force to hold atoms at unnatural separations temporarily is not the sort of solution I'm looking for.
They are not being held by brute force or by any other kind of force  their functionality is practically halted by their extreme speed of movement through space, so the solution is fully valid.
That hardly tells us anything.
Well, you didn't provide a speed, but the back end of your metrelong ship will have to be doing whatever speed you haven't provided practically instantly (starting from zero speed and with no contraction applied to it), and high contraction will then be needed on it, so either you're going to have that contraction exist on it by magic in an instant or you're going to have to use my method of accelerating it from the back end to contract it down in a fraction longer than zero time in order to get the atoms to comfortable separations for that speed.
If so, how do you get the back end up to such a high speed and get it to contract to the appropriate length for that speed in an instant?
Don't understand this question.
Why not? You have a ship that's stationary in one frame and you have starting points and destinations which are also stationary in that frame. You want to move the ship from the start to the end. You suddenly have the tail end moving at high speed in this frame and decelerating back down to zero speed while the front end slowly accelerates from zero to high speed, and when it reaches the destination point, the front end's moving at high speed and the tail end has stopped. That's what comes out of the numbers that you provided (the speed of the tail going down from 452 to 0 and the front end going up from 0 to 452).
The contraction happens over the course of acceleration, not in an instant.
The contraction on the tail is wrong at the start because the tail is moving at 0, but an instant later it's moving at 452 and it gradually decelerates from there.
The speed of the object is undefined at two points, and hence the proper length of the object at that moment (in the inertial frame of half the max speed of the object). That's the singularity. I didn't say anything was moving at c.
There are no points at which the speed of anything is undefined. Each atom has a specific speed and specific accelerations are applied to it at specific times. The ship also has a specific length at all times which can be measured as the distance from the rearmost atom to the leading atom. There is nothing in any of that that breaks the laws of physics, so I don't understand your problem.
I simplified that case by using the halfway inertial frame.
I don't think you have simplified it. You have the back end moving more slowly than it could and you have it decelerating much more gently than necessary, while the result of this is that you're constraining the possibilities for moving the front end. You haven't begun to cover the complex kind of system I'm visualising for moving the ship  it would require a combination of an infinite number of waves of accelerations.
If only the mathematics of those contrived accelerated reference frames worked. Sorry, you're on your own if you want to do it the hard way.
I'm not asking you to do it. I intend to do it with the help of a simulation to find out what it tends towards as I add more waves. I'm sure there are tricks in maths to get to an answer more directly, but I don't have the right tools for that in my head.
Oh, I thought you were doing it to all of them at once.
In the newest method, I do accelerate them all at once (to a fraction under c, relying on their functionality being practically halted to keep them in place), but in the old method I insist on the atoms being at comfortable separations during the trip at any times when they're not being accelerated, and that means contracting and uncontracting the ship from the rear.
Doing it in a wave still has that undefined speed singularity, and not sure why you'd want to do it so fast since it takes nearly 100 years for that wave to make it it the other end of the object.
We established right at the start that if you use a single wave for the caterpillar and contract the back with it to nearly 2D, the wave propagates forwards at a little under c. If we add in another wave at the opposite extreme, we can have the front end move an instant after the tail starts to move, but the front end can hardly move forwards at all, so this fastestpropagating wave is one which provides almost no acceleration. We can add in a third wave which propagates more slowly, but when it reaches the front end it will allow the front to accelerate significantly. Another wave that propagates more quickly than the third will reach the front more quickly but accelerate it less, while another wave that propagates more slowly than the third will reach the front later but accelerate it more. We want an infinite number of waves like these acting together, and the later each one reaches the front end, the more it accelerates it. The only thing that's undefined about the speed is that I haven't worked out any of the values for the propagation times and the amount of acceleration they provide for the front end. All of these accelerations have to be combined, which sounds easy, but each must be applied to the front end at a different time with the front end at a different location, and that's hard to handle.
In the halfway inertial frame, it is the entire object that has a completely undefined speed, all at once. That's a singularity. The thing has no defined proper length. If you do it as a finite small wave that moves, there is no singularity, and the contracted length of certain parts of the object are always different than actual separation of them, so it breaks. Again, considering it from that middle frame makes this clear.
I don't understand your objection. Nothing I'm doing breaks the laws of physics  each atom has a viable speed and there are no infinite accelerations. There is a possible problem that I can see building up as more waves are added, but if it is a problem, it will apply as soon as any movement of the front end is made without waiting for the contracted part to reach it after a hundred years, so if that turns out to be an illegal move, so is your method.

From post 88:
It seems the caterpillar method can get the ship up to 3135 km/sec and do the trip in under 6 days, doing the movement in under 4 days and the wave taking just under 2 days to move up the 100 lightyear ship. That's like 11% of the 55 days I got via the other method.
Did I get all the math right?
I am beginning to wonder if the mathematics is wrong. The front has a max acceleration else the rear of the object will fall behind, and yet if we ignore the singularity involved, we manage to get the front to move faster than its limit.
So as an experiment, I propose a race between the two objects, one moving as described in post 37 and taking 55 days to get the front to the finish line, and the other the caterpillar method that has the front not moving at all, but it crosses the finish line in 6 days. Let's hold a race between these two methods, except the first one never turns off the acceleration, but just goes at it indefinitely. The second one never does the retrocaterpillar move, so it gets up to 3135 km/sec and never goes faster. Obviously the first object will win in the long run, but the second should get ahead at first, but also cannot, which is a contradiction. I need to understand that contradiction.
For the most part I am going to use the original frame as my coordinate system, except where explicitly noted.
Object 1 has a tail at just beyond point 0 (0 represents the Rindler horizon) and the head at point 100 LY. All parts have proper acceleration of c²/D (per post 93) where D is the original distance from point 0. So the tail accelerates at arbitrarily high G force and the head at 0.09513 m/sec² .
Object 2 has a completely different strategy, and only accelerates the rear at first to 3135 km/second, with the parts ahead of it accelerating in a singularity wave that moves fast enough to reach the other end of the 100 LY object in 2 days. After those 2 days go by, the object coasts permanently at 3135 km/sec. There is no Rindler horizon for this object since it does not experience continuous acceleration.
Day 2:
Object 1: Tail is 2 light days from 0. Head is about 1.4 billion meters from its starting point and currently moving at 16.4 km/sec. A light hour is about 1.08 trillion meters, so we have a ways to go.
Object 2: Tail has been moving at 3135 km/sec for 172800 seconds, so it has moved about 540 billion meters. The head of the object has just barely started moving, but the whole thing is now moving in inertial motion. At that speed, contraction of a 100 LY object would be 2 light days, so things are as they should be. The object is losing the race since the head of object 1 has been moving from the start, but the whole thing is moving at 270 billion meters a day.
Day 4:
Object 2's tail has traveled the requisite light hour, but we're going to just let it keep going. The head is 540 billion meters out from its start, halfway there.
Object 1's head is now moving at 32800 m/sec and has moved 5.67 billion meters. The second object passed it long ago. It is at maximum acceleration, so how did the other object pass it?
The singularity let us do that of course, but how do we visualize the offense in more concrete terms? It seems that the infinite acceleration we're giving it puts all of the object that is behind the point of acceleration beyond the event horizon (Rindler horizon) and thus not in the universe. I plan to kill a bus load of people, so my solution is to toss them in a black hole, thus ending their existence in the universe. I do the offensive thing that would kill them, then switch the black hole off and find the busload still intact, but different. Can't hurt them if they don't exist.
Where is the object in the frame of the head of the object, day 4?
With object 1, the object is always stationary in its own frame. It is moving at 32800 m/sec and the initial tail event (point 0,0) is simultaneous with the head. All is good.
With object 2, the thing is moving at 3135000 m/sec in the initial frame and it has been in inertial motion for 2 days. At that speed, the head event is simultaneous with the tail at a time over a year before the tail got moving. That means that object 2 might well all be moving inertially (all at the same speed, not accelerating) in the original frame, but it certainly isn't in its own inertial frame. It will not become stationary in its entirety for over a year. I don't see a problem with that, so I can't point to it as a second way to illustrate the inconsistency.

You can translate that, if you will to an inertial statement:
At any event at point in the object, in the inertial frame of the object at that event, the other parts of the object are also stationary. There it is in inertial terms.
At any point in the object, the inertial frame in which that point is stationary has other parts of the ship moving through it rather than stationary (except for half way through the journey when the whole thing might be moving at the same speed).
That makes no sense. The entire object is stationary in its own inertial frame. If it is moving, you've chosen the wrong frame.
The caterpillar method has a singularity for speed along its entire length at once in an inertial frame, and hence hides the contraction calculation as an undefined value.
There is nothing hidden or undefined about it. The compression is to a specific separation between atoms at which they sit comfortably, all dictated by the speed of movement through space.
Relativistic contraction is a function of speed, and that speed is undefined at the singularity, hence the contraction (the length that it should be if not under strain) is undefined.
In a single inertial frame they are moving at different speeds.
That's true of all frames except one. Even in the caterpillar method, there exists one frame where they all move at the same speed, except at the moments of the singularity, where it has no speed at all.
I'm talking about 4D Spacetime locations, but to spell things out more precisely than I did last time, we've got three of them. We have two of them at great distance apart, but if we move something at great speed from each of them towards the other, they meet at a third Spacetime location.
???? Can you draw a picture of this? How can 4D spacetime locations move? Points in spacetime don't have a property of speed. They're fixed points, not worldlines.
I know you're a presentist, but it seem you don't have any understanding at all of the contrasting view. How can you assert your view is the correct one if you don't understand spacetime?
They are not being held by brute force or by any other kind of force  their functionality is practically halted by their extreme speed of movement through space, so the solution is fully valid.
Speed is not absolute, and their functionality is not changed at all in their own frame. By increasing your acceleration, you are increasing the violence done to the object at a rate greater than you are decreasing the duration of that violence. Playing the action in slow motion by describing events in a very different frame does not make that violence any less violent.
Well, you didn't provide a speed
I did. It is accelerating arbitrarily hard, so it is going as fast as it can to get that meterrod to move the lighthour. That is closer to c than can be expressed by 12 digits of precision, and since I'm working with say 34 digits of precision, the back effectively accelerates to c.
but the back end of your metrelong ship will have to be doing whatever speed you haven't provided practically instantly (starting from zero speed and with no contraction applied to it), and high contraction will then be needed on it, so either you're going to have that contraction exist on it by magic in an instant or you're going to have to use my method of accelerating it from the back end to contract it down in a fraction longer than zero time in order to get the atoms to comfortable separations for that speed.
No idea what you are talking about. I'm using the same method as the 55.3 day method for the longer object. Both accelerate the rear at arbitrarily high levels, but the long object quits accelerating once 452 km/sec occurs, and the short object quits at a higher speed that is very very close to c. Yes, the rod gets very contracted (by a factor of about 1.079e12) at top speed and travels close to that compression most of the distance, but there is no caterpillar method being used. I'm accelerating all parts of the object so the strain on the object (and hence the stress) is zero. The front accelerates at about 9e17 g, which is considerably less than the acceleration of the rear. I specified the acceleration of every point along the length of the object, which is the same as the acceleration along the length of my longer object. The only difference is the speed where I reverse the process and begin slowing it down.
If so, how do you get the back end up to such a high speed and get it to contract to the appropriate length for that speed in an instant?
Don't understand this question.
Why not? You have a ship that's stationary in one frame and you have starting points and destinations which are also stationary in that frame. You want to move the ship from the start to the end. You suddenly have the tail end moving at high speed in this frame and decelerating back down to zero speed while the front end slowly accelerates from zero to high speed, and when it reaches the destination point, the front end's moving at high speed and the tail end has stopped. That's what comes out of the numbers that you provided (the speed of the tail going down from 452 to 0 and the front end going up from 0 to 452).
Yes, that's a description of the flight plan, so to speak. You ask how I get the back end up to such high speed so quickly. Answer: Same way I slow down the front at the end of the trip: with arbitrarily high acceleration. The point one meter from the rear is accelerating at nearly 9e17 g, so the very tail must be accelerating far harder than that. Let's just say 1e1000 g, just to pick a number, since I think 3 digits of precision is enough. So it doesn't happen in an instant. It takes time to get up to speed at that acceleration. It just doesn't take very much time.
The contraction happens over the course of acceleration, not in an instant.
The contraction on the tail is wrong at the start because the tail is moving at 0, but an instant later it's moving at 452 and it gradually decelerates from there.
The tail is a point and has no length to contract. So I'm unclear what you are trying to convey with this statement. And as I said, it takes a short but finite time to get up to 452 km/sec at 1e1000 g. It isn't instantly.
There are no points at which the speed of anything is undefined.
That was referring to the caterpillar method. Of course the speed is undefined at the point where the wave is, especially in the one frame where there is no wave. If it is defined, what is it? The speed (in the original frame) is zero before the singularity, and 3135 km/sec after it, but what about during the singularity? The question essentially asks for the slope of a triangle wave function at one of the inversion points. Curves have varying slopes along their lengths. Angles don't, at least not at the point of the angle. The slope there is undefined.
Each atom has a specific speed and specific accelerations are applied to it at specific times. The ship also has a specific length at all times which can be measured as the distance from the rearmost atom to the leading atom.
In the halfway frame (of 226 km/sec), the object does not have a proper length, which should be measurable as the sum of proper distances between all the atoms. Everything in physics has a proper length, and nothing in physics accelerates at an infinite rate except at certain singularities which destroy any object present at it, even despite the slow motion seen by a distant observer. Even then, the object only seems to approach arbitrarily close to that singularity, and not actually achieve infinite acceleration.
I simplified that case by using the halfway inertial frame.
I don't think you have simplified it. You have the back end moving more slowly than it could and you have it decelerating much more gently than necessary
The halfway frame was for the caterpillar method. You seem to be going on about the finiteacceleration method, which is simplified by considering the inertial frame of the object at the midpoint of the trip.
I do not have the back moving more slowly than it could be. Suggest a better speed if you have one, but do so without singularities. It also does not decelerate slower than it needs to, since it is doing so at the same rate as all points on the object, which is c²/D.
You haven't begun to cover the complex kind of system I'm visualising for moving the ship  it would require a combination of an infinite number of waves of accelerations.
An infinite number of waves would approach a curve as the stairstep singularities become smaller and smaller. It would approach a valid solution of finite acceleration. The small velocity steps for each wave would make each wave travel faster and faster, approaching infinite speed as you use more and more of them. So time for the wave to travel approaches zero. Thus the front can being to move right away.
I encourage exploration of this method, but I think it will converge on the 55 day answer, not something short.
Edit: I take that back. I think it will converge on something even better than 6 days.
I'm not asking you to do it. I intend to do it with the help of a simulation to find out what it tends towards as I add more waves. I'm sure there are tricks in maths to get to an answer more directly, but I don't have the right tools for that in my head.
If you write something, I can review it.
I did a quick one in my head (plus the numbers in post 88), using two waves instead of one. The original wave was to 3135 km/sec which took 2 days for the wave and 4 days to move one light hour at that speed. Total time is nearly 6 days.
Lets bump the rear up to 2220 km/sec, at which speed the wave moves to the other end in only 1 day. Then we immediately bump the rear again by a similar 2nd wave. The time to move the light hour is now 2.8 days instead of 4, at least for the parts of the object moving at full speed, which none of them do for the whole distance. The total time to move the object is now 4.8 days (each point is stopped for one day, half speed for 2 days, and full speed for 1.8 days). Damn... The method seems to be an improvement if I did that right. Breaking the accelerations into two steps shorted the 6 day trip by 20%. If we do it in infinite steps, the singularity approaches a defined value for velocity at all times, so the method is valid.
In my prior post I attempted some sort of argument about how my 55 days solution cannot be improved upon, and I was dissatisfied that I had done that. This simple 2step thing shows a trend towards a faster trip than 6 days, not a trend towards the 55 day mark. I have hope for it.
In the newest method, I do accelerate them all at once (to a fraction under c, relying on their functionality being practically halted to keep them in place)
Answers that change the proper length of the object, however briefly, do not qualify as valid solutions.
The proper length can be integrated, so there is no requirement that the entire object be moving at the same speed at once. There is no such restriction in nature. Any accelerating object moves at different speeds along its length, and that alone doesn't cause stress. It is mathematically necessary in fact.
but in the old method I insist on the atoms being at comfortable separations during the trip at any times when they're not being accelerated
They need to be at comfortable separations at all times, even during acceleration.
We established right at the start that if you use a single wave for the caterpillar and contract the back with it to nearly 2D, the wave propagates forwards at a little under c. If we add in another wave at the opposite extreme, we can have the front end move an instant after the tail starts to move, but the front end can hardly move forwards at all, so this fastestpropagating wave is one which provides almost no acceleration. We can add in a third wave which propagates more slowly, but when it reaches the front end it will allow the front to accelerate significantly. Another wave that propagates more quickly than the third will reach the front more quickly but accelerate it less, while another wave that propagates more slowly than the third will reach the front later but accelerate it more. We want an infinite number of waves like these acting together, and the later each one reaches the front end, the more it accelerates it.
Exactly. I actually have reasonable expectations of this method, but if it works, the optimal solution will seemingly have a top speed well under light speed. I just picked an arbitrary value that gave a top speed a little more than 3135, and it resulted in an improvement. If I picked several steps that added up to a much higher speed, I suspect the total time would get much worse.
The only thing that's undefined about the speed is that I haven't worked out any of the values for the propagation times and the amount of acceleration they provide for the front end.
The propagation time is in my code posted in 88, and it is time relative to the frame before the bump in speed. The acceleration of any part of the object is undefined (a singularity) for a given bump in speed. As the velocity bumps approach zero change, acceleration at a given point becomes defined as the size of the bump divided by the frequency at which they occur. That is a real acceleration.
All of these accelerations have to be combined, which sounds easy, but each must be applied to the front end at a different time with the front end at a different location, and that's hard to handle.
I did it pretty easily with just two bumps, but if you use a lot of little ones (or even just 3), yes, it gets complicated. Computers are your friend. Play with a small number of bumps and see where the trends are, and then write something that reflects that correctly. Now do it in say 1000 steps and vary the top speed up and down until you find an optimal value. At 1000 steps, the solution will be very close to one with continuous acceleration and no singularities.
Then I have to explain why it works better than every part accelerating at the maximum amount, or I have to explain why the solution isn't valid. I think it is valid, and my 55 day solution is lousy because it unreasonably insists on the object always being stationary in its own frame.
Nothing I'm doing breaks the laws of physics  each atom has a viable speed and there are no infinite accelerations.
The wave method in post 88 (that yielded a 6 day solution) assumed infinite acceleration. If you're speaking of some other solution, then I need to know which it is. The one with a lot of little waves approaches defined speeds and finite acceleration, so that solution is valid, but we have no numbers for it so far.
There is a possible problem that I can see building up as more waves are added, but if it is a problem, it will apply as soon as any movement of the front end is made without waiting for the contracted part to reach it after a hundred years, so if that turns out to be an illegal move, so is your method.
There is no wave in my method, so nothing travels the length. The length of the object is always consistent with its contracted size in any frame, so there is zero strain, and thus zero stress. There are also no singularities. That makes the solution valid, if not optimal. I really think your method here is going to yield a far better solution, and I don't think that was my opinion until the last couple posts.

DC 118;
With inertial frames too, we know that one of them must be a true representation of reality (because it provides the correct speeds for light relative to an object in every direction) while all the rest must be false. However, because we can't tell which one is true, we have to treat all inertial frames as potentially true. We shouldn't do that with an accelerated frame though because it's guaranteed not to be true.
[All inertial frames measure light speed as constant, because light speed is independent of any source.
Accelerated motion between two objects interferes with synchronization, which is corrected by periodic updates as in the GPS system.]
In the same way, a ship of any length that's accelerated to a speed that practically stops functionality will not contract significantly
[This has to be as observed from outside. A moving object is affected by length contraction to the same degree as time dilation. That's why an observer moving with the object cannot measure any difference.]
However, all of that is predicated on the idea that light can travel at speeds approaching c in the first place. In 4D models, light must actually travel at zero speed because it has no option other than to reduce all the paths it follows to zero length
[An observers world gets smaller the faster he moves in space. Near zero distance is perceived by the moving observer only.]
[Relativity defines the propagation speed of light, relative to space, not relative to an object!]

I haven't read through all replies to this thread but I have to address one point. That clocks at one point in the ship run differently to those in another. This was said to be like those at different altitudes on a planet and was mentioned in connection with uniform gravitational fields. A uniform gravitational field has the value of g the same everywhere. Therefore, clocks will run at the same rate everywhere. The acceleration is linear in this situation. Since you require all parts of your ship to accelerate at the same rate you are producing an equivalent situation and so all your clocks will also run at the same rate.

That makes no sense. The entire object is stationary in its own inertial frame. If it is moving, you've chosen the wrong frame.
I'm choosing an inertial frame in which part of your object is stationary while other parts are not.
Relativistic contraction is a function of speed, and that speed is undefined at the singularity, hence the contraction (the length that it should be if not under strain) is undefined.
The speed of each atom is defined and so is the local contraction.
Even in the caterpillar method, there exists one frame where they all move at the same speed, except at the moments of the singularity, where it has no speed at all.
And it's a warped, fake frame.
]???? Can you draw a picture of this? How can 4D spacetime locations move? Points in spacetime don't have a property of speed. They're fixed points, not worldlines.
Why are you trying to move the Spacetime locations? They're fixed. The light is moving from two Spacetime locations (X and Z) to a single Spacetime location (Y) to the future of the original two. The light follows zerolength paths (XY and ZY) from the earlier locations to the later one.
Speed is not absolute, and their functionality is not changed at all in their own frame.
We have a frame in which the start and finish line are stationary. The speeds are measured from that frame and have clear finite values at all times. The speed of functionality of material is measured by that frame too  high speed of travel means slowed functionality. If you want to play games where you change frame continually to try to keep the ship stationary within such a chameleon frame, that's fine (the only problems being that it drowns you in complexity and diverts you away from the clearer approach), but I'm looking at this through a single real frame throughout, and if it works in that frame, it necessarily works in all others.
By increasing your acceleration, you are increasing the violence done to the object at a rate greater than you are decreasing the duration of that violence. Playing the action in slow motion by describing events in a very different frame does not make that violence any less violent.
Can you put a figure on how violent an acceleration is allowed to be before your arbitrary objection kicks in?
Well, you didn't provide a speed
I did. It is accelerating arbitrarily hard, so it is going as fast as it can to get that meterrod to move the lighthour. That is closer to c than can be expressed by 12 digits of precision, and since I'm working with say 34 digits of precision, the back effectively accelerates to c.
So you now have the very kind of violent acceleration for your method that you want to deny me the right to use with mine.
I'm accelerating all parts of the object so the strain on the object (and hence the stress) is zero.
If you're taking the rear of the short object up to c in an instant, your separation distances between atoms are going to be way out until the contraction occurs, so you're in the same position as I am with my movethewholeshebangatnearlyc forthewholetrip solution.
You ask how I get the back end up to such high speed so quickly. Answer: Same way I slow down the front at the end of the trip: with arbitrarily high acceleration.
Isn't that "breaking the egg"?
The tail is a point and has no length to contract. So I'm unclear what you are trying to convey with this statement. And as I said, it takes a short but finite time to get up to 452 km/sec at 1e1000 g. It isn't instantly.
The tail is more than just the atom at the back. It's an arbitrary length starting from the back, but let's make it just the two atoms at the back with one ahead of the other. If you suddenly accelerate them to a fraction under c (as in the 1mlong ship), the separation between them is wildly wrong. Choose a longer ship than that where you don't practicallyhalt the functionality but still need high contraction, and you're going to have those atoms accelerate together and impact violently.
Of course the speed is undefined at the point where the wave is, especially in the one frame where there is no wave. If it is defined, what is it?
If you're going to use an overly complex frame, it's your job to convert from a simple frame in which the speeds of all the atoms are defined at all times. Your inability to do that conversion does not break the valid physics in the frame I'm using.
The speed (in the original frame) is zero before the singularity, and 3135 km/sec after it, but what about during the singularity? The question essentially asks for the slope of a triangle wave function at one of the inversion points. Curves have varying slopes along their lengths. Angles don't, at least not at the point of the angle. The slope there is undefined.
I don't see where the difficulty is. What we're calling a wave is simply a point moving along the length of the ship which triggers the acceleration of the local atoms as it goes. There's nothing in that that breaks the laws of physics.
Everything in physics has a proper length, and nothing in physics accelerates at an infinite rate except at certain singularities which destroy any object present at it, even despite the slow motion seen by a distant observer. Even then, the object only seems to approach arbitrarily close to that singularity, and not actually achieve infinite acceleration.
What rules for accelerating atoms am I breaking that you aren't breaking too in your 1mlong ship example?
I do not have the back moving more slowly than it could be. Suggest a better speed if you have one, but do so without singularities.
If your 1mlong ship can get its tail end up to nearly c in an instant without singularities, you should be able to do the same with the back end of your 100ly ship.
Damn... The method seems to be an improvement if I did that right. Breaking the accelerations into two steps shorted the 6 day trip by 20%. If we do it in infinite steps, the singularity approaches a defined value for velocity at all times, so the method is valid.
I wouldn't bet on it being valid, but if it breaks, it may also break your 55 day method.
Answers that change the proper length of the object, however briefly, do not qualify as valid solutions.
That depends on the rules you're applying. If you want to conform to the rules of some specific type of chameleon frame, then fine. I'm just looking for methods which don't break the ship (if we ignore the business of how you accelerated an atom hard without destroying it, but you seem to be happy to use extremely hard accelerations too for the 1mlong ship).
but in the old method I insist on the atoms being at comfortable separations during the trip at any times when they're not being accelerated
They need to be at comfortable separations at all times, even during acceleration.
Then you can't accelerate the back end of your 1mlong ship anything like as quickly as you have tried to. Indeed, you can't accelerate them at all without those forces between atoms becoming a little uncomfortable. That's why by my rules (which your method depends on too, even if you don't realise it), you're allowed to have uncomfortable acceleration distances between atoms while accelerating them to new speeds, but when you've finished accelerating them, they must be back to comfortable separations if they aren't moving fast enough to rely on slowed functionality to prevent them from ripping the object to pieces.
If you're speaking of some other solution, then I need to know which it is. The one with a lot of little waves approaches defined speeds and finite acceleration, so that solution is valid, but we have no numbers for it so far.
The numbers for each "wave" depend on making sure that the front two atoms are the right distance apart for the speed they're moving at. The second atom has to move faster than the first, and the higher the speed of the first, the closer the atom behind it has to get to it. The same applies to the second and third atoms. Maybe the fastest way to work out how to solve this problem is to work out the maximum speed for a twoatomlong ship, then a threeatomlong ship, then a fouratomlong ship, etc. A pattern will emerge from this, and may make it easy to calculate what happens for a ship of any chosen length.
For two atoms, we can accelerate atom 2 to a fraction under c, then do the same to atom 1 as soon as the separation is right for comfortable separation at that high speed. This is the same as compressing the rear.
For three atoms, we do the same thing as before but for atoms 3 and 2 this time. Atom 1 could creep forward a bit as soon as atom 2 has started moving towards it instead of waiting until atom 2 has reached the right separation for atom 1 to move at nearly c too. We can also allow atom 2 to creep forward early though, as soon as atom 3 has begun to move, and that in turn allows atom 1 to creep forward even sooner. The amount of creep of the forward atoms could increase gradually through a range of speeds that maintain correct separation for them back to where the particle behind them is at any point in time based on their own speed. That is the process I'd want to simulate, lengthening the ship by an atom each time and seeing what happens as a result. Note though that the particle behind cannot also be at a comfortable distance from the one ahead of it until they are doing the same speed as each other, so if we were to require it to be, we couldn't accelerate the ship at all. The particle ahead may not be at a comfortable distance from the one behind it either even if the separation is right for its current speed because it takes time for the propagation of forces to adjust to stable levels even after both atoms have stopped accelerating, but again we probably have to ignore this if we're going to accelerate the ship at all.
There is no wave in my method, so nothing travels the length. The length of the object is always consistent with its contracted size in any frame, so there is zero strain, and thus zero stress. There are also no singularities. That makes the solution valid, if not optimal. I really think your method here is going to yield a far better solution, and I don't think that was my opinion until the last couple posts.
In your method, the front accelerates right from the gun, just as it does with mine. If mine's breaking rules by doing that, so must be yours. My method includes yours as a subset of possible implementations, except for what you're doing at the back end where I think you're accelerating it too quickly by imagining an instant contraction suddenly existing on it right after the gun. If your rear atoms are at the right separation once your instant acceleration has been applied, most of those atoms will have had to teleport backwards to take up the correct positions if your rearmost atom is still in the same place as it was before the gun.

I'm choosing an inertial frame in which part of your object is stationary while other parts are not.
That doesn't happen with my solution, but I don't think that solution is optimal.
The speed of each atom is defined and so is the local contraction.
Not in the caterpillar method, no. We're putting infinite acceleration on each atom, giving it an undefined speed.
Even in the caterpillar method, there exists one frame where they all move at the same speed, except at the moments of the singularity, where it has no speed at all.
And it's a warped, fake frame.
It is a nice clean inertial frame.
The light is moving from two Spacetime locations (X and Z) to a single Spacetime location (Y) to the future of the original two. The light follows zerolength paths (XY and ZY) from the earlier locations to the later one.
Those paths are not zero length. That's what I've been saying. There is a separation (a frame independent one) between X and Y, and that separation is not zero.
We have a frame in which the start and finish line are stationary. The speeds are measured from that frame and have clear finite values at all times. The speed of functionality of material is measured by that frame too  high speed of travel means slowed functionality.
Agreed. But slowing down the destruction by a factor of X means you increase the violence done in that time by far more than X. The object breaks all the harder the faster you change its speed.
Can you put a figure on how violent an acceleration is allowed to be before your arbitrary objection kicks in?
Any acceleration, if done everywhere at once, equally. This was one of the solutions, to just move the entire object all at once at near c, reducing the time to an hour.
Another disallowed case is infinite acceleration that is not approached by a valid curve, which is the case in the caterpillar method.
The method of moving the rear faster than 452 and not keeping the entire object stationary in its own frame seems to not violate either of these conditions. This is approximated by a series of small waves which approach waves of zero speed changes, which thus approaches a valid solution.
Well, you didn't provide a speed
I did. It is accelerating arbitrarily hard, so it is going as fast as it can to get that meterrod to move the lighthour. That is closer to c than can be expressed by 12 digits of precision, and since I'm working with say 34 digits of precision, the back effectively accelerates to c.
So you now have the very kind of violent acceleration for your method that you want to deny me the right to use with mine.
I didn't do it uniformly. The front acceleration of this meterlong object is many orders of magnitude (like 980 orders of magnitude) lower to allow the rear to catch up so that the contraction of the object always matches its speed. If the front accelerated as hard as the rear, the object would break. That seems to be what you have sometimes proposed.
I'm accelerating all parts of the object so the strain on the object (and hence the stress) is zero.
If you're taking the rear of the short object up to c in an instant, your separation distances between atoms are going to be way out until the contraction occurs, so you're in the same position as I am with my movethewholeshebangatnearlyc forthewholetrip solution.
Sorry, I don't follow this. "Going to be way out"? What does that mean? The contraction occurs as the speed increases during the finite acceleration, and since the front accelerates so much less than the rear, the two draw near each other exactly in sync with their contraction.
You ask how I get the back end up to such high speed so quickly. Answer: Same way I slow down the front at the end of the trip: with arbitrarily high acceleration.
Isn't that "breaking the egg"?
Not if the strain is zero, no. Speed is always defined (since acceleration is not infinite) and the separation due to movement is always matched by the relativistic contraction.
The tail is a point and has no length to contract. So I'm unclear what you are trying to convey with this statement. And as I said, it takes a short but finite time to get up to 452 km/sec at 1e1000 g. It isn't instantly.
The tail is more than just the atom at the back. It's an arbitrary length starting from the back, but let's make it just the two atoms at the back with one ahead of the other. If you suddenly accelerate them to a fraction under c, as in the 1mlong ship), the separation between them is wildly wrong.
The tail is only the atom in the back. The atom just in front of it accelerates at a far lower rate. I do this for both the long and the short object, but with the long one, I cap the acceleration at the much lower speed of 452 km/sec. The rear one obviously gets to that speed first since it accelerates so much harder than the 2nd atom.
I gave the acceleration of each atom, so you can compute the value yourself and see the vastly lower rate between those two atoms.
It seems that after all these posts, you still don't understand my initial solution. It is very simple, but apparently not optimal. But you seem to think it isn't a valid solution.
Of course the speed is undefined at the point where the wave is, especially in the one frame where there is no wave. If it is defined, what is it?
If you're going to use an overly complex frame
I didn't. I said the original frame just below where you quote me.
it's your job to convert from a simple frame in which the speeds of all the atoms are defined at all times.
In the frame of your choice, what is the speed of the object at the point where the wave is? We're talking the pure caterpillar method now. That speed is undefined in any frame (since if it were defined in one, it would be defined in any frame). It is delimited (somewhere between A and B), but not defined.
The speed (in the original frame) is zero before the singularity, and 3135 km/sec after it, but what about during the singularity? The question essentially asks for the slope of a triangle wave function at one of the inversion points. Curves have varying slopes along their lengths. Angles don't, at least not at the point of the angle. The slope there is undefined.
I don't see where the difficulty is. What we're calling a wave is simply a point moving along the length of the ship which triggers the acceleration of the local atoms as it goes. There's nothing in that that breaks the laws of physics.
But the atom has no defined speed at that point. If all of those points are simultaneous, then the entire object has no defined speed at that moment. You're right that it doesn't break physics, but all objects break under such physics, as I describe below.
Everything in physics has a proper length, and nothing in physics accelerates at an infinite rate except at certain singularities which destroy any object present at it, even despite the slow motion seen by a distant observer. Even then, the object only seems to approach arbitrarily close to that singularity, and not actually achieve infinite acceleration.
What rules for accelerating atoms am I breaking that you aren't breaking too in your 1mlong ship example?
I never use infinite acceleration, and never let the proper distance between any parts of the object change for the duration of the motion.
If your 1mlong ship can get its tail end up to nearly c in an instant without singularities, you should be able to do the same with the back end of your 100ly ship.
I did not do it in an instant. I used an arbitrarily short time. Yes, we can do it with the superlong object as well if we want, but the acceleration has to be finite so that it always has a proper length.
Damn... The method seems to be an improvement if I did that right. Breaking the accelerations into two steps shorted the 6 day trip by 20%. If we do it in infinite steps, the singularity approaches a defined value for velocity at all times, so the method is valid.
I wouldn't bet on it being valid, but if it breaks, it may also break your 55 day method.
Well, 2 steps still isn't valid, but breaking it into an arbitrarily high number of small steps does approach a valid solution. 20 is probably enough to approximate that. I'd have to play with it to see how many steps are needed before the end time stops varying.
What do you mean 'break my 55 day method'? Break the object, or break the speed record? It certainly seem to have the potential to do the latter.
Answers that change the proper length of the object, however briefly, do not qualify as valid solutions.
That depends on the rules you're applying.
I don't see how you can not have this rule and still retain the problem. Without it, you're moving a line of sand, which can be moved one light hour in an hour, a trivial solution. If the proper length of a Bornrigid object changes, then the object breaks, by definition.
If you want to conform to the rules of some specific type of chameleon frame, then fine. I'm just looking for methods which don't break the ship (if we ignore the business of how you accelerated an atom hard without destroying it, but you seem to be happy to use extremely hard accelerations too for the 1mlong ship).
That I am because I'm doing it from a mathematical standpoint, not an engineering one. Indeed, I know of no real way to put the sort of force on any real piece of matter to get it to accelerate arbitrarily hard. A railgun uses EM force to achieve the acceleration desired. This is how they do it in particle accelerators, and those use far more power than a whole country combined to move a few atoms at far lower acceleration rates than my 'arbitrarily large' values. My mathematical atoms are 'points at distance X from the end of the object, or from the event horizon that the object nearly reaches, but not quite.
[The 'atoms' need to maintain their proper separation] at all times, even during acceleration.
Then you can't accelerate the back end of your 1mlong ship anything like as quickly as you have tried to.
You keep repeating this, but you're wrong. If I didn't accelerate the tail that hard, it would lag behind the atom in front of it and the object would break as the proper distance between the two grew to a larger value.
Maybe the fastest way to work out how to solve this problem is to work out the maximum speed for a twoatomlong ship, then a threeatomlong ship, then a fouratomlong ship, etc. A pattern will emerge from this, and may make it easy to calculate what happens for a ship of any chosen length.
I assumed a 2atom object at first, but those atoms were 100 LY apart.
My method of choice was to assume one wave at first, then two, three, twenty, 100, etc. At some point, adding more (and smaller) waves will not change the total time, and then we know that we've approached the answer with a continuous wave with no singularities.
One we know that, then we need to know the top speed much like the analysis I did in post 88 where I found the optimal speed for a single wave.
For two atoms, we can accelerate atom 2 to a fraction under c, then do the same to atom 1 as soon as the separation is right for comfortable separation at that high speed. This is the same as compressing the rear.
For small separations of the two atoms, this works great, but not so much for a large separation of the two atoms.
For three atoms, we do the same thing as before but for atoms 3 and 2 this time.
I predict that this method will yield the same total time as the two atom case where the middle of the 3 atoms is missing. The atom in the middle adds nothing I think, which is why only 2 are needed. The ones in the middle are interesting, helping you see what is going on, but adding atoms between the initial two doesn't change the end answer. Adding them beyond the ends (as you describe below) does of course change the answer since that changes the total length, but then you could have done that total length with just 2 atoms again.
Atom 1 could creep forward a bit as soon as atom 2 has started moving towards it instead of waiting until atom 2 has reached the right separation for atom 1 to move at nearly c too. We can also allow atom 2 to creep forward early though, as soon as atom 3 has begun to move, and that in turn allows atom 1 to creep forward even sooner. The amount of creep of the forward atoms could increase gradually through a range of speeds that maintain correct separation for them back to where the particle behind them is at any point in time based on their own speed.
That sounds an awful lot like my initial version. That converges to 55 days. I suggest you don't do the creep, but do a lot of tiny waves instead with no creepahead. That would be a different solution, and seemingly a much faster one. That isn't intuitive, and I was caught by surprise to see the better results.
I think I will try to find some time to attempt to find an optimal speed at which to do that, but not anytime real soon.
Note though that the particle behind cannot also be at a comfortable distance from the one ahead of it until they are doing the same speed as each other
This is not true. If the object is viewed as a continuous object with defined speed everywhere, that speed and thus the contraction and proper length can be integrated over the length of the object. So different points (the atoms) along that curved line have a computable proper separation despite a difference in speed due to the noninertial motion of the object. As long as that computed proper separation never changes, the distance between any two atoms is comfortable.
so if we were to require it to be, we couldn't accelerate the ship at all.
Indeed, acceleration of any extended object is mathematically impossible without different parts of the object moving at different speeds in some frames. This is trivial to demonstrate using relativity of simultaneity. This does not imply that there is ever uncomfortable separation of parts of a rigid object. There will be a change in proper length if the force that accelerates the object is applied at only one point and not all points. This can be used to disprove the existence of unobtanium, a finite density material which cannot deform by application of force.
The particle ahead may not be at a comfortable distance from the one behind it either even if the separation is right for its current speed because it takes time for the propagation of forces to adjust to stable levels
Forces never propagate in any Bornrigid object. All forces that cause any accelerations are applied from outside, never from the material nearby, with which we, if the object is not broken, are in equilibrium.
In your method, the front accelerates right from the gun, just as it does with mine. If mine's breaking rules by doing that, so must be yours.
The discreet wave method did that, but not necessarily this new thing proposed.
My method includes yours as a subset of possible implementations, except for what you're doing at the back end where I think you're accelerating it too quickly by imagining an instant contraction suddenly existing on it right after the gun.
I never said anything about instant contraction. It takes time to contract, and since the material immediately in front of the rear of the object accelerates so very much less than does the absolute rear, that contraction is exactly in sync with the speed of the object.

All inertial frames measure light speed as constant, because light speed is independent of any source.
All inertial frames measure light speed as constant because they assert a particular speed for it and adjust everything else to conform to that requirement.
In the same way, a ship of any length that's accelerated to a speed that practically stops functionality will not contract significantly
This has to be as observed from outside. A moving object is affected by length contraction to the same degree as time dilation. That's why an observer moving with the object cannot measure any difference.
An observer on the ship will see the trip as taking no time due to the practically halted functionality. An observer stationary relative to the start and finish lines will see the ship travelling for an hour without contracting  it will appear to be an unstable length, but its functionality is frozen, as expected for an object moving at such high speed.
An observers world gets smaller the faster he moves in space. Near zero distance is perceived by the moving observer only.
In the 4D nonEuclidean geometry of STR and GTR, those zerolength distances exist. If we sent a ship at nearly c to M32 and back, it would return to us at a different location from the one it left, but the first leg of its trip would be shortened to next to zero length, and so would the second leg of its trip. The time it would pass through for the trip would be next to zero too. Light would make an equivalent trip in zero time of zero distance. That is a mathematical necessity of the model.
Relativity defines the propagation speed of light, relative to space, not relative to an object!
Which Relativity? With LET, yes  it's the propagation speed of light relative to space. With STR and GTR, it's just a constant which represents the apparent propagation speed of light relative to space, but with those models the real speed of light is zero. If you don't want it to be zero, don't use a 4D model.

In the same way, a ship of any length that's accelerated to a speed that practically stops functionality will not contract significantly
So if I plug .99999999999c into my Lorentz contraction calculation, I will get close to 1 (no significant contraction) because functionality is practically stopped. Hmm, my calculator doesn't yield that result. Or did I not use enough 9's?

I'm choosing an inertial frame in which part of your object is stationary while other parts are not.
That doesn't happen with my solution, but I don't think that solution is optimal.
Look at your ship before you start it moving. It's all stationary relative to the start line, and relative to the finish line. That's the initial frame, and it's the one I continue to use throughout. As soon as you start moving your ship, you have the back end moving through this frame while the front end begins to accelerate slowly from zero. You have different parts of the ship moving at different speeds relative to this frame. The spacing between the atoms at the back end is immediately wrong  it was right before you started moving the back, but as soon as you started moving it, you broke that. At the moment of the gun, the speed of the rear two atoms has gone from 0 to 452km/s even though they have travelled zero distance at that moment, while the distance between them is the same as it was when they were at rest. Do the same thing with the 1mlong ship and instant acceleration to nearly c and you should recognise the problem. By the time the rear atom has moved 1/1000th of the way towards where the atom ahead of it was itting before the gun, the correct spacing between it and that atom ahead of it can only be realised by moving the atom ahead backwards by almost 999/1000 of the original distance between atoms. You either have to teleport it back there or you have to teleport the rear atom forward the same distance instead (and further forward again to get correct spacing relative to the next atom beyond that, and the same again for the one beyond that, etc.). Your starting move is illegal.
The light is moving from two Spacetime locations (X and Z) to a single Spacetime location (Y) to the future of the original two. The light follows zerolength paths (XY and ZY) from the earlier locations to the later one.
Those paths are not zero length. That's what I've been saying. There is a separation (a frame independent one) between X and Y, and that separation is not zero.
For light, that separation is most certainly zero. I refer you to my previous post in this thread. If you're going to use a 4D model, you have a duty to accept its mathematical requirements, and these zerolength paths are unavoidable features of that kind of geometry. The reluctance of most physicists to admit that should not be allowed to mislead you. Recognising that 4D geometry works this way doesn't break the STR or GTR models  it merely forces you to see that any talk of the speed of light being c with such a model is actually the result of mixing incompatible models. Light only moves at c in 3D models. In 4D models light merely has an apparent speed of c while its actual speed is always zero. I don't know why people have so much difficulty accepting this when at the same time they have highspeed particles travelling through the same 4D geometry on nearzero length, near zerotime paths. If you want to ban that too, you're going to have to ditch the time dimension and bring in an absolute frame, at which point you're doing LET instead. You need to make up your mind which model you want to use and stick to its rules. You can't combine them in a single model  they're incompatible.
If the front accelerated as hard as the rear, the object would break. That seems to be what you have sometimes proposed.
With one set of rules (where things are allowed to sit at uncomfortable separations if their functionality is practically halted), that is what I proposed. With another set of rules, I do not have the front accelerate as hard as the rear.
In the frame of your choice, what is the speed of the object at the point where the wave is? We're talking the pure caterpillar method now. That speed is undefined in any frame (since if it were defined in one, it would be defined in any frame). It is delimited (somewhere between A and B), but not defined.
If I discuss a scenario in which a car drives around an oval track but I don't give you the speed that it's moving at, that speed is undefined. Does that mean it's breaking the laws of physics by going round the track at an undefined speed? No. If it accelerates by an undefined amount and now does each lap faster than the one before, does that mean it's breaking the laws of physics? No. My method has each atom move at legal speeds and accelerate between legal speeds and can have these accelerations apply over lengths of time slightly greater than zero. I don't know what those speeds or accelerations are, but none of them break the laws of physics.
But the atom has no defined speed at that point.
It will do once we've worked out what the ideal speed for it will be.
If all of those points are simultaneous, then the entire object has no defined speed at that moment.
The object is a composite with different parts moving at different speeds. If you want a defined speed for the object at any moment, it will have to be an average speed, and again we won't know what that speed is until we've worked out what it needs to be.
I never use infinite acceleration, and never let the proper distance between any parts of the object change for the duration of the motion.
What are you doing with the back end of the 1mlong ship if that isn't infinite acceleration? Whatever it is, I'm doing the same, except that I don't have to teleport atoms around to shift them to the right separations by magic when the gun goes off.
If your 1mlong ship can get its tail end up to nearly c in an instant without singularities, you should be able to do the same with the back end of your 100ly ship.
I did not do it in an instant. I used an arbitrarily short time.[/quote]
I do everything in arbitrarily short times too.
What do you mean 'break my 55 day method'? Break the object, or break the speed record? It certainly seem to have the potential to do the latter.
If my method is breaking the rules, yours must be too. My method covers a case in which the front end accelerates identically to yours, so if it turns out that I'm not allowed to accelerate it that quickly, you won't be allowed to do so either.
I don't see how you can not have this rule and still retain the problem. Without it, you're moving a line of sand, which can be moved one light hour in an hour, a trivial solution. If the proper length of a Bornrigid object changes, then the object breaks, by definition.
I think you're already breaking that rule with the way you accelerate the back end. The same will apply when you halt the front end, because the second atom from the front will have to jump backwards to its destination.
You keep repeating this, but you're wrong. If I didn't accelerate the tail that hard, it would lag behind the atom in front of it and the object would break as the proper distance between the two grew to a larger value.
I'm not wrong. Your second last atom has to teleport backwards in every single case  it's just a lot more obvious with the 1mlong ship than with the 100ly ship.
For two atoms, we can accelerate atom 2 to a fraction under c, then do the same to atom 1 as soon as the separation is right for comfortable separation at that high speed. This is the same as compressing the rear.
For small separations of the two atoms, this works great, but not so much for a large separation of the two atoms.
It needs to be done with the small separations that would exist between atoms of the real ship.
I predict that this method will yield the same total time as the two atom case where the middle of the 3 atoms is missing. The atom in the middle adds nothing I think, which is why only 2 are needed. The ones in the middle are interesting, helping you see what is going on, but adding atoms between the initial two doesn't change the end answer. Adding them beyond the ends (as you describe below) does of course change the answer since that changes the total length, but then you could have done that total length with just 2 atoms again.
Case 1:
With two atoms at normal separation, the rear one is almost instantly moving at almost c, so we just treat it as if it's doing c right from the starting gun. By the time it's reduced the distance between it and the lead atom to 0.5 the original length, the front atom should be doing 0.866c. Because the front atom starts moving before that point in time though, working out where both atoms are at the moment when the gap hits 0.5 hard. I'm sure it's dead easy if you know how to apply calculus to it, but I don't. (I could probably work out how to apply it through experimentation, but I don't know how long it would take me to find the right approach.)
Case 2a:
With two atoms at doublenormal separation, by the time the rear one has reduced the distance between it and the lead atom to 0.5 the original length, the front atom should be doing 0.866c, as before, but it must take exactly twice as long to reach that point as in the first case. In this case, the speed of the leading atom will be half that of the equivalent atom in case one at any point in time.
Case 2b:
We can imagine a version of case 2 where the atom separations are normal rather than double and where the rear atom moves at 0.5c with the rear atom reaching 0.433c at the point when the separation becomes 0.5. This provides the same timings as case 2a. (You'll see how useful this is later.)
Case 3:
With three atoms at normal separations, the first case applies to the rear two atoms too  it will be identical. The front atom has to accelerate more slowly though. Its relation to the behaviour of the middle atom is clearly different because the middle atom accelerates slowly rather than in a near instant, but its relation to the behaviour of the rear atom certainly looks similar to the original case, but can we prove that it's the same shape of relationship? In cases 1 and 2b, the acceleration of the lead atom is governed by an atom chasing it at a constant speed. In case 3, the acceleration of the lead atom is governed by an atom, the middle one, chasing it at very low speeds initially  much lower than the 0.5c in case 2b. I think that proves that it's a different curve, and if I'm right, then you can't just consider two atoms.
I never said anything about instant contraction. It takes time to contract, and since the material immediately in front of the rear of the object accelerates so very much less than does the absolute rear, that contraction is exactly in sync with the speed of the object.
The contraction with the 1mlong ship will move some atoms backwards, and they'll then run into other atoms at high energies and break the ship.

In the same way, a ship of any length that's accelerated to a speed that practically stops functionality will not contract significantly
So if I plug .99999999999c into my Lorentz contraction calculation, I will get close to 1 (no significant contraction) because functionality is practically stopped. Hmm, my calculator doesn't yield that result. Or did I not use enough 9's?
You'll get a contraction figure to next to zero length, but you also get halted functionality which prevents the ship from achieving that contraction  it has insufficient time to contract any significant amount at all. The contraction doesn't suddenly apply in full by magic  it takes time to contract the ship, and we aren't giving it that time.

You'll get a contraction figure to next to zero length, but you also get halted functionality which prevents the ship from achieving that contraction  it has insufficient time to contract any significant amount at all.
Exactly. Preventing its contraction is what breaks it, and why I will not consider such a solution.
The thing needs to be held at that unnatural length for an hour in the original frame, so the high speed does not in any way hide from us the incorrect length of the object.
Really, we're working on a viable solution that breaks no rules, and it isn't an obvious one. Most importantly, it seems to have the potential to be 10x faster than my simple method that restricts itself to always being stationary in its own inertial frame.

You'll get a contraction figure to next to zero length, but you also get halted functionality which prevents the ship from achieving that contraction  it has insufficient time to contract any significant amount at all.
Exactly. Preventing its contraction is what breaks it, and why I will not consider such a solution.
It doesn't break though because its functionality is slowed to a halt  the atoms don't have time to apply any significant contraction.
The thing needs to be held at that unnatural length for an hour in the original frame, so the high speed does not in any way hide from us the incorrect length of the object.
We don't need the incorrectness of the length to be hidden, and maintaining that for an hour is not a problem  we know that something moving that fast will have practicallyhalted functionality and we'd be shocked if we saw it breaking the laws of physics by contracting.
Really, we're working on a viable solution that breaks no rules, and it isn't an obvious one.
I did say that there are different sets of rules and different winning methods for some or each set. If the only rule is that you get the object there without breaking it and that no severity of acceleration of an atom will break that atom, then this is the fastest solution  the object is moved at a fraction under c and arrives undamaged. Moving to another set of rules does not dethrone this solution as the winner of its category.
Most importantly, it seems to have the potential to be 10x faster than my simple method that restricts itself to always being stationary in its own inertial frame.
The more restrictive sets of rules ban reliance on frozen functionality, requiring atoms to sit at correct separations, but how much of the time are we allowed to break that rule? With the fastest, multiwave version of the caterpillar method, we try to keep each atom the right distance ahead of the one behind it at all times, but the one behind isn't at the right distance from it because it's going faster  it's impossible to satisfy both atoms at once, and with the leading atom accelerating throughout the entire trip, the one behind it will never feel at a comfortable distance from it. I don't think there are any viable sets of rules for doing what we're trying to do without having some kind of arbitrarily allowed exceptions. If the separations are always to be comfortable, we can't accelerate the ship at all.
With your method where you claim the separations are always comfortable, you're trying to hide the uncomfortable separations by imagining them away through the use of a composite frame that hides their existence. It may be possible to hide their existence if you do that: when you accelerate something, you create contraction forces in it and when you decelerate it you create decontraction forces instead, but viewed from another frame, those forces can be seen as acting the other way round. Pick another frame that accelerates an object from v to v in an instant and you have no correction of the length being made at all. If you assume that this last way of looking it is the reality in all cases, then you can deny the existence of all such imbalances by changing real frame an infinite number of times in order to make each little change in speed look like a change from v to v. In LET though, that's illegal  you have to stick to one real frame throughout instead of using a fake, composite frame.

I did say that there are different sets of rules and different winning methods for some or each set. If the only rule is that you get the object there without breaking it and that no severity of acceleration of an atom will break that atom, then this is the fastest solution
But that wasn't the rule. The rule was to never change the proper length of the object. The solution you suggest is a trivial one. Any object can be moved a light hour in an hour that way. What's the point in figuring that out?
Most importantly, it seems to have the potential to be 10x faster than my simple method that restricts itself to always being stationary in its own inertial frame.
The more restrictive sets of rules ban reliance on frozen functionality, requiring atoms to sit at correct separations, but how much of the time are we allowed to break that rule?
I don't ban the frozen fuctionality. I ban the lack of correct separation. There's no minimum time that can be violated.
With the fastest, multiwave version of the caterpillar method, we try to keep each atom the right distance ahead of the one behind it at all times, but the one behind isn't at the right distance from it because it's going faster
Not if it is a continuous wave. One atom is allowed to be faster or slower than the other if the proper separation never changes. You seem not to realize that.
The discreet waves are illegal of course (since they involve small singularities), but making them smaller is a way of integrating the continuous wave solution that is not illegal. The solution approaches a valid one. Just making everything go as fast as you can does not do that.
I don't think there are any viable sets of rules for doing what we're trying to do without having some kind of arbitrarily allowed exceptions.
My 55 day solution had zero exceptions. The proper length of the thing was fixed the whole time, and didn't even need integration to compute it since it wasn't a curve. The optimal solution would seem to require integration to compute the proper length of the object enroute.
With your method where you claim the separations are always comfortable
They're not merely comfortable. They're exactly correct. There is not a small wiggle margin I'm allowing.
, you're trying to hide the uncomfortable separations by imagining them away through the use of a composite frame that hides their existence.
An inertial frame is not composite, but a curved object will need such a composite frame since in no frame will it be all moving at the same speed. Anyway, with my 55 day solution, I invite you to point out where the proper separation of two points of the object are different that the original value.
The mathematics is pretty easy with that case. Every point along its length accelerates at a proper rate of c²/D where D is the distance from a point arbitrarily close behind the tail of the object for acceleration, and a point similarly just beyond the nose of the object for deceleration. Each point changes from acceleration to deceleration abruptly when 452 km/sec is achieved. From that description, you can compute the exact location of any point on the object at any time, and notice that the proper separation between any two points is fixed the entire way.
It may be possible to hide their existence if you do that: when you accelerate something, you create contraction forces in it and when you decelerate it you create decontraction forces instead
Since I am accelerating at a modest pace for most of the time, these forces would indeed exist iff there was a change in proper separation, so it is a good thing we don't do that.
but viewed from another frame
Proper length of an object is frame invariant. Looking at it from another frame won't change the answer.
In LET though, that's illegal  you have to stick to one real frame throughout instead of using a fake, composite frame.
Not sure what the one real frame is going to buy you when computing the proper length of something not stationary. As I said, that computation is not different from one frame to the next, but for a nonrigid object, it might be different from one moment to the next, like changing the proper length of a rubber band by pulling it.
I suppose you could have a string that is half Born rigid where its proper length is not allowed to change, but it can bend effortlessly in any spaghetti curve you like. Could we move such a (straight) string faster than a similar rod of the same dimensions? I think not. The problem is equivalent to allowing a reduction in the original proper length of the rod, but not allowing an increase of it. More food for thought.

Proper length of an object is frame invariant.
This is debatable. Proper length is of an object is, by definition the length in its own frame, but the figure can be computed in a different frame by integrating length/contraction over all simultaneous points in a given frame, which will give a different answer if the state (stretched or not say) of the object changes over time. For the purpose of demanding that the proper length never changes, it is meaningful to compute said value in a frame of choice and it should not be different, but only because of this rigid property we're giving the object. A nonrigid object could have a frame dependent proper length at a given time as defined by the chosen frame.
So if this computation yields a different proper length figure, we know we've violated the rules.

I did a quick one in my head (plus the numbers in post 88), using two waves instead of one. The original wave was to 3135 km/sec which took 2 days for the wave and 4 days to move one light hour at that speed. Total time is nearly 6 days.
So even if we allowed singularities, this solution is not optimal since we spend 4 days just coasting inertially, days which could be put to good use with some extra acceleration and deceleration, which would be perhaps another wave. So of course more waves are better, especially since they also get smaller as you increase their number, and smaller waves have smaller singularities which gradually fade to nonexistence.
Lets bump the rear up to 2220 km/sec, at which speed the wave moves to the other end in only 1 day. Then we immediately bump the rear again by a similar 2nd wave. The time to move the light hour is now 2.8 days instead of 4, at least for the parts of the object moving at full speed, which none of them do for the whole distance. The total time to move the object is now 4.8 days (each point is stopped for one day, half speed for 2 days, and full speed for 1.8 days).
Here I want to note that doing it in 2 waves reduces the fullspeed coasting time to 1.8 days from 4. Half the original 4 days were simultaneous in the original frame. There are 2 full days where the entire object is moving at 3135 km/sec in the original frame, and 2 days that any particular point is dead stopped. With the 2wave method, there is 1 day of stopped and 1.8 days of full speed, and at no point in the original frame does the entire object move at that speed. Some part of the object is always moving at half speed. Both the stopped time and the 1.8 days of high speed is still a waste, time that could be used to milk a little more efficiency from the thing. The optimal solution would reduce both stopped time and maxspeed time to zero just like the 55 day solution. For any given part of the object, acceleration will continue (at fixed or varying acceleration) until max speed is hit, at which point deceleration will immediately commence.
I will try to write something to do this, and it will seemingly not need any parameters like the first function. There will be no sweet spot for which I need to search. It will just keep reducing the wave magnitude and use more and more of them until we cannot add more without overshooting our destination. As wave magnitude decreases, the answer will converge to a valid solution. When adding more waves makes no significant change to that final duration, we've got our answer. At that point we can attack/defend the plan for being valid or not, and also search for further improvements to shave off even more time.

DC#133;
All inertial frames measure light speed as constant because they assert a particular speed for it and adjust everything else to conform to that requirement.
[Observers have no control over the effects of td and lc, which modifies their measurements. The effects result from a constant independent speed of light. I.e. it's built into the physical behavior of the universe.]
Quote
This has to be as observed from outside. A moving object is affected by length contraction to the same degree as time dilation. That's why an observer moving with the object cannot measure any difference.
An observer on the ship will see the trip as taking no time due to the practically halted functionality. An observer stationary relative to the start and finish lines will see the ship travelling for an hour without contracting  it will appear to be an unstable length, but its functionality is frozen, as expected for an object moving at such high speed
.
[Length contraction occurs at high speeds.]
Quote
An observers world gets smaller the faster he moves in space. Near zero distance is perceived by the moving observer only.
In the 4D nonEuclidean geometry of STR and GTR, those zerolength distances exist. If we sent a ship at nearly c to M32 and back, it would return to us at a different location from the one it left, but the first leg of its trip would be shortened to next to zero length, and so would the second leg of its trip. The time it would pass through for the trip would be next to zero too. Light would make an equivalent trip in zero time of zero distance. That is a mathematical necessity of the model.
[A distance of zero is meaningless. SR is Euclidean geometry. GR is non Euclidean geometry. Observer A's clock would record less time, as observed by E on the earth. A has a choice.
1. Assume an inertial frame and conclude the universe has contracted, thus M32 arrived early.
2. Assume he left E in a ship, knows SR, so concludes he is experiencing time dilation.]
Quote
Relativity defines the propagation speed of light, relative to space, not relative to an object!
Which Relativity? With LET, yes  it's the propagation speed of light relative to space. With STR and GTR, it's just a constant which represents the apparent propagation speed of light relative to space, but with those models the real speed of light is zero. If you don't want it to be zero, don't use a 4D model.
[SR or LET, there is no difference, especially since the coordinate transformations are equivalent! Both used Maxwell's equations as a basis for light propagation. The Lorentz version required a late correction (1905) by Poincare to maintain invariance.

I just wondered something; how does an object know if it is "long"?

I just wondered something; how does an object know if it is "long"?
You get a small ruler (not moving relative to the segment being measured) and see how many of them fit from end to end. That's its proper length. You can also just paint marks along the length of it, sort of like boats do to show draft (or draught), but painted marks become incorrect if the object experiences strain. I'm not allowing any strain on my object, so that's not a problem for this topic.
Knowing the measurement doesn't tell you if it is "long" since nobody has provided a definition for that. My example object is 100 light years in proper length, which seems "long" until you start talking about distances within and between galaxies.

I'm going to focus on a single point here which must not be lost in the noise.
With your method where you claim the separations are always comfortable
They're not merely comfortable. They're exactly correct. There is not a small wiggle margin I'm allowing.
They are not correct. Look at the atoms sitting at the back. Here's a diagram of them:
OOOOO
That's them sitting at rest before the starting gun. They're going to move to the right when the gun fires. What do they look like the tiniest moment of time after the gun goes off? This:
00000
You have to teleport them to the left before they can start moving to the right.

Observers have no control over the effects of td and lc, which modifies their measurements. The effects result from a constant independent speed of light. I.e. it's built into the physical behavior of the universe.
If you are stationary or moving at constant speed and you assert that the speed of light relative to you from the north is c, if you then accelerate north to a different constant speed, the speed of light relative to you from the north is no longer c. If you want to claim it is now c relative to you, it can not have been c relative to you before. If you want it to be the same speed relative to you for both frames, you need to use a 4D Spacetime model in which the speed for light relative to you in both cases is zero. There is no valid alternative to these options in mathematics.
Length contraction occurs at high speeds.
Length contraction is not applied by magic. If you start with two ships sitting a mile apart in frame A with one directly ahead of the other and you accelerate them both identically to 0.866c (in the direction they're pointing), they will still be a mile apart in frame A after the acceleration. If you do the same thing with a single ship that's a mile long, that ship will have contracted to half a mile long (if the acceleration is gentle enough for the contraction to apply or if the acceleration was applied from the rear). In one case the contraction was applied, but in the other it was not. If I accelerate every atom of a metre long stick to a fraction under c in an instant, those atoms will still be sitting at the same separations after the acceleration  the contraction has not been applied, just as it wasn't with the two ships a mile apart. With the functionality of this stick effectively frozen, the contraction will be applied very slowly  so slowly that it will be impossible to measure it if the speed is close enough to c. For any finite length of time that you want to prevent the contraction from becoming visible, there is a valid speed less than c which will provide that.
A distance of zero is meaningless. SR is Euclidean geometry. GR is non Euclidean geometry.
The same 4D model covers both. And the distance of zero is not meaningless  it means that there is a path available that has no separation between two points. Such paths exist between all Spacetime locations (although most of these require two zerolength steps to be combined).
Observer A's clock would record less time, as observed by E on the earth. A has a choice.
1. Assume an inertial frame and conclude the universe has contracted/, thus M32 arrived early.
2. Assume he left E in a ship, knows SR, so concludes he is experiencing time dilation.
If he chooses 2, he is using an absolute frame mechanism, so he's abandoned STR.
Which Relativity? With LET, yes  it's the propagation speed of light relative to space. With STR and GTR, it's just a constant which represents the apparent propagation speed of light relative to space, but with those models the real speed of light is zero. If you don't want it to be zero, don't use a 4D model.
SR or LET, there is no difference, especially since the coordinate transformations are equivalent! Both used Maxwell's equations as a basis for light propagation. The Lorentz version required a late correction (1905) by Poincare to maintain invariance.
There is a major difference. However, if you keep mixing models and imagine that you're doing SR while you're actually mixing LET and SR, then no wonder you're confused. In LET there is an absolute frame. In SR there is not, so you are banned from having time dilation  time cannot dilate for a stationary object, and all objects are stationary in SR.
Take the twins paradox. Twin A stays at home. Twin B goes away and back, recording less time passing than twin A. Did time dilate? Twin B is not moving according to SR during the first leg, so no  it could not dilate. Twin B is not moving according to SR during the second leg, so again no  it could not dilate. Twin A is also not moving according to SR, so again time did not dilate. You cannot have time dilation without an absolute frame mechanism, and you cannot have multiple absolute frames to switch between whenever it suits you because you are changing the speed of light relative to the content every time you change frame, breaking the rules of the universe where the speed of light is constant through space.
It is only by going to the 4D model that you can eliminate the contradictions, and you can only do that with a static block universe version of it, but even there the contradictions are still actually present  they are merely brushed under the carpet by refusing to address the generation phase of a block universe.

I'm going to focus on a single point here which must not be lost in the noise.
With your method where you claim the separations are always comfortable
They're not merely comfortable. They're exactly correct. There is not a small wiggle margin I'm allowing.
They are not correct. Look at the atoms sitting at the back. Here's a diagram of them:
OOOOO
That's them sitting at rest before the starting gun. They're going to move to the right when the gun fires. What do they look like the tiniest moment of time after the gun goes off? This:
00000
You have to teleport them to the left before they can start moving to the right.
Not entirely clear picture. If they move to the right, why does the picture show them having moved to the left?
Anyway, perhaps I see what you're trying to convey. The leftmost one accelerates the most and closes the distance to the next atom the most. So you'd expect them not to be the same distance apart since they're not moving at the same speed, and thus contracting differently along its length. It seems you understand this since you've drawn it, but point it out like it is something wrong.
Oh.... You really are moving them to the left. No, I'm not doing that. No acceleration takes place so fast that things have to move left to keep the thing the correct length. The left atom needs to move to the right to catch up with the ones to the right. Nothing moves left. You're contracting the thing before it begins to move. Run the numbers into the acceleration formula I gave and you see that movement is always to the right, even if the picture looks like you 2nd one after the time it takes to move the leftmost atom a considerable distance to the right.
Here's a picture of the progression of the atoms you picture:
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fwww.gregegan.net%2FSCIENCE%2FRindler%2FCoords.gif&hash=9e35d482118fe5a45c2e4c9bb6d30f07)
The seven lines at the bottom are the atoms, vertical at first (no speed), but each curving to the right (never left) as it picks up speed, getting closer to each other all the time at any horizontal line (simultaneous in the original frame) as the contraction takes effect. Never mind the q= lines, which are irrelevant to what you're pointing out. The q lines complete a coordinate system.
The picture assumes continuous acceleration, not reversing when some speed like 452km/sec is reached, so it is a fair depiction of the leftmost atoms of our meterstick being moved a lighthour.

lets make this simple. when gamma rays burst are detected via multiple radio waves signals and the radio signals appear as mutliple repeating signal burst, at the same time from the same location in space, it can be constued that they at one time constitued a single burst from a single source. if this in fact is the case, you have the answer as to
" What limits does relativity put on acceleration of long objects?". a simple time measurement of a single radio burst from a larger packet of radio bursts, can be back functioned in conjunction with a calculated algorithm, that determines the time/length spread function between qamma rays and radio wave over distance in space. once the spread of how long it takes for a gamma wave to elongate into a radio wave, you have the basis of determining the distance, speed and length variables for an accelerated light object. by interpolating the spread length betwen gamma and radio waves, multiplied by a time period of a single radio burst in a mulitple radio burst packet, you have an approximation of velocity, distance and length. simple.
.

lets make this simple. when gamma rays burst are detected via multiple radio waves signals and the radio signals appear as mutliple repeating signal burst, at the same time from the same location in space, it can be constued that they at one time constitued a single burst from a single source. if this in fact is the case, you have the answer as to
" What limits does relativity put on acceleration of long objects?"
A gamma ray burst is not a rigid object, nor does it accelerate from a stop nor come to a stop at its destination.

Anyway, perhaps I see what you're trying to convey. The leftmost one accelerates the most and closes the distance to the next atom the most. So you'd expect them not to be the same distance apart since they're not moving at the same speed, and thus contracting differently along its length. It seems you understand this since you've drawn it, but point it out like it is something wrong.
But it does show something wrong. I had two options as to how to illustrate the problem, but I chose the one where the rear atom stays almost where it was before the starting gun while the rest move to their correct spacings from it for their newly acquired high speed. That requires them to be teleported to the left. The alternative way to illustrate the problem would have been to teleport the whole lot to the right, and that would be the better illustration because the object before the starting gun has every part of it stationary and no length contraction acting on it, whereas immediately after the gun there will be length contraction acting on it which means you have to jump the rear atoms forwards in an instant. How big a problem is this? Well, with your 100 lightyear long ship you're going to have significant length contraction acting on it even with the tail only moving at 452km/s. It's hard to work out the right contraction when different parts are moving at different speeds (and the front end doing 0), but if the whole thing was doing 452km/s the length contraction on the ship would be one lighthour. I'm going to make a guess that the contraction on the actual ship might be one lightminute rather than a lighthour, which would mean your rear atom is going to have to move that far before all the atoms are at comfortable separations, and given that it's moving at about 0.0015c, it's going to take 11 hours for it to settle to the right length, and throughout that time it is breaking your rules.
You'll have the same issue with the front end at the finish line if you want to halt that part of the ship at its destination: another 11 hours of breaking the rules.

But it does show something wrong. I had two options as to how to illustrate the problem, but I chose the one where the rear atom stays almost where it was before the starting gun while the rest move to their correct spacings from it for their newly acquired high speed. That requires them to be teleported to the left.
If you look at the diagram, you see that nothing gets this 'newly acquired high speed' ahead of its allowed contraction. The first atom accelerates far more than the next one, which is essentially still stationary at the first moment no matter how close we put the first atom to the dotted line.
Yes, if we accelerated the right any more than this maximum limit (such as you suggest in all your posts trying to hide the lack of contraction by reducing its duration to negligible time in one frame), the the atoms to the right would indeed need to teleport left to maintain correct spacing. That's what keeps us from getting there any faster.
The alternative way to illustrate the problem would have been to teleport the whole lot to the right
No teleportation. Each part of the object (be they atoms or lightyear markers) follow the acceleration given by my specified formula c²/D, which is depicted by the dark lines in the picture. Note that motion is contiguous (no teleportation) and always to the right, not the left. Local contraction is always appropriate for the local speed.
How big a problem is this? Well, with your 100 lightyear long ship you're going to have significant length contraction acting on it even with the tail only moving at 452km/s.
Yes. Exactly one light hour of contraction to be exact, which is the distance we wish to move. It takes 55 days for the head (100 LY of D) to accelerate to that speed. It takes more than 12 hours for the 1LY mark to get to that speed. These hours are needed to prevent needing to move anything backwards to account for length contraction.
It's hard to work out the right contraction when different parts are moving at different speeds (and the front end doing 0),
The whole thing is doing 0 at first, but the tail has high acceleration so it doesn't stay that speed for long. All parts could just keep accelerating forever at that rate if we weren't worried about ever stopping the thing.
but if the whole thing was doing 452km/s the length contraction on the ship would be one lighthour.
In the original frame, the whole thing never goes full speed like that. At midtrip, the object has a total contraction of perhaps 3/4 light hour, but the speed varies along its length, going fastest in the middle.
I'm going to make a guess that the contraction on the actual ship might be one lightminute rather than a lighthour
In what frame? I guessed 3/4 hour. It isn't exact, but at such low speeds, it is really close to that. At higher speeds, the 3/4 figure goes up, so it's hard to compute. Calculus is your friend.
I notice you've not run any numbers demonstrating this fictional strain that you claim. Show any segment of the object at some moment during the motion and the length of that segment will be correct for its speed. If the two ends of the segment are moving at significantly different speeds, you will have to integrate the contraction over the length of the object, or just consider the contraction to be some figure that falls between the contraction for the two different speeds.
It seems I cannot describe a different way of moving the object when you cannot even see that the original slow way is a valid solution, if not optimal. You claim the contraction will break it, but you've demonstrated no separation/length numbers that don't match.

If you look at the diagram, you see that nothing gets this 'newly acquired high speed' ahead of its allowed contraction. The first atom accelerates far more than the next one, which is essentially still stationary at the first moment no matter how close we put the first atom to the dotted line.
You are now using the caterpillar method for perhaps the first 11 hours of the trip before you get to a point where you have a regular speed distribution in place along the ship. You can reduce that time by moving the atoms faster during this phase, and indeed you'll have to if they're to catch up with the places they should be in, so you'll have to decelerate them to 452km/s once the length is right so as to avoid damage with the ship absorbing all the excess force. Your method isn't as pure as you made it out to be.
How big a problem is this? Well, with your 100 lightyear long ship you're going to have significant length contraction acting on it even with the tail only moving at 452km/s.
Yes. Exactly one light hour of contraction to be exact, which is the distance we wish to move.[/quote]
One light hour would be the contraction acting on it if the whole ship was moving at 452km/s, but you only have one end of the ship doing that at a time, so the total contraction will be a lot less.
I notice you've not run any numbers demonstrating this fictional strain that you claim. Show any segment of the object at some moment during the motion and the length of that segment will be correct for its speed.
I've already shown you that it's wrong at the start. The rear atom has to travel at 904km/s for perhaps 11 hours to get to where it should be, and when it gets there, the excess energy that it's carrying has to be taken off it to get it to the correct speed to conform to your description of how the ship behaves.
It seems I cannot describe a different way of moving the object when you cannot even see that the original slow way is a valid solution, if not optimal. You claim the contraction will break it, but you've demonstrated no separation/length numbers that don't match.
It may be a valid solution, but the atoms at the back have to follow more complex rules than the ones they follow subsequently  it already depends on the caterpillar method.

If you look at the diagram, you see that nothing gets this 'newly acquired high speed' ahead of its allowed contraction. The first atom accelerates far more than the next one, which is essentially still stationary at the first moment no matter how close we put the first atom to the dotted line.
You are now using the caterpillar method for perhaps the first 11 hours of the trip before you get to a point where you have a regular speed distribution in place along the ship.
No idea what you're talking about. There is no wave, except I suppose for the point at which the ship moves at max speed, which moves south to north in frames where the object is mostly northbound, moves north to south in frames where the object is mostly southbound. But if we're just talking about acceleration and not turning around, there is no wave at all. c²/D does not involve a wave. The new method I'm working on does.
One light hour would be the contraction acting on it if the whole ship was moving at 452km/s, but you only have one end of the ship doing that at a time, so the total contraction will be a lot less.
Not a lot less. 3/4 I figure since halfway, the ship is moving at 3/4 of the max speed on average.
452 was chosen because in the ship frame, the universe contracts a light hour over 100 LY, so in that frame the tail at the beginning and the head at the finish line are nearly (arbitrarily close) simultaneous events. Go any faster than that, and the universe contracts more than a light hour and we'll have overshot the destination before we can stop. So it took me by surprise to find a method that allowed us to go a lot faster, but it does it by having no inertial frame in which the object is at rest but the universe is unreasonably contracted.
I notice you've not run any numbers demonstrating this fictional strain that you claim. Show any segment of the object at some moment during the motion and the length of that segment will be correct for its speed.
I've already shown you that it's wrong at the start.
No, you're just asserting it. You've not shown anything. The acceleration of everything is always to the right. No correction is made for inappropriate contraction, so show me that the contraction doesn't match the speed it is going. Use numbers...
The rear atom has to travel at 904km/s for perhaps 11 hours to get to where it should be,
904 km/s for 11 hours is 36 million km (ish) or a couple light minutes. Why does it need to be there in 11 hours?
The contraction will be a lot more than 36M km. I think that was perhaps a guess on your part, but we have 27.6 days of the rear moving faster than the front to allow it to reduce the separation of the two, so it does it in 27.6 days, not 11 hours. No need for anything to move at 904.
It may be a valid solution, but the atoms at the back have to follow more complex rules than the ones they follow subsequently  it already depends on the caterpillar method.
Another thing I don't understand. All atoms everywhere accelerate at a finite c²/D, and decelerate at c²/D' (where D and D' are distances to points in space arbitrarily close to the start event at the rear and beyond the finish event at the nose, respectively). Since all atoms have finite acceleration and deceleration, they're all treated identically. No special rules for any point.

Not a lot less. 3/4 I figure since halfway, the ship is moving at 3/4 of the max speed on average.
Bogus math on my part. If the object is moving an average speed of 339, that yields an overall contraction somewhere around half an hour, not 3/4 of an hour. The nose at the tail draw about that much closer in the original frame at midtrip.

"If the rear acceleration takes 10 years (measured in local accelerating frame) to get up to say .866c, the front acceleration will take place for 10.866 years to get to that speed iff it ignites and ceases at the same time (object frame) as the rear acceleration."
.866c is essentially light, is it not?
Not sure what you mean. Light is not a speed, even if it has a speed.
.866c is not essentially light speed since the acceleration can continue at the same g force for any amount of time past the 10 years and still not get to "essentially light speed", meaning anybody onboard might notice any difference without looking out of the window.
the object is a light year long, it must travel as a very intense frequency? does it not?
Objects like rocks don't travel at a frequency, intense or otherwise. So no idea what you're talking about here.

"If the rear acceleration takes 10 years (measured in local accelerating frame) to get up to say .866c, the front acceleration will take place for 10.866 years to get to that speed iff it ignites and ceases at the same time (object frame) as the rear acceleration."
.866c is essentially light, is it not?
Not sure what you mean. Light is not a speed, even if it has a speed.
.866c is not essentially light speed since the acceleration can continue at the same g force for any amount of time past the 10 years and still not get to "essentially light speed", meaning anybody onboard might notice any difference without looking out of the window.
the object is a light year long, it must travel as a very intense frequency? does it not?
Objects like rocks don't travel at a frequency, intense or otherwise. So no idea what you're talking about here.
it seems obvious to me that anything traveling at or near the speed of light must adopt the parameters of light.
or else rock would be capable of traveling at the speed of light. nevermind!

DC#146;
1. If you are stationary or moving at constant speed and you assert that the speed of light relative to you from the north is c, if you then accelerate north to a different constant speed, the speed of light relative to you from the north is no longer c. If you want to claim it is now c relative to you, it can not have been c relative to you before.
2. If you want it to be the same speed relative to you for both frames, you need to use a 4D Spacetime model in which the speed for light relative to you in both cases is zero. There is no valid alternative to these options in mathematics.
[1. That's as observed by a second party. In my inertial frame, light speed in space is always c, regardless of my speed. Light speed is independent of its source, i.e. it does not acquire the speed of the source, which differs from material objects.
2. "the speed for light relative to you in both cases is zero.", as observed by ?]
If you start with two ships sitting a mile apart in frame A with one directly ahead of the other and you accelerate them both identically to 0.866c (in the direction they're pointing), they will still be a mile apart in frame A after the acceleration.
[Agree for frame A. In the ship frames, they will measure their separation as .5 miles.]
If I accelerate every atom of a metre long stick to a fraction under c in an instant, those atoms will still be sitting at the same separations after the acceleration  the contraction has not been applied
[A mass cannot be accelerated instantly. Length contraction happens at light speed over microscopic distances (electron cloud), which will be faster than a transfer of energy between particles. The incremental energy transfer will require increasing transit times as it progresses This is also the reason why a material object cannot be accelerated to light speed. It's NOT due to increasing mass.]
If he chooses 2, he is using an absolute frame mechanism, so he's abandoned STR.
[ His conclusion is based on 'he knows SR', and there is no absolute frame, which is the basis for the 'relativity principle'.]
The following quotes from the 1905 paper by the author of SR:
"Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the ``light medium,'' suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest."
"The introduction of a ``luminiferous ether'' will prove to be superfluous inasmuch as the view here to be developed will not require an ``absolutely stationary space'' provided with special properties,"

DC#146;
continued:
There is a major difference. However, if you keep mixing models and imagine that you're doing SR while you're actually mixing LET and SR, then no wonder you're confused. In LET there is an absolute frame. In SR there is not, so you are banned from having time dilation  time cannot dilate for a stationary object, and all objects are stationary in SR
[There is no mixing. It's common knowledge that LET hypothesizes a fixed ether frame that serves as a medium for light Human thinking desires to interpret new things in terms of older established things (supposedly) understood. Government laws may ban certain activities, theories do not.
Time dilation doesn't require an ether or a fixed frame. The effect results from motion, which alters the distance light must move in any EM process. There is no difference. In SR, events don’t move, which is equivalent to a fixed medium.
So who is confused? Have you read any publications on SR?]
Take the twins paradox. Twin A stays at home. Twin B goes away and back, recording less time passing than twin A. Did time dilate? Twin B is not moving according to SR during the first leg, so no  it could not dilate. Twin B is not moving according to SR during the second leg, so again no  it could not dilate. Twin A is also not moving according to SR, so again time did not dilate. You cannot have time dilation without an absolute frame mechanism, and you cannot have multiple absolute frames to switch between whenever it suits you because you are changing the speed of light relative to the content every time you change frame, breaking the rules of the universe where the speed of light is constant through space
[There's one serious misinterpretation (red). SR does not state or imply the red portion. It states postulate 1 as: "the laws of physics are the same for all inertial (constant velocity) frames of reference". This translates to, any inertial frame may serve as a reference. A and B qualify as inertial frames, but still have to consider their relative motion in any measurement process.]
The purpose of the 'twin scenario' is to demonstrate that relative motion causes clocks (EM processes) to run slower relative to a reference clock.
From the 1905 paper, par.4:
"If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be second slow."
The graphic is another 'twin scenario'. It consists of 2 clocks, A and B, moving in separate spaceships to the right. The A path 0 to .4 at .4c and the B path 0 to.8 at .8c.
We examine it from before 1900. The trip time for each is 1.00. If B moved a greater distance than A, in the same time interval, B must have moved faster than A.
Now examine it after 1905, when theory predicts the faster moving clock runs slowest.
The revised conclusion is, the B clock indicates less time than the A clock. If the B clock changes direction to return to A via the 3rd short line, at .8c, its time is still less. All clocks are moving, and therefore all lose time. We only measure the difference. Where the circular arc crosses the vertical distance lines indicates the clock time. At reunion, At=.92 and Bt = .60.
No magic, just a little geometry.]
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If you start with two ships sitting a mile apart in frame A with one directly ahead of the other and you accelerate them both identically to 0.866c (in the direction they're pointing), they will still be a mile apart in frame A after the acceleration.
[Agree for frame A. In the ship frames, they will measure their separation as .5 miles.]
For frame A, the separation is a mile, just like in the beginning. In the frame of the ships, the separation will be 2 miles. David knows his relativity at least this well.
If I accelerate every atom of a metre long stick to a fraction under c in an instant, those atoms will still be sitting at the same separations after the acceleration  the contraction has not been applied
[A mass cannot be accelerated instantly. Length contraction happens at light speed over microscopic distances (electron cloud), which will be faster than a transfer of energy between particles. The incremental energy transfer will require increasing transit times as it progresses This is also the reason why a material object cannot be accelerated to light speed. It's NOT due to increasing mass.]
Well, I agree with the assessment of instant acceleration, but the rest is word salad. If I accelerate every atom of a meter long stick to a fraction under c in a much shorter time than it take light to travel a meter, those atoms will still be sitting at the same separations after the acceleration. The stick will still be a meter long, or 2 meters in the frame of the stick. This is the same concept as the first quote above.

In LET there is an absolute frame. In SR there is not, so you are banned from having time dilation  time cannot dilate for a stationary object, and all objects are stationary in SR
David is known for misquoting relativity when it serves his purposes. This statement is indeed false, and the theory would easily be falsified if it said that.
[There's one serious misinterpretation (red). SR does not state or imply the red portion. It states postulate 1 as: "the laws of physics are the same for all inertial (constant velocity) frames of reference". This translates to, any inertial frame may serve as a reference. A and B qualify as inertial frames, but still have to consider their relative motion in any measurement process.]
I'm on your side on this statement. B is not moving in the frame of B in the first leg, so it is A whose time is dilated in that frame, and likewise for the return leg in that frame, but David's comment omits those frame references.
The graphic is another 'twin scenario'. It consists of 2 clocks, A and B, moving in separate spaceships to the right. The A path 0 to .4 at .4c and the B path 0 to.8 at .8c.
We examine it from before 1900. The trip time for each is 1.00. If B moved a greater distance than A, in the same time interval, B must have moved faster than A.
Now examine it after 1905, when theory predicts the faster moving clock runs slowest.
It is unclear what you are doing. How can time be compared if the two ships are in different places? Such comparisons are very frame dependent. In some different frame, it is A that is twice as fast as the B ship (both moving to the left). There is no objective way to compare which clock is ahead of the other.
Bigger note:
Why is this being discussed in this topic? Open a new one if you want to defend relativity vs. LET or something. You're not contributing to the discussion going on.

[1. That's as observed by a second party. In my inertial frame, light speed in space is always c, regardless of my speed. Light speed is independent of its source, i.e. it does not acquire the speed of the source, which differs from material objects.
That's exactly the point  it doesn't acquire the speed of the source, which means that if the light is coming at you from the north at c relative to you in the first place, it cannot still be coming at you from the north at c relative to you after you've accelerated towards the north. To assert that it is still moving at c relative to you from that direction after the acceleration is to change retrospectively the speed of light relative to you from that direction before the acceleration. That is not legal in mathematics. That is one of the reasons why Minkowski changed STR into a 4D model  he could see that Einstein's original version was mathematically illegal.
2. "the speed for light relative to you in both cases is zero.", as observed by ?
As observed by any competent mathematician who looks at the 4D model.
If you start with two ships sitting a mile apart in frame A with one directly ahead of the other and you accelerate them both identically to 0.866c (in the direction they're pointing), they will still be a mile apart in frame A after the acceleration.
[Agree for frame A. In the ship frames, they will measure their separation as .5 miles.]
No they won't  they'll measure it to be 2 miles. The key point here though is that no contraction is applied in this kind of case.
A mass cannot be accelerated instantly.
Make it near instant and what I said still holds.
Length contraction happens at light speed over microscopic distances (electron cloud), which will be faster than a transfer of energy between particles. The incremental energy transfer will require increasing transit times as it progresses This is also the reason why a material object cannot be accelerated to light speed. It's NOT due to increasing mass.]
Length contraction doesn't happen by magic  it takes time, and it's done by the particles adjusting to correct their relative positions. This certainly will not happen at the speed of light.
If he chooses 2 ["2. Assume he left E in a ship, knows SR, so concludes he is experiencing time dilation."], he is using an absolute frame mechanism, so he's abandoned STR.
His conclusion is based on 'he knows SR', and there is no absolute frame, which is the basis for the 'relativity principle'.
If there is no absolute frame, there can be no time dilation because there is no mechanism to support time dilation. All the clocks are stationary and cannot tick at different rates.
The following quotes from the 1905 paper by the author of SR:
"Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the ``light medium,'' suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest."
They don't suggest anything of the kind. They simply show that the maths of relativity makes it impossible to pin it down.
"The introduction of a ``luminiferous ether'' will prove to be superfluous inasmuch as the view here to be developed will not require an ``absolutely stationary space'' provided with special properties,"
If you're using a model in which light moves through space at c, that requirement demands an absolute stationary space for your light to travel through at c. Without it, you have no means of controlling its speed through space.
The moving twin's clock runs slow > slowed by movement through an absolute frame. (If not slowed by this, cannot be slowed.)
The moving twin's clock takes a shortcut into the future > shortcut only available when moving through an absolute frame. (If not moving, cannot take shortcut.)

There is no mixing. It's common knowledge that LET hypothesizes a fixed ether frame that serves as a medium for light Human thinking desires to interpret new things in terms of older established things (supposedly) understood. Government laws may ban certain activities, theories do not.
Time dilation doesn't require an ether or a fixed frame. The effect results from motion, which alters the distance light must move in any EM process. There is no difference. In SR, events don’t move, which is equivalent to a fixed medium.
So who is confused? Have you read any publications on SR?
I have built models which show that STR doesn't work, and no one in the world has ever built any models in which STR does work  they all cheat by breaking the rules of the model to create the illusion of it working. They bring in an extra kind of time tied to an absolute frame to coordinate the action on different paths and then pretend they haven't done so, but in every single case they have. My models of STR are openly available and have been for a decade. Your side has completely failed to counter them by showing the simplest model that can handle the same action without cheating. A working model of STR is impossible if it works purely on STR's rules. It has to cheat because the model is broken.
The purpose of the 'twin scenario' is to demonstrate that relative motion causes clocks (EM processes) to run slower relative to a reference clock.
And the model doesn't work unless you put an absolute frame into it, so what do you do  you put an absolute frame in and use it to coordinate the action, then you deny that you depend on that absolute frame. Run a simulation of the model to test it properly and you'll see the problem right in front of your eyes  it has an absolute frame which causes the clocks on some paths to run slow. You can't run a simulation without selecting an absolute frame to coordinate the action.

In LET there is an absolute frame. In SR there is not, so you are banned from having time dilation  time cannot dilate for a stationary object, and all objects are stationary in SR
David is known for misquoting relativity when it serves his purposes. This statement is indeed false, and the theory would easily be falsified if it said that.
I'm not misquoting it. I'm telling you what it logically requires when you apply the laws of mathematics to it correctly. You cannot have a clock run slow if it isn't moving, and all objects in STR can be treated as if they aren't moving, so they cannot be running slow. It isn't valid to play games where one of the clocks is still and the other's moving so that the moving one can run slow and then to reanalyse the same event and reverse the assertion about which one's moving in order to make the other clock run slow instead. The only way that mathematics lets you get away with playing that kind of game at all is in the 4D model, but even there you cannot do so in any version with running time (and running causality). Mixing incompatible models is not acceptable.

If you look at the diagram, you see that nothing gets this 'newly acquired high speed' ahead of its allowed contraction. The first atom accelerates far more than the next one, which is essentially still stationary at the first moment no matter how close we put the first atom to the dotted line.
You are now using the caterpillar method for perhaps the first 11 hours of the trip before you get to a point where you have a regular speed distribution in place along the ship.
No idea what you're talking about.
You're moving the atoms at the rear in a manner where they are not at the correct separations for a long time, just like the caterpillar method with an infinite number of waves. You don't have them at the right separations from the ones they're chasing, although they may be at the right separations from the point of view of the member of each pair that's being chased. You only get out of this phase once the correct length contraction on the ship has been achieved.
I've already shown you that it's wrong at the start.
No, you're just asserting it. You've not shown anything. The acceleration of everything is always to the right. No correction is made for inappropriate contraction, so show me that the contraction doesn't match the speed it is going. Use numbers...
I gave you numbers, such as 904km/s for the tail applying for 11 hours to get to the right location to conform to the correct length contraction acting on the ship.
Why does it need to be there in 11 hours?
It doesn't. If you want to, it can take a lot longer than that before you get all your atoms in the right places to conform to the required length contraction on the ship, or alternatively you can move the rear atoms at much higher speed than 904km/s to reduce the 11 hour figure  whichever way you do it, this reveals that your atoms at the back are not in the right places for quite some time after the gun. If you want to reduce that time, then you have to use higher and higher speeds for the rear end to make the correction, and the extra energy they're carrying will then need to be scrubbed off to avoid your egg being smashed by a hammer.
The contraction will be a lot more than 36M km. I think that was perhaps a guess on your part, but we have 27.6 days of the rear moving faster than the front to allow it to reduce the separation of the two, so it does it in 27.6 days, not 11 hours. No need for anything to move at 904.
I think a simulation's going to be needed to make it clear what's going on and which rules are being bent when. It's just too inefficient trying to discuss it in the air.
Another thing I don't understand. All atoms everywhere accelerate at a finite c²/D, and decelerate at c²/D' (where D and D' are distances to points in space arbitrarily close to the start event at the rear and beyond the finish event at the nose, respectively). Since all atoms have finite acceleration and deceleration, they're all treated identically. No special rules for any point.
The issue is with how you get the ship to conform to the correct amount of length contraction so that there are no stresses on it. As soon as it starts moving, it's too long to be comfortable, and it takes a long time to correct that.

You are now using the caterpillar method for perhaps the first 11 hours of the trip before you get to a point where you have a regular speed distribution in place along the ship.
No idea what you're talking about.
You're moving the atoms at the rear in a manner where they are not at the correct separations for a long time, just like the caterpillar method with an infinite number of waves.
This is getting old. They're at correct separations at all times. They're at the correct separation in the caterpillar method as well, except at the singularity, where separation is bounded but undefined.
You don't have them at the right separations from the ones they're chasing, although they may be at the right separations from the point of view of the member of each pair that's being chased.
If the two atoms are moving at different speeds, you need to integrate the motion between them (which is the same as adding more atoms). If you will not do this, then the contraction between the two atoms moving at different speeds is bounded by the contractions for the two speeds in question. If it falls between those two bounds, it is no strain, to the precision of one atom. As you add atoms, those those bounds approach each other.
I gave you numbers, such as 904km/s for the tail applying for 11 hours to get to the right location to conform to the correct length contraction acting on the ship.
My object never moves that fast. Show where the separation is wrong at any point along its length at time X. You're seemingly claiming that it takes 11 hours for one atom to catch up with the nearly stationary one right in front of it.
At what point in time is the separation wrong? What separation exists (between which two points) at that time, and what should it be if there is to be no strain? It takes 27.6 days to achieve maximum contraction. That is far longer than 11 hours, so we have plenty of time to move both ends.
I think a simulation's going to be needed to make it clear what's going on and which rules are being bent when. It's just too inefficient trying to discuss it in the air.
Fine. A simulation will do since it will show the numbers.
The issue is with how you get the ship to conform to the correct amount of length contraction so that there are no stresses on it. As soon as it starts moving, it's too long to be comfortable, and it takes a long time to correct that.
As soon as it starts moving, it is still essentially still stopped everywhere except possibly the tail (depending on how far back that arbitrarily close point is). It has no contraction except at the hindmost bit. So it hardly has changed in overall length, and doesn't need to because it is almost entirely still stopped.
We're talking in air as you say. I see it always being the exact correct length. It's not like I'm the first one to do the mathematics behind it. Where do you think that picture came from?
The wave method is another thing. I've found no sites that describe that sort of motion. I'm seemingly on my own.

I have built models which show that STR doesn't work, and no one in the world has ever built any models in which STR does work  they all cheat by breaking the rules of the model to create the illusion of it working. They bring in an extra kind of time tied to an absolute frame to coordinate the action on different paths and then pretend they haven't done so, but in every single case they have. My models of STR are openly available and have been for a decade. Your side has completely failed to counter them by showing the simplest model that can handle the same action without cheating. A working model of STR is impossible if it works purely on STR's rules. It has to cheat because the model is broken.
I have no associations with science organizations. You might submit your work to an established research center to make them aware of your models.

I gave you numbers, such as 904km/s for the tail applying for 11 hours to get to the right location to conform to the correct length contraction acting on the ship.
My object never moves that fast. Show where the separation is wrong at any point along its length at time X. You're seemingly claiming that it takes 11 hours for one atom to catch up with the nearly stationary one right in front of it.
The 11 hours (which relates to a lowend guess at the amount of contraction over the whole ship once the back end starts moving) is for how long that rear atom has to move at double the speed it's supposed to be moving at before your ship begins to be the right length. It was the right length before the gun when the whole thing was stationary, but as soon as the back end started moving (and not just the back end, because most of the ship instantly starts moving), it's no longer the right length for the contraction which should be applying to it. A simulation would make that clear, but I don't have time to write one for it now and would rather wait until I have built the right tools to be able to build it in a fraction of the time. All I'm trying to do in the meantime is point out places where your ship isn't functioning in accordance with the rules you claim it conforms to. No one will die though if you don't want to recognise that until there's a simulation that makes it plain, so it isn't important.
As soon as it starts moving, it is still essentially still stopped everywhere except possibly the tail (depending on how far back that arbitrarily close point is). It has no contraction except at the hindmost bit. So it hardly has changed in overall length, and doesn't need to because it is almost entirely still stopped.
I didn't think it was only the back of the ship that you're moving. You have the back moving at 452 and the front at 0, so I assumed the middle would be doing some speed in between the two and moving at the same seed as that at the finish. When does the middle start and stop moving? Most of the contraction that I'm guessing will apply to the ship will apply towards the back end where the speed is highest, and I still think it will likely involve 11 hours to get the rear atom into the right place with it moving at double speed to get there. That is a significant issue. It may be a small change in overall length, but with your ship spread out across a hundred lightyears, it adds up to a big difference for the sections at the back which span multiple lightyears.
We're talking in air as you say. I see it always being the exact correct length. It's not like I'm the first one to do the mathematics behind it. Where do you think that picture came from?
I would assume that you've taken the idea from a place where it doesn't start with the whole thing stationary and then suddenly have the back end moving at speed with the wrong length contraction on it.

I have no associations with science organizations. You might submit your work to an established research center to make them aware of your models.
I considered writing it up for a science journal, but I assumed I would just be ignored due to my lack of the right qualifications and the difficulty of showing things on paper without software, so I've simply communicated directly with people on science forums where I have discussed things with dozens of professional physicists (who are universally irrational when it comes to Einstein's models). However, I looked into it carefully a couple of years ago and found that they don't actually have to see who you are, and you can include software, so it is an option, but I still have every expectation that they simply wouldn't bother to look at it as soon as they see what is claimed, which means preparing a new text for them and versions of the software that don't run in JavaScript or in machine code on top of my own operating system would be a terrible waste of effort, and a costly one in terms of delays to something much more important.

The 11 hours (which relates to a lowend guess at the amount of contraction over the whole ship once the back end starts moving)
If only the back end is moving at any significant speed, only the back end needs to contract. The rest is still essentially stopped, and it would be quite the strain if it were to contract at that point already.
You seem to be under the impression that I'm accelerating all parts equally. You know that you can't do that with a rigid object.
as soon as the back end started moving (and not just the back end, because most of the ship instantly starts moving)
Moving, yes, but still at zero speed to an awful lot of digits. You've given no time, so I'm taking the moment in time that the rear finishes acceleration and has hit 452 km/s. At that moment, any point not at the absolute rear is still stationary to arbitrary precision, depending on how close you put D. At zero speed, it requires zero contraction.
A simulation would make that clear
Indeed it would.
All I'm trying to do in the meantime is point out places where your ship isn't functioning in accordance with the rules you claim it conforms to.
You haven't done that. You're claiming that a stationary object needs to contract which is just plain wrong. If you think it isn't stationary (to arbitrary precision), then you haven't applied or understood my acceleration curve of c²/D. Only the very rear is moving, and thus only that rear arbitrarily small segment needs to contract a tiny bit, which it does when the rear moves.
I didn't think it was only the back of the ship that you're moving. You have the back moving at 452 and the front at 0, so I assumed the middle would be doing some speed in between the two and moving
As I suspected, you didn't apply my rule at all. You just assume wrong things. If we make D a meter behind the object (we can put it a lot closer), then the rear accelerates at c²/D or 9e16 / 1 = 9e16 m/sec² so it takes about 5e12 seconds to get up to max speed. The front accelerates at 9e16 / 9.5e17 = 0.095 m/sec or a bit less than 1% of a g. After that tiny fraction of a second, it is still stopped to over 20 digits. The middle accelerates at 9e16 / 4.7e17 or a bit less than 2% of a g. It is also stopped still, not at all moving at some pace half way between the front and rear as you assumed.
How about a point almost at the rear, say 1km in? That would accelerate at 9e16 / 1000 = 9e13 m/sec² which is some pretty impressive acceleration until you do it for only 5e12 seconds and find that its speed is 452 m/sec and has moved about a nanometer. That last km of object has contracted by somewhat more than 1 micron.
The contraction for a km object moving at 452 m/sec is about 1.1 nm, but the object is moving faster than 452 in points between. So 1 microns is between the bound of 1.1 nm and the 1.1 mm contraction needed if the whole km segment was moving at full speed. If you want to compute the contraction more accurately than to the millimeter, cut the km into smaller segments and integrate your way through it. Or put D a bit further back.
When does the middle start and stop moving?
All points start at the same time, and finish at the same time. Not so with the caterpillar method.
I computed the acceleration rate of the middle above. That acceleration commences immediately.
I would assume that you've taken the idea from a place where it doesn't start with the whole thing stationary and then suddenly have the back end moving at speed with the wrong length contraction on it.
It assumes the whole thing stationary, and all parts accelerating continuously forever. I had to make modifications to get it to stop at the desired place. It doesn't specify how far away the rear is from D. It doesn't matter. For the back to move suddenly at speed, it needs to be right next to D (the point at lower left in the picture).

I am running into all sorts of troubles with the wave method using lots of small waves.
Sure, the thing gets faster with smaller waves, but it also approaches the 55 day solution.
So I went back here in search of an error:
...
while (speedK < speedK10)
{
speedC = speedK / 300000.; // Compute speed as fraction of c
factorD = sqrt(1  speedC * speedC); // Lorentz contraction
tDmov = kmLH / speedK / SpD; // Days to move 1 LH at that speed
tDwav = 36500 * (1.  factorD); // Wave time: 36500 light day ship len
...
Oopsie: That last line is supposed to compute wave time. The 36500 converts 100 LY to light days, but it computes distance, not time. So I'm calculating the time it takes light to move the contraction distance, not the time it takes the object (moving at speedK) to move that distance.
The whole wave thing is back on the floor. I don't think it is competitive with the original 55 day method.

A simulation would make that clear
Mind you, I have yet to run any sort of simulation. I've computed times and answers to some of your questions, but never using a simulation. The 55.3 day time was a pretty trivial computation and did not involve iteration or simulation. Just one Lorentz calculation.

Updated calculation for the singlewave method of moving the object, which involves a singularity.
I corrected the code in post 88 as far as I can tell, but nobody found the first bug, so nobody is probably going to find bugs with this new version.
// Time units in hours.
// Input speed in km/sec, but calculations take place as fraction of c
#include <stdio.h>
#include <math.h>
#define SoL 299792.46 // speed of light, km/sec
#define lenLH 876600. // hours in a century, len of object in LH
int main(int ac, char **av)
{
double factorD, // lorentz factor (down)
speedC, // speed as fraction of c
speedK, // input speed in km/sec
speedK10, step, // range limit km/sec
tHmov, tHwav; // time in hours
sscanf(*++av, "%lf", &speedK); // km/sec, but we convert to hrs
sscanf(*++av, "%lf", &speedK10);
step = (speedK10speedK)/10.0;
speedK10 += step/3;
while (speedK < speedK10)
{
speedC = speedK / SoL; // Compute speed as fraction of c
factorD = sqrt(1  speedC * speedC); // Lorentz contraction
tHmov = 1. / speedC; // Hours to move 1 LH at that speed
tHwav = lenLH * (1.  factorD) / speedC; // Hours to move contraction len
printf("S %.2f T %.9f W %.9f = %.9f \n", // Print in km/sec, days
speedK, tHmov/24, tHwav/24, (tHmov+tHwav)/24);
speedK += step;
}
return 0;
}
The sweet spot is still near 450 km/sec, same as the continuous acceleration optimal speed.
Interestingly, it takes half the time to move the object at that speed, and the other half of the time for the wave to move the 100 light years. Here is one run:
> caterpillar 350 550
S 350.00 T 35.689578571 W 21.321007134 = 57.010585706
S 370.00 T 33.760412162 W 22.539351300 = 56.299763462
S 390.00 T 32.029108974 W 23.757695620 = 55.786804594
S 410.00 T 30.466713415 W 24.976040097 = 55.442753511
S 430.00 T 29.049656977 W 26.194384738 = 55.244041714
S 450.00 T 27.758561111 W 27.412729556 = 55.171290667
S 470.00 T 26.577345745 W 28.631074559 = 55.208420304
S 490.00 T 25.492556122 W 29.849419750 = 55.341975873
S 510.00 T 24.492848039 W 31.067765143 = 55.560613182
S 530.00 T 23.568589623 W 32.286110742 = 55.854700364
S 550.00 T 22.711550000 W 33.504456555 = 56.216006555
Fastest time is at 452.83 km/sec, taking about 55 days and 4 hours, shorter by a smidge than the inertial method.
Perhaps this is because I used a more correct speed of light than the round 300000 figure, but slower light speed would seem to make things a bit slower, not faster.