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I will refer to this wikipedia page: https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox and especially this diagram:

enter image description here It appears clearly in frame S' that the length of the rope is longer than at rest in that referential, therefore it breaks. Nevertheless, I can't see why in the S frame the rope should break as for the S frame point of view, the length of the rope stays the same (L).

Can someone explain how in this diagram the S frame should conclude as well that rope breaks ?

The argument given in the text is that the rope moves so it experiences Lorentz contraction from a frame S point of view. But this does not seem to appear on the diagram, or does it ?

Thanks for your help.

Santa
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1 Answers1

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From a frame S point of view, one has to compare to what the accelerating rope profile would look like in that diagram and would realize that it would look smaller in frame S. Therefore frame S would conclude that rope should snap. That information is not in the diagram as it is.

If we were used to look at relativistic phenomenons we would always have seen ropes reducing in size when they accelerate. And if forcing it to maintain the same length when accelerating, we would therefore naturally conclude that it should snap.

Santa
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