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nosepot
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Can someone please clarify for me whether length contraction in special relativity is considered a physical effect (a contraction of a cohesive material) or a kinematic effect (applied to the space the material occupies)? I've been thinking about Bell's Spaceship Paradox this week and realized that it stems from a discrepancy between these two different viewpoints.
The spaceships are identically accelerated from rest to some speed. Therefore they will keep their separation, L, before and after acceleration (as observed in their original rest frame); although, each spaceship will be length contracted due to its speed relative to the rest frame.
The paradox arises from the following. If the experiment is repeated with an inelastic string attached to the same point on each spaceship (say the back, near the rocket), then the entire connected setup can be considered as one large spaceship and so should under go length contraction as a whole, causing the string and hence the distance between the string attachment points to decrease. However, Bell poses the paradox in such a way that the string is too weak to draw the spaceships closer, and hence breaks.
If length contraction is purely kinematic, then the string should feel no stress as the entire setup contracts; but then why are the spaceships not drawn closer when accelerated without a string present? A notion that resolves the issue is that the interatomic forces of the contracting string draw the spaceships closer as the string contracts, but I think this is at odds with standard interpretations of what length contraction means in special relativity (or is it?).
I've seen some proposed solutions to this which move from the rest frame to the frame of the spaceships, but this does not seem necessary, as the paradox occurs in the original rest frame, so it should be possible to resolve it without changing frames.
Any ideas? Thanks.
The spaceships are identically accelerated from rest to some speed. Therefore they will keep their separation, L, before and after acceleration (as observed in their original rest frame); although, each spaceship will be length contracted due to its speed relative to the rest frame.
The paradox arises from the following. If the experiment is repeated with an inelastic string attached to the same point on each spaceship (say the back, near the rocket), then the entire connected setup can be considered as one large spaceship and so should under go length contraction as a whole, causing the string and hence the distance between the string attachment points to decrease. However, Bell poses the paradox in such a way that the string is too weak to draw the spaceships closer, and hence breaks.
If length contraction is purely kinematic, then the string should feel no stress as the entire setup contracts; but then why are the spaceships not drawn closer when accelerated without a string present? A notion that resolves the issue is that the interatomic forces of the contracting string draw the spaceships closer as the string contracts, but I think this is at odds with standard interpretations of what length contraction means in special relativity (or is it?).
I've seen some proposed solutions to this which move from the rest frame to the frame of the spaceships, but this does not seem necessary, as the paradox occurs in the original rest frame, so it should be possible to resolve it without changing frames.
Any ideas? Thanks.