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I am trying to understand thisBell's Spaceship Paradox, which is basically asking when there is a thread connected between two spaceship (A,B) and an observer C observes a "constant" acceleration, then whether this thread will break or not by Lorentz Contraction.

I think the problem is a little bit ill-defined in Crowell's book. But what if we refine the question as like this:

1) Att=0, the two spaceship (A, B) and the observer C was at rest.

2) A & B started to accelerate att=0 with "constant" acceleration in the sense that they both engaged the same engine power (as defined in D'Inverono's "Introducing Einstein's Relativity" p.37).

Then, as in D'inverono's deduction, the location of two spaceships aftertcan be written as :

(x-x0) = (c/a) sqrt(c^2 + a^2(t-t0)^2)-c^2/a

From this, I think the separation between A & B will remain constantall the timeand there is no reason that the thread connecting A & B should break. But this (my) conclusion is the opposite with Bell's and Crowell's argument.

Crowell says "By the equivalence principle, any experiments done by A and B give the same results as if they were immersed in a gravitational field. The leading ship B sees A as experiencing a gravitational time dilation. According to B, the slowpoke A isn’t accelerating as rapidly as it should, causing the string to break." It sounds persuading too.

Could any one help me to understand this discrepancy?

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# Bell's Spaceship Paradox - Shouldn't the thread stay connected?

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