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This paper discusses the Bell spaceship paradox:

Petkov, "Accelerating spaceships paradox and physical meaning of length contraction," http://arxiv.org/abs/0903.5128

PF has a FAQ on this paradox: https://www.physicsforums.com/showthread.php?t=742729 My purpose in creating this thread is *not* to open yet another general discussion of the paradox. My purpose is to discuss one specific passage in the Petkov paper.

The following occurs on p. 4:

Petkov's reasoning seems clearly wrong to me on at least one count, since nobody ever claimed that length contraction was the *only* way that stress could occur. In one frame there is stress because of Lorentz contraction. In another frame there is stress because the ships have gotten farther apart.

Petkov also seems to impute to Bell the claim that the thread is stressed in one frame but not another. This also seems clearly wrong to me. Bell claimed that the thread would be stressed in all frames -- hence all observers agree that it breaks.

However, the reason I'm posting here is yet a third logical point, which is Petkov's statement that if stress occurs in one frame, it must occur in all frames. He argues that this is because the "stress tensor," by which I assume he means the stress-energy tensor, must vanish in all frames if it vanishes in one frame. This argument doesn't make a lot of sense to me. It's certainly true that if a tensor vanishes in one frame it must vanish in every other. But the stress-energy tensor of the thread is not going to vanish in any frame, since the thread has mass. It's perfectly possible, for example, that we have [itex]T^{xx}=0[/itex] in one frame but [itex]T^{x'x'}\ne0[/itex] in another. I suppose the correct test to see whether the thread is under stress is to check the eigenvalues of the stress-energy tensor. If they look like [itex](\rho,0,0,0)[/itex], then I guess there would be a frame, interpreted as the rest frame of the thread, in which it experienced no stress; and it would then follow that the thread would not stretch, break, etc. Both the test (eigenvalues) and the interpretation (whether it stretches, breaks, etc.) are frame-independent.

Is my interpretation correct? If so, then how are we to interpret the case where some matter has [itex]T^{xx}=0[/itex] in one frame but [itex]T^{x'x'}\ne0[/itex] in another? Should we interpret [itex]T^{x'x'}[/itex] as some kind of pressure, or not? If so, then why is it a pressure that doesn't produce effects on the matter (e.g., breaking)? After all, if you take dust in its rest frame and transform to another frame, you have [itex]T^{xx}=0[/itex] in the rest frame but [itex]T^{x'x'}\ne0[/itex] in any other. This [itex]T^{x'x'}[/itex] is a transport of x-momentum in the x direction, but I probably wouldn't interpret it as pressure.

One often sees the elements of the stress-energy tensor in a given frame described in a certain way, with, e.g., the space-space components being interpreted as pressure. E.g.: http://en.wikipedia.org/wiki/File:StressEnergyTensor_contravariant.svg This doesn't seem quite right in the example of dust in a frame other than its rest frame.

Petkov, "Accelerating spaceships paradox and physical meaning of length contraction," http://arxiv.org/abs/0903.5128

PF has a FAQ on this paradox: https://www.physicsforums.com/showthread.php?t=742729 My purpose in creating this thread is *not* to open yet another general discussion of the paradox. My purpose is to discuss one specific passage in the Petkov paper.

The following occurs on p. 4:

Bell thought that the thread breaks as a result of a stress arising in it since a stress,

according to him, is always present when there is length contraction. But stress is an absolute

(frame-independent) physical quantity, which is represented by a tensor. This means that if the

stress tensor is zero in one reference frame it should be zero in all reference frames. Therefore,

for observers in B and C, who measure the constant proper length of the thread in Fig. 2, the

stress tensor should be zero, which means that from A’s viewpoint there should be no stress in

the relativistically contracted thread either.

Petkov's reasoning seems clearly wrong to me on at least one count, since nobody ever claimed that length contraction was the *only* way that stress could occur. In one frame there is stress because of Lorentz contraction. In another frame there is stress because the ships have gotten farther apart.

Petkov also seems to impute to Bell the claim that the thread is stressed in one frame but not another. This also seems clearly wrong to me. Bell claimed that the thread would be stressed in all frames -- hence all observers agree that it breaks.

However, the reason I'm posting here is yet a third logical point, which is Petkov's statement that if stress occurs in one frame, it must occur in all frames. He argues that this is because the "stress tensor," by which I assume he means the stress-energy tensor, must vanish in all frames if it vanishes in one frame. This argument doesn't make a lot of sense to me. It's certainly true that if a tensor vanishes in one frame it must vanish in every other. But the stress-energy tensor of the thread is not going to vanish in any frame, since the thread has mass. It's perfectly possible, for example, that we have [itex]T^{xx}=0[/itex] in one frame but [itex]T^{x'x'}\ne0[/itex] in another. I suppose the correct test to see whether the thread is under stress is to check the eigenvalues of the stress-energy tensor. If they look like [itex](\rho,0,0,0)[/itex], then I guess there would be a frame, interpreted as the rest frame of the thread, in which it experienced no stress; and it would then follow that the thread would not stretch, break, etc. Both the test (eigenvalues) and the interpretation (whether it stretches, breaks, etc.) are frame-independent.

Is my interpretation correct? If so, then how are we to interpret the case where some matter has [itex]T^{xx}=0[/itex] in one frame but [itex]T^{x'x'}\ne0[/itex] in another? Should we interpret [itex]T^{x'x'}[/itex] as some kind of pressure, or not? If so, then why is it a pressure that doesn't produce effects on the matter (e.g., breaking)? After all, if you take dust in its rest frame and transform to another frame, you have [itex]T^{xx}=0[/itex] in the rest frame but [itex]T^{x'x'}\ne0[/itex] in any other. This [itex]T^{x'x'}[/itex] is a transport of x-momentum in the x direction, but I probably wouldn't interpret it as pressure.

One often sees the elements of the stress-energy tensor in a given frame described in a certain way, with, e.g., the space-space components being interpreted as pressure. E.g.: http://en.wikipedia.org/wiki/File:StressEnergyTensor_contravariant.svg This doesn't seem quite right in the example of dust in a frame other than its rest frame.

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