[yor_on]

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.

[Halc (OP)]

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.

[yor_on]

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

[Halc (OP)]

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 born-rigid ship that is 100 light years long, and we wish to move that ship a distance of 1 light-hour (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 light-year 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 instant-acceleration 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 light-hour.  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 death-grip 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 light-year, and yet I can move my meter-stick 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 light-year 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 length-marks 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 middle-frame 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 atom-by-atom 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 space-like manner.
By the same argument, that force (stress/strain) admittedly cannot exist during an instantaneous direction-change.  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 speed-of-light 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.

[Halc (OP)]

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 super-low 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.

[David Cooper]

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 two-atom "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 greater-than-zero 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 length-marks 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 space-like 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 whole-ship 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 longer-than-zero 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.

[yor_on]

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 :)

[Halc (OP)]

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 two-atom "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 Born-rigid 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 non-infinite 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 infinite-acceleration 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 light-hour 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 whole-ship 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 finite-acceleration 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.

[PmbPhy]

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.

[Halc (OP)]

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.

[David Cooper]

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 beyond-microscopic 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 non-infinite 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 infinite-acceleration 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 atom-to-atom 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 differently-contracted 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.

[Halc (OP)]

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 infinite-acceleration 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 atom-to-atom 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 rear-most piece stays the same proper distance from it at all times.

[Halc (OP)]

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.

[yor_on]

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.

[Halc (OP)]

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 Born-rigid 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.

[yor_on]

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.

[David Cooper]

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 GR-approved 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 rear-most 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 GR-approved 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.

[Halc (OP)]

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 GR-approved 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.

[David Cooper]

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 semi-reasonable 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 event-meshing 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 practically-halted 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.

[guest4091]

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. 
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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 g-force will not be uniform for its length, resulting in deformation.

May the Farce be with you.

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