[Halc (OP)]

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/rail-guns 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 space-like 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 strain-free 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.

[Bored chemist]

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

How?

[Halc (OP)]

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.

[alancalverd]

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 high-revving engines.

[Bored chemist]

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.

[Halc (OP)]

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 high-revving 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 thread-breaking topic in the new-theories 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 micro-compensation for it.

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.

[yor_on]

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 :)

[yor_on]

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.
=

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?

[Bored chemist]

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.

[Janus]

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

[Halc (OP)]

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 5.
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, as per Bell's spaceship 'paradox'.

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?

[Bored chemist]

I had replied (with a reference) in post 9.

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).

[Halc (OP)]

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.

[Bored chemist]

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.

[Halc (OP)]

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.

[alancalverd]

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?

[Bored chemist]

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.

[jeffreyH]

Ok so you have a ship 1 light-year 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?

[Halc (OP)]

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.

[Bored chemist]

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.