# Lorentz contraction

## Main Question or Discussion Point

I think I am correct in saying that Lorentz relativity and standard SR are experimentally indistinguishable. I think it is also the case that in the first, the space between objects does not contract while in the second evrything inclding space contracts pro rata. As a personal choice I prefer standard SR. Its simpler.

Reading up on Bell's standard spaceship paradox in wiki and other places, I see quite a heated argument and some physicists being accused of some basic misunderstandings. To cut a long story short, one of the arguments is that in one formulation the string breaks and in the other it does not, because space does not contract in one but it does in the other. Now if this argument was valid would it not be possible experimentally to decide between the two formulations.

I have always understood that the formulations are not distinguishable and see no reason to change my mind. So someones argument is wrong. Can anyone correct my suppositions or enlighten me in any other way.

Matheinste.

## Answers and Replies

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Doc Al
Mentor
Reading up on Bell's standard spaceship paradox in wiki and other places, I see quite a heated argument and some physicists being accused of some basic misunderstandings. To cut a long story short, one of the arguments is that in one formulation the string breaks and in the other it does not, because space does not contract in one but it does in the other. Now if this argument was valid would it not be possible experimentally to decide between the two formulations.
I don't quite understand the controversy. In Bell's paper, if I recall correctly, he shows that the string breaks using the Lorentz approach. It certainly breaks according to standard SR.

Dale
Mentor
I think I am correct in saying that Lorentz relativity and standard SR are experimentally indistinguishable.
Yes, they are indistinguishable, they both use the Lorentz transform to make their predictions.

I don't quite understand the controversy. In Bell's paper, if I recall correctly, he shows that the string breaks using the Lorentz approach. It certainly breaks according to standard SR.
DocAl

Thanks for you quick response. The arguments were mostly on the discussion page of the Wiki entry. I will take a longer, closer look and perhaps I can learn even from the incorrect ones. While I am hardly conversant with the subject, I have always found it surprsing that there have been differing opinions. If you stick by the postulates and physical laws and use logic, surely there is no room for controversy. I must say that some of the discussions seem quite heated and almost personal.

DaleSpam. Thanks also.

Matheinste.

atyy
Meir Achuz
Homework Helper
Gold Member
I think Bell claims that the distance between the ships does not change, but a rope connecting them gets shorter. That is wrong.

I think Bell claims that the distance between the ships does not change, but a rope connecting them gets shorter. That is wrong.
So it would break. So do you think Bell is correct for the wrong reasons?

My reading in the last couple of days leads me to conclude that the string breaks. Whether it breaks or not was initially of no interest to me. What was of interest was how such a proposed scenario could result in opposite outcomes when analysed by physicists who knew their subject. Perhaps I made the mistake of including some of the contributors to the discussion page of the Wiki entry on Bell's paradox in that category. However, I have learnt a lot from it.

Matheinste.

So it would break. So do you think Bell is correct for the wrong reasons?

My reading in the last couple of days leads me to conclude that the string breaks. Whether it breaks or not was initially of no interest to me. What was of interest was how such a proposed scenario could result in opposite outcomes when analysed by physicists who knew their subject. Perhaps I made the mistake of including some of the contributors to the discussion page of the Wiki entry on Bell's paradox in that category. However, I have learnt a lot from it.

Matheinste.
This is the standard on the paradox.
http://www.mathpages.com/home/kmath422/kmath422.htm

If I read it correctly though, the equations assume the string is pulled by the forward ship. What I do not see in the equations is the corresponding push by the accelerating ship from behind.

Also, here are some excellent papers on calculating the integral for constant acceleration.

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken]
http://arxiv.org/PS_cache/physics/pdf/0411/0411233v1.pdf
http://www.ejournal.unam.mx/rmf/no521/RMF52110.pdf

I simply cannot see why the string will break though that is what most folks think.

If the perspective of the launch frame is utilized and the accelerations are perfectly the same, the launch frame applies the acceleration equations and sees the distance between the ships maintained perfectly.

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JesseM
I simply cannot see why the string will break though that is what most folks think.

If the perspective of the launch frame is utilized and the accelerations are perfectly the same, the launch frame applies the acceleration equations and sees the distance between the ships maintained perfectly.
But the electromagnetic forces between atoms in the string will be constantly changing, increasing the tension in the string until it reaches the breaking point. This should be true even if you analyze things wholly in the launch frame, although the details of such a calculation would be beyond me. Still, it's obvious they must change--just think of the case of two identical springs, one at rest in the launch frame and one moving at relativistic velocity, the equilibrium length of the fast-moving spring must be shorter than the equilibrium length of the spring that's at rest in this frame, due to Lorentz contraction. If there were no change in electromagnetic force between atoms as a function of distance in the launch frame, then the two springs would have the same equilibrium spacing between atoms in this frame and therefore the same equilibrium length.

But the electromagnetic forces between atoms in the string will be constantly changing, increasing the tension in the string until it reaches the breaking point. This should be true even if you analyze things wholly in the launch frame, although the details of such a calculation would be beyond me. Still, it's obvious they must change--just think of the case of two identical springs, one at rest in the launch frame and one moving at relativistic velocity, the equilibrium length of the fast-moving spring must be shorter than the equilibrium length of the spring that's at rest in this frame, due to Lorentz contraction. If there were no change in electromagnetic force between atoms as a function of distance in the launch frame, then the two springs would have the same equilibrium spacing between atoms in this frame and therefore the same equilibrium length.
I agree, the front part of the string will be pulled and the back part will be pushed.

Equilibrium will occur in the middle.

If it breaks, it would be on the front ship side between the middle and the front.

But, the launch frame in and of itself presents a problem.

For all t, the equations predict if d is the initial distance between the ships, then d wil be the distance for the ships during the acceleration.

You can see this in the links to the papers I presented by calculating x after any burntime in the proper time of the launch frame given a constant acceleration.

JesseM
But, the launch frame in and of itself presents a problem.

For all t, the equations predict if d is the initial distance between the ships, then d wil be the distance for the ships during the acceleration.
But why do you think this presents a problem? Presumably a detailed calculation of the inter-atomic forces inside the string done from the perspective of the launch frame would show that these forces depend on the velocity of the atoms as well as their distance, so that the tension in the string can be continually increasing even if the length (and the average spacing between atoms) remains constant.

But why do you think this presents a problem? Presumably a detailed calculation of the inter-atomic forces inside the string done from the perspective of the launch frame would show that these forces depend on the velocity of the atoms as well as their distance, so that the tension in the string can be continually increasing even if the length (and the average spacing between atoms) remains constant.
Yea, I think of it another way and only from the front ship side.

Given any segment of the string, there exists a "gravity" potential difference between the side toward the front and the side toward the back.

Hopefully you agree the back side is not in play because of the reverse gravity potential difference.

Therefore, there exists a constant distance for the string to operate but a difference in gravity potentials given any segment of the string.

Now, the original solution claims the string stretches and then breaks without considering the back side and thus the distance between the ships apparently increases.

I would therefore say, it needs to be decided with this stretching in the front part, because of the gravity differential, what the maximum stress on the string will be.

Therefore, unless this string is of perfect rigidity, it is not decidable if it will break.

JesseM
Yea, I think of it another way and only from the front ship side.

Given any segment of the string, there exists a "gravity" potential difference between the side toward the front and the side toward the back.
Gravity? This is an SR problem...are you talking about a fictitious force in an accelerating frame? I thought you wanted to analyze things from the inertial launch frame.
cfrogue said:
Hopefully you agree the back side is not in play because of the reverse gravity potential difference.

Therefore, there exists a constant distance for the string to operate but a difference in gravity potentials given any segment of the string.
Since I don't understand what you mean by "gravity" none of this makes any sense to me.
cfrogue said:
Now, the original solution claims the string stretches and then breaks without considering the back side and thus the distance between the ships apparently increases.
What do you mean "without considering the back side"? The distance only increases if you analyze things from the perspective of either ship's instantaneous inertial rest frame at different moments, the distance in the instantaneous rest frame will be increasing regardless if you are looking at the instantaneous rest frame of the back or the front (or of some segment of string in the middle).
cfrogue said:
Therefore, unless this string is of perfect rigidity, it is not decidable if it will break.
Since your analysis seems to be based on some hard-to-follow conceptual picture and not on any math, and physicists who have done the math all agree the string will break, this suggests that there must be some error in your thinking. If you want help trying to understand where your conceptual picture goes wrong we can discuss that, but this forum is not the place to advance original ideas which contradict mainstream thinking.

Gravity? This is an SR problem...are you talking about a fictitious force in an accelerating frame? I thought you wanted to analyze things from the inertial launch frame.

Since I don't understand what you mean by "gravity" none of this makes any sense to me.

What do you mean "without considering the back side"? The distance only increases if you analyze things from the perspective of either ship's instantaneous inertial rest frame at different moments, the distance in the instantaneous rest frame will be increasing regardless if you are looking at the instantaneous rest frame of the back or the front (or of some segment of string in the middle).

Pages 8 and 9 indicate a well known equivalence between acceleration and gravity.

Since your analysis seems to be based on some hard-to-follow conceptual picture and not on any math, and physicists who have done the math all agree the string will break, this suggests that there must be some error in your thinking. If you want help trying to understand where your conceptual picture goes wrong we can discuss that, but this forum is not the place to advance original ideas which contradict mainstream thinking.
Not true, CERN's theory division asserted the string would not break.

Objections and counter-objections have been published to the above analysis. For example, Paul Nawrocki suggests that the string should not break,[3] while Edmond Dewan defends his original analysis from these objections in a reply.[4] Bell reported that he encountered much skepticism from "a distinguished experimentalist" when he presented the paradox. To attempt to resolve the dispute, an informal and non-systematic canvas was made of the CERN theory division. According to Bell, a "clear consensus" of the CERN theory division arrived at the answer that the string would not break

All this emphasises my point. With such levels of disagreement, quote and counter quote, reference and counter reference do not help or give any learners confidence in the answers. A clear and carefully presented analysis should speak for itself. The answer cannot depend on who we care to believe.

Break or not break is a discusson I would not get involved in. With such "eminent" names being cited as references with different conclusions no-one would, or should, take notice of anything someone at my level has to say.

Matheinste.

JesseM

Pages 8 and 9 indicate a well known equivalence between acceleration and gravity.
But the pseudo-gravitational force only appears in an accelerating coordinate system, there is no such force observed in an inertial coordinate system like the launch frame. In any case, you really need to explain your ideas in more detail, I still have no idea what you mean by phrases like "without considering the back side" or "reverse gravity potential".
cfrogue said:
Not true, CERN's theory division asserted the string would not break.

Objections and counter-objections have been published to the above analysis. For example, Paul Nawrocki suggests that the string should not break,[3] while Edmond Dewan defends his original analysis from these objections in a reply.[4] Bell reported that he encountered much skepticism from "a distinguished experimentalist" when he presented the paradox. To attempt to resolve the dispute, an informal and non-systematic canvas was made of the CERN theory division. According to Bell, a "clear consensus" of the CERN theory division arrived at the answer that the string would not break
This sounds like it was just an informal canvas in which physicists were asked for their initial reaction to hearing the paradox, much like the different reactions of physicists to hearing Feynman's underwater sprinkler puzzle. You cut out the part where Bell added "Of course, many people who get the wrong answer at first get the right answer on further reflection", and this paper says on p. 11 that "Though many of Bell's CERN colleagues originally thought the thread would not break, it is now universally agreed that it, indeed, will." And this paper on the paradox notes on p.4 that "stress is an absolute (frame-independent) physical quantity, which is represented by a tensor". So I'm pretty confident you wouldn't find any peer-reviewed papers disagreeing with the claim that the stress in the string will continually increase as the ships accelerate--the references to the papers by Dewan and Nawrocki are impossible to judge without seeing the details of these papers, but this abstract of another paper refers to the existence of a special case of the Dewan's thought-experiment where the string never breaks, suggesting Dewan might agree that in other cases where the distance is constant in the launch frame it would break (perhaps the special case could be one where the stress in the string increases but in a way that approaches a finite limit instead of increasing without bound, so that if the string was strong enough to withstand the stress of that limit it would never break?)

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Al68
I think I am correct in saying that Lorentz relativity and standard SR are experimentally indistinguishable. I think it is also the case that in the first, the space between objects does not contract while in the second evrything inclding space contracts pro rata.
Assuming that the distance between two objects would be equal to the length of a rope stretched between them, what is the difference between "length contraction" and "space contraction"? It seems to me that if the "space between objects does not contract" then a rope stretched between them would not be contracted either.

It's not like a rope would stretch between two objects in their rest frame, but only reach part way as viewed from a different frame, because the rope contracted while the distance between the objects didn't.

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But the pseudo-gravitational force only appears in an accelerating coordinate system, there is no such force observed in an inertial coordinate system like the launch frame. In any case, you really need to explain your ideas in more detail, I still have no idea what you mean by phrases like "without considering the back side" or "reverse gravity potential".
Obviously, I was talking about the instantaneous frame of the rockets. And, these are not my ideas. The description of the rope I as talking about was from this link.

Consider a uniform distribution of particles at rest along some segment of the x axis of an inertial coordinate system x,t at the time t = 0. Each particle is subjected to a constant proper acceleration (hyperbolic motion) such that, with respect to its instantaneously co-moving inertial rest frames, the distances to each of the other particles remain constant
http://www.mathpages.com/home/kmath422/kmath422.htm

This sounds like it was just an informal canvas in which physicists were asked for their initial reaction to hearing the paradox, much like the different reactions of physicists to hearing Feynman's underwater sprinkler puzzle. You cut out the part where Bell added "Of course, many people who get the wrong answer at first get the right answer on further reflection", and this paper says on p. 11 that "Though many of Bell's CERN colleagues originally thought the thread would not break, it is now universally agreed that it, indeed, will." And this paper on the paradox notes on p.4 that "stress is an absolute (frame-independent) physical quantity, which is represented by a tensor". So I'm pretty confident you wouldn't find any peer-reviewed papers disagreeing with the claim that the stress in the string will continually increase as the ships accelerate--the references to the papers by Dewan and Nawrocki are impossible to judge without seeing the details of these papers, but this abstract of another paper refers to the existence of a special case of the Dewan's thought-experiment where the string never breaks, suggesting Dewan might agree that in other cases where the distance is constant in the launch frame it would break (perhaps the special case could be one where the stress in the string increases but in a way that approaches a finite limit instead of increasing without bound, so that if the string was strong enough to withstand the stress of that limit it would never break?)

Well, the article did not state that CERN changed its mind. Further, I am not in a position to claim that CERN would look at a problem casually.

Finally, there is no literature that I am aware of that says CERN backed away from its decision on the rope.

Here is the x for constant acceleration.
It is in the links I posted.
x(t) = c^2/a ( sqrt( 1 + (a t/c)^2 ) -1 )

Now, by adding 0, ie choosing the back back to initialize at 0 and x0 for the front rocket, you can readily see the x(t) is based only on a and t from the launch frame. Thus, the launch frame will not see a deviation with the distance between the rockets.

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All this emphasises my point. With such levels of disagreement, quote and counter quote, reference and counter reference do not help or give any learners confidence in the answers. A clear and carefully presented analysis should speak for itself. The answer cannot depend on who we care to believe.

Break or not break is a discusson I would not get involved in. With such "eminent" names being cited as references with different conclusions no-one would, or should, take notice of anything someone at my level has to say.

Matheinste.
I was aware of the fracture for solving this problem.

I gave both sides to the problem, one by doing the integral in the instantaneous frame of the rockets and rope here
http://www.mathpages.com/home/kmath422/kmath422.htm

And, the other by viewing the problem from the launch frame using the constant acceleration equations of SR here
http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken]
http://arxiv.org/PS_cache/physics/pdf/0411/0411233v1.pdf
http://www.ejournal.unam.mx/rmf/no521/RMF52110.pdf

Then, I began analyzing the problem but Jesse does not want me to so I am going to stop.

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I was aware of the fracture for solving this problem.

I gave both sides to the problem, one by doing the integral in the instantaneous frame of the rockets and rope here
http://www.mathpages.com/home/kmath422/kmath422.htm

And, the other by viewing the problem from the launch frame using the constant acceleration equations of SR here
http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken]
http://arxiv.org/PS_cache/physics/pdf/0411/0411233v1.pdf
http://www.ejournal.unam.mx/rmf/no521/RMF52110.pdf

Then, I began analyzing the problem but Jesse does not want me to so I am going to stop.
Hello cfrogue,

I can asure you that my remarks were not aimed at you personally. I was commenting generally on the confusion amomg people, many of which I assume, are well versed in relativity.

My position is that from what I have read I believe that the correct answer is that the string breaks. However, I am as yet not confident in my ability to explain the reasons to anyone else, which of course is the acid test of understanding. I am also aware that there are variations on the scenario and so we may not all be singing from the same songbook.

Matheinste.

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JesseM
Obviously, I was talking about the instantaneous frame of the rockets.
That wasn't too obvious, because earlier you had suggested you wanted to focus on the launch frame when you said: "But, the launch frame in and of itself presents a problem." And "instantaneous frame of the rockets" is still too vague, the instantaneous frame at any given instant is an inertial frame so there will be no gravitational force in this frame, I think what you really mean is an accelerating frame whose definitions of distance and simultaneity at each moment match those of the instantaneous inertial frame at the same moment.
cfrogue said:
And, these are not my ideas.
I never suggested the idea of gravity in an accelerating frame was "your idea", but it is your own reasoning that leads you to the conclusion there is some doubt about whether the string breaks, since you have not pointed to any papers that mirrored your argument that the original paper failed to consider the "back side" (and you still haven't explained what you meant by that phrase), or that there is any disagreement among physicists that the string will break in the standard version of the problem.
cfrogue said:
Well, the article did not state that CERN changed its mind. Further, I am not in a position to claim that CERN would look at a problem casually.

Finally, there is no literature that I am aware of that says CERN backed away from its decision on the rope.
You're talking as though "CERN" as an institution issued some official position about the rope not breaking, but this is obviously not the case--the article clearly states that Bell just took an "informal and non-systematic" poll of his colleagues at CERN, and that most of them thought it wouldn't break. He adds that many of them changed their mind (i.e. 'backed away from their decision') after further reflection, and I also quoted a paper that said "Though many of Bell's CERN colleagues originally thought the thread would not break, it is now universally agreed that it, indeed, will."

If you think there is any dispute among modern physicists about what would happen in this thought-experiment, you need to post some actual peer-reviewed literature, not a reference to an informal poll taken back when the idea was totally new. I am quite confident that there is no actual dispute about the fact that the stress increases, although as I said there could be types of accelerations where the stress increases but the string doesn't break (maybe because in certain types of accelerations the stress would approach a fixed limit rather than increasing without bound).
cfrogue said:
Here is the x for constant acceleration.
It is in the links I posted.
x(t) = c^2/a ( sqrt( 1 + (a t/c)^2 ) -1 )

Now, by adding 0, ie choosing the back back to initialize at 0 and x0 for the front rocket, you can readily see the x(t) is based only on a and t from the launch frame. Thus, the launch from will not see a deviation with the distance between the rockets.
Neither I nor anyone else on this thread has disputed the claim that the distance will remain constant in the launch frame if both ships have the same coordinate acceleration in this frame. Again, the point is that the stress in the string will be continually increasing even though its length in the launch frame is remaining constant.

Assuming that the distance between two objects would be equal to the length of a rope stretched between them, what is the difference between "length contraction" and "space contraction"? It seems to me that if the "space between objects does not contract" then a rope stretched between them would not be contracted either.

It's not like a rope would stretch between two objects in their rest frame, but only reach part way as viewed from a different frame, because the rope contracted while the distance between the objects didn't.
I think that the in LET the space between solid objects is considered not to contract and the contraction of solid objects is due to stresses or other effects between the interatomic forces. There are of course all the other complications with local time etc. required to make the theory work. In Einsteins' formulation everything contracts.

The reason I asked for confirmation of this is that some commentators on the paradox claim that the break/non-break outcomes are a result of the two differing approaches. I believe that the differing outcomes are due to faulty reasoning on the part of one side or the other. If the claims of those commentators are correct, then there would be an experimental method to decide between the formulations. If the two formulations are generally accepted, by proponents of both formulations , to be experimentally induistinguishable I would consider such claims for the reasons of the differring outcomesto be invalid.

Matheinste.

That wasn't too obvious, because earlier you had suggested you wanted to focus on the launch frame when you said: "But, the launch frame in and of itself presents a problem." And "instantaneous frame of the rockets" is still too vague, the instantaneous frame at any given instant is an inertial frame so there will be no gravitational force in this frame, I think what you really mean is an accelerating frame whose definitions of distance and simultaneity at each moment match those of the instantaneous inertial frame at the same moment.

I never suggested the idea of gravity in an accelerating frame was "your idea", but it is your own reasoning that leads you to the conclusion there is some doubt about whether the string breaks, since you have not pointed to any papers that mirrored your argument that the original paper failed to consider the "back side" (and you still haven't explained what you meant by that phrase), or that there is any disagreement among physicists that the string will break in the standard version of the problem.

You're talking as though "CERN" as an institution issued some official position about the rope not breaking, but this is obviously not the case--the article clearly states that Bell just took an "informal and non-systematic" poll of his colleagues at CERN, and that most of them thought it wouldn't break. He adds that many of them changed their mind (i.e. 'backed away from their decision') after further reflection, and I also quoted a paper that said "Though many of Bell's CERN colleagues originally thought the thread would not break, it is now universally agreed that it, indeed, will."

If you think there is any dispute among modern physicists about what would happen in this thought-experiment, you need to post some actual peer-reviewed literature, not a reference to an informal poll taken back when the idea was totally new. I am quite confident that there is no actual dispute about the fact that the stress increases, although as I said there could be types of accelerations where the stress increases but the string doesn't break (maybe because in certain types of accelerations the stress would approach a fixed limit rather than increasing without bound).

Neither I nor anyone else on this thread has disputed the claim that the distance will remain constant in the launch frame if both ships have the same coordinate acceleration in this frame. Again, the point is that the stress in the string will be continually increasing even though its length in the launch frame is remaining constant.

Neither I nor anyone else on this thread has disputed the claim that the distance will remain constant in the launch frame if both ships have the same coordinate acceleration in this frame. Again, the point is that the stress in the string will be continually increasing even though its length in the launch frame is remaining constant
.

This peer reviewed paper proves the string contracts and that is the reason for the string to break. See theorem 3.
http://arxiv.org/PS_cache/arxiv/pdf/0902/0902.2032v2.pdf

Neither I nor anyone else on this thread has disputed the claim that the distance will remain constant in the launch frame if both ships have the same coordinate acceleration in this frame. Again, the point is that the stress in the string will be continually increasing even though its length in the launch frame is remaining constant
.
No - the point is that the stress in the string will be continually increasing because its length in the launch frame is remaining constant.

Imagine two rockets separated by d=1 light-second, whereby the rockets are connected by a rope. In the launch frame the rockets accelerate simultaneously up to a velocity of 0,8c and therefore the distance between the rockets will remain the same. However, because of length contraction the rope (not the distance between the rockets) tends to get contracted to $$d/\gamma=0,6$$ light-seconds. This generates stresses within the rope, so it will break.

On the other hand, the observers within the rockets will note that the acceleration of the rockets was not simultaneous, so the calculation shows that after the acceleration the distance between the rockets is increased to $$d\cdot\gamma=1,67$$ light-second. Now, because the http://en.wikipedia.org/wiki/Proper_length" [Broken] of the rope is still 1 light-second, the rope will also break in the (new) rocket-frame.

So in both frames the rope will break.

Regards,

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No - the point is that the stress in the string will be continually increasing because its length in the launch frame is remaining constant.

Imagine two rockets separated by d=1 light-second, whereby the rockets are connected by a rope. In the launch frame the rockets accelerate simultaneously up to a velocity of 0,8c and therefore the distance between the rockets will remain the same. However, because of length contraction the rope (not the distance between the rockets) tends to get contracted to $$d/\gamma=0,6$$ light-seconds. This generates stresses within the rope, so it will break.

On the other hand, the observers within the rockets will note that the acceleration of the rockets was not simultaneous, so the calculation shows that after the acceleration the distance between the rockets is increased to $$d\cdot\gamma=1,67$$ light-second. Now, because the http://en.wikipedia.org/wiki/Proper_length" [Broken] of the rope is still 1 light-second, the rope will also break in the (new) rocket-frame.

So in both frames the rope will break.

Regards,
Here is a peer reviewed paper just published Oct 18, 2009

Bell’s paradox was that his intuition told him the cable would break, yet there was no change in the distance between the ships in system S. He suggested resolving the paradox by stating that a cable between the ships would shorten due to the contraction of a physical object proposed by Fitzgerald and Lorentz, while the distance between the ships would not change. This resolution however contradicts special relativity which allows no such difference in any measurement of these two equal lengths.

Conclusion:
For two spaceships having equal accelerations, as in Bell’s spaceship example, the distance between the moving ships appears to be constant, but the rest frame distance between
them continually increases.

http://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1919v2.pdf [Broken]

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