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In Bell's Spaceship Paradox, are there any direct observations that the stationary observer can make that would justify the breaking of the string without taking into consideration as to what's taking place in the frames of the ships?

In other words, can it observe any changes in the string's properties that would justify the break without having to switch or calculate in other frames?

If the string is replaced by a bar that can stretch a bit before it breaks, in the rocket's frame it would appear that the stripes become broader before the bar breaks. What would the stationary observer observe?

The bar

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  • $\begingroup$ The stationary observer will see the string attempt to length contract, while the coordinate distance between the rockets stays the same - this will lead to increasing tension in the string, which eventually breaks it. $\endgroup$
    – G. Paily
    Commented Jun 14, 2023 at 4:43
  • $\begingroup$ @G.Paily Could you please elaborate? I have seen this line of reasoning before but it never made sense to me, as length contraction seems to be acting preferentially on the object instead of the space itself. $\endgroup$
    – Alan Whitteaker
    Commented Jun 14, 2023 at 5:17
  • $\begingroup$ Duplicate: physics.stackexchange.com/questions/244315/… $\endgroup$
    – WillO
    Commented Jun 14, 2023 at 11:00
  • $\begingroup$ @WillO None of the answers clear my question. I've done the calculations and I see that it breaks, but can this be explained by some effect in the string in the stationary frame? $\endgroup$
    – Alan Whitteaker
    Commented Jun 14, 2023 at 12:08

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The effect in Bell's rocket paradox is no different to length contraction, in the sense that it is a physical effect that arises from the nature of spacetime. You can't expect to explain it without taking SR into account. It is rather like looking for an explanation of the extended lifetime of moving muons without taking relativity into account. Yes, you might be able to come up with some ether theory in which the electrical forces holding together the molecules of the string are altered in some way by the movement of the string through the ether, but what's the point of going to all that trouble when SR tells you what is happening? You see the string break because it is being stretched in its rest frame.

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  • $\begingroup$ I do understand this, but the entire point of the question was to determine if there is another way of explaining what is observed in the stationary observer's frame. $\endgroup$
    – Alan Whitteaker
    Commented Jun 14, 2023 at 8:57
  • $\begingroup$ And the entire point of my answer is that there is not. $\endgroup$
    – Marco Ocram
    Commented Jun 14, 2023 at 10:11
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Are you asking how string changes in the rest frame of a still standing observer?

The non-tensioned length of the string gets smaller, that is what happens in the rest frame of a still standing observer.

Atoms of the string contract. A metal string gets thinner. According to a still standing observer.

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  • $\begingroup$ I'm not sure if that is a suitable method to determine whether the string is accelerating and will break. Let us suppose that the stationary observer is made to accelerate instead of the string. In it's frame, the string will appear to accelerate and it will observe the same atom contraction. However, the string does not break. $\endgroup$
    – Alan Whitteaker
    Commented Jun 15, 2023 at 5:17
  • $\begingroup$ @AlanWhitteaker Yes. I decided to not say anything about the case where the observer accelerates. And about the case where an inertial observer sees the ships slowing down, the string getting longer, and breaking. $\endgroup$
    – stuffu
    Commented Jun 15, 2023 at 7:57

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