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JesseM is offline
Nov15-09, 03:08 PM
Sci Advisor
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Quote Quote by cfrogue View Post
Quote 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.
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 Quote by cfrogue View Post
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.

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 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.