# Lorentz contraction

by matheinste
Tags: contraction, lorentz
P: 687
 Quote by matheinste 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/physic...SR/rocket.html
http://arxiv.org/PS_cache/physics/pd.../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.
P: 1,060
 Quote by cfrogue 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/physic...SR/rocket.html http://arxiv.org/PS_cache/physics/pd.../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.
P: 8,430
 Quote by cfrogue 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.
 Quote by cfrogue 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.
 Quote by cfrogue 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).
 Quote by cfrogue 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.
P: 1,060
 Quote by Al68 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.
P: 687

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/...902.2032v2.pdf
P: 82
 Quote by cfrogue 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 proper length 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,
P: 687
 Quote by Histspec 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 proper length 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/...906.1919v2.pdf
P: 82
 Quote by cfrogue Here is a peer reviewed paper....
Arxiv preprints are not necessarily "peer reviewed".
P: 687
 Quote by Histspec Arxiv preprints are not necessarily "peer reviewed".
Oh.

How do you tell if they are not reviewed?
 Mentor P: 15,575 If they don't also show up in a peer-reviewed journal.
 PF Patron Sci Advisor P: 1,772 In the case of the article in question http://arxiv.org/abs/0906.1919 shows the article has been submitted to the European Journal of Physics http://www.iop.org/EJ/journal/-page=forthart/0143-0807 shows it has been accepted for publication and is "provisionally scheduled for October 2009"(!)
P: 687
 Quote by DrGreg In the case of the article in question http://arxiv.org/abs/0906.1919 shows the article has been submitted to the European Journal of Physics http://www.iop.org/EJ/journal/-page=forthart/0143-0807 shows it has been accepted for publication and is "provisionally scheduled for October 2009"(!)
I have a question.

From what I have seen, all calculations agree the launch frame observer believes there is no distance differential between the two ships.

Is this correct as far as you know?
P: 1,060
 Quote by DrGreg In the case of the article in question http://arxiv.org/abs/0906.1919 shows the article has been submitted to the European Journal of Physics http://www.iop.org/EJ/journal/-page=forthart/0143-0807 shows it has been accepted for publication and is "provisionally scheduled for October 2009"(!)
On page 3 the author seems to be using the fact that Lorentz transforms (coordinate transforms) do not induce stress in an object as proof that Lorentz contraction, in the original Lorentzian use of the term, do not either.-----"-One other point to be considered is whether strains and stresses can be induced by Lorentz contraction, as is contended in Refs. [1,2,4,5]. Our answer to this is clear from the previous discussion. Just as a 3D rotation of an object does not induce strain, a 4D rotation (Lorentz transformation) will not induce strain and consequent stress."--------

Also the fact that he describes the apparent relativistic contraction of length as illusory is a bit unusual.-------"And, just as the “shortening” of a stick that is rotated in three dimensions is an illusion, we now can see that the “shortening” of a stick that is rotated in four dimensions by a Lorentz transformation is also illusory."----------

I have not read the rest of the article closely yet but the above points disturb me a little.
Of course it may just be my reading of the text that is in error.

Matheinste.
P: 8,430
Quote by cfrogue
 Quote by JesseM 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/...902.2032v2.pdf
I don't know what you mean by "theorem 3"--what page are you looking at? In any case, looking over the paper, in equation 3.12 at the bottom of p. 11 they explicitly show that the length of the string does not change in the frame where the ships have identical coordinate accelerations (and started accelerating simultaneously). I'm sure you won't find any physicists who dispute this very obvious and trivial point.
 Quote by cfrogue 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/...906.1919v2.pdf
This paper does not dispute Bell's claim that the cable would break! Instead it calls for a rethinking of the reason the cable breaks...the author's argument seems to be that the only physical way of defining an object's length is by looking at its own rest frame, so that treating "length contraction" as a change in length is overly confusing...from p. 3:
 This suggests the need for a definition of “length” that is the same for any state of uniform motion. This would correspond to the use in relativity of “proper time” and “invariant mass” for time and mass, but the terms “proper length” and “invariant length” have already been used in the literature with other meanings. The term we recommend for length is “rest frame length”, which we define as the length a moving object has after a Lorentz transformation to its rest system. If length is to be considered a physical attribute of an object, then this physical attribute should be the rest frame length. This length, of course, would not be changed by uniform motion.
The author then points out that the "rest frame length" of the cable or string does grow as the ships accelerate, even though the distance between them in the observer's frame does not change, and that this should be seen as the true reason a cable or string would break, not length contraction:
 Although the spaceships are accelerating, the system S′ is a Lorentz system moving at constant velocity. Since each ship is instantaneously at rest in this system, the length d′ = gamma*d is the rest frame distance between the ships. As such, it is the physical distance between the ships. If there were an inextensible cable between the ships, it would snap at the start of motion of the ships. An elastic cable would stretch until it reached its maximum possible length dMax, at which point it would snap.
PF Patron
P: 1,772
 Quote by cfrogue I have a question. From what I have seen, all calculations agree the launch frame observer believes there is no distance differential between the two ships. Is this correct as far as you know?
Yes.

There is no doubt about this. In the launch frame the distance between the ships is constant. You gave a valid explanation at the end of post #18.

If the string was attached to the front ship only, trailing behind it, it would initially be touching the back ship, but as soon as the acceleration begins, the length of the string contracts as measured in the launch frame (assuming its "rest length" remains constant i.e. its length in any frame in which it is momentarily at rest).

Therefore if you had attached the string to the back ship, if the string was elastic it would stretch and if it couldn't stretch it would break.

I think this agrees with what everyone else has been saying in this thread and what the quoted paper says.

There is certainly no disagreement amongst experts that the string will break (despite the fact that long ago some experts initially got it wrong when they heard of the problem for the first time; even experts can make mistakes occasionally but now there is consensus as to what the correct answer is).
P: 687
 Quote by DrGreg Yes. There is no doubt about this. In the launch frame the distance between the ships is constant. You gave a valid explanation at the end of post #18. If the string was attached to the front ship only, trailing behind it, it would initially be touching the back ship, but as soon as the acceleration begins, the length of the string contracts as measured in the launch frame (assuming its "rest length" remains constant i.e. its length in any frame in which it is momentarily at rest). Therefore if you had attached the string to the back ship, if the string was elastic it would stretch and if it couldn't stretch it would break. I think this agrees with what everyone else has been saying in this thread and what the quoted paper says. There is certainly no disagreement amongst experts that the string will break (despite the fact that long ago some experts initially got it wrong when they heard of the problem for the first time; even experts can make mistakes occasionally but now there is consensus as to what the correct answer is).
OK, would the rest frame/launch frame conclude the string will break given the distance does not change between the ships from the POV of the rest frame?

In other words, does the launch frame conclude the distance does not change yet the string contracts?
P: 8,430
 Quote by cfrogue OK, would the rest frame/launch frame conclude the string will break given the distance does not change between the ships from the POV of the rest frame? In other words, does the launch frame conclude the distance does not change yet the string contracts?
In the launch frame the string won't experience any change in length until it snaps. As I've said, the stress in the string will increase though. I think when people cite "Lorentz contraction" as an explanation for the string breaking, what they're getting at is that the string "wants" to contract but can't because it's attached to the ships...it may be easier to make sense of this if we think of a spring rather than a string, since you may remember from classical mechanics that springs have a "rest length" that they naturally assume when nothing is pulling or pushing on them (the rest length minimizing the stress in the spring), and that when they are pulled to a greater length than the rest length they pull back with greater and greater force, as if they are "trying" to return to that length (and obviously if you pull a spring far enough past its rest length, it'll snap). If you had two identical springs traveling alongside each other, one attached to the two ships and one with its ends free whose length was equal to its rest length, then the length of the free spring would grow shorter and shorter as seen by the launch frame as its velocity increased, which implies that the spring attached to the ships, whose length does not change in this frame, is being extended farther and farther past its own natural rest length.
P: 687
 Quote by JesseM In the launch frame the string won't experience any change in length until it snaps. As I've said, the stress in the string will increase though. I think when people cite "Lorentz contraction" as an explanation for the string breaking, what they're getting at is that the string "wants" to contract but can't because it's attached to the ships...it may be easier to make sense of this if we think of a spring rather than a string, since you may remember from classical mechanics that springs have a "rest length" that they naturally assume when nothing is pulling or pushing on them (the rest length minimizing the stress in the spring), and that when they are pulled to a greater length than the rest length they pull back with greater and greater force, as if they are "trying" to return to that length (and obviously if you pull a spring far enough past its rest length, it'll snap). If you had two identical springs traveling alongside each other, one attached to the two ships and one with its ends free whose length was equal to its rest length, then the length of the free spring would grow shorter and shorter as seen by the launch frame as its velocity increased, which implies that the spring attached to the ships, whose length does not change in this frame, is being extended farther and farther past its own natural rest length.
Well, the SR acceleration equations indicate the distance between ther ships will not change.

From the POV of the rest observer, what is the math to indicate the space remains constant but a rod will contract if allowed between the two ships.

All these links show what happens from the POV of the accelerating ships.

I want to concentrate on the math from the rest/launch frame's POV.

Also, this paper seems to say something different.

4 Conclusion
We have seen that the physical length of an object is the rest frame length as
measured in the instantaneous rest frame of the object. 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. This means that a cable between the two ships must
eventually break if the acceleration continues.

http://arxiv.org/PS_cache/arxiv/pdf/...906.1919v2.pdf

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