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.

  • $\begingroup$ Possible duplicate: physics.stackexchange.com/questions/244315/… $\endgroup$ – WillO Oct 19 '16 at 12:33
  • $\begingroup$ @WillO It's linked with the duplicate you suggest, but my specific question is about the included diagram: how does frame S conclude that the rope should snap in that diagram ? And if the information is not there, why ? $\endgroup$ – Santa Oct 20 '16 at 7:50
  • $\begingroup$ I still think it's essentially the same question. The other question basically asks "Can an observer in frame $S$ explain the snapping without using relativity?", or in other words "Can an observer in frame $S$ explain the snapping without referring to frame $S'$?". Your question asks pretty much exactly the same thing. $\endgroup$ – WillO Oct 20 '16 at 14:35
  • $\begingroup$ In this question, I'm not asking to explain the snapping without using relativity. I'm asking why in the diagram, it is obvious on the frame S' point of view the rope is snapping when I can't see in the diagram why it should be obvious from frame S. I know believe the information is just not there in the diagram: the contraction of a train "normally" accelerating is not represented and should turn out to be a "smaller" train from a frame S point of view. So my answer seems to be "the information is not in the diagram". $\endgroup$ – Santa Oct 21 '16 at 7:57

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.

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  • $\begingroup$ Couldn't we treat the spaceships attached by a rope as a single object for the purposes of this thought experiment? Wouldn't the entire system then appear to be contracted from a stationary observer? Wouldn't the system seem normal to any perspective within that inertial frame? I'm not sure i see why the rope would snap anymore than why the spaceships would snap. $\endgroup$ – Yogi DMT Oct 21 '16 at 13:43
  • $\begingroup$ @YogiDMT You have not understood the scenario correctly. The scenario is one in which the spaceships are deliberately made to move in such a way that the distance between them is constant in the inertial frame where they were at rest at the beginning. Your suggestion that they be treated as a single object that contracts is simply not the scenario under discussion. $\endgroup$ – Andrew Steane Jul 10 '19 at 21:53

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