Suppose there is a ridiculously large bridge, fixed at either end (light seconds long at least). The bridge is constantly under the influence of gravity. If the ends are severed simultaneously, the whole bridge will fall. I assume simultaneity isn't a problem as the bridge is all in one reference frame? Will an observer in the middle register the change of inertia, but be unable to see or detect any damage to the ends of the bridge until the light from each end or the signal from electronic sensors has caught up at light speed? If so, does this mean that they can infer from the fall that the ends must be severed I.e. have they recieved information about the state of the ends faster than lightspeed? Or will they not begin to fall until the information about the severed ends has caught up?
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3$\begingroup$ The "information" that the ends were severed will travel at the speed of sound through the bridge, typically much slower than the speed of light. So the central parts of the bridge won't start falling right away. $\endgroup$– StenCommented Aug 10, 2023 at 20:14
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$\begingroup$ But if gravity is constant, how come it wouldn't fall immediately? Would it fall, but the bridge would act as though it was still connected? Otherwise wouldn't it be anti-gravity? $\endgroup$– TigerCommented Aug 10, 2023 at 20:19
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$\begingroup$ P.s. thanks for answering, I'm not arguing, just confused! $\endgroup$– TigerCommented Aug 10, 2023 at 20:20
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5$\begingroup$ @Tiger: a perfectly rigid bridge like you're imaginging isn't allowed by the rules of special relativity, exactly because a construction like this would allow you to transmit information faster than the speed of light. Real objects will deform or bend somehow, and that will be governed by a time scale determined by the speed of sound in the material. So, in a real bridge that is that large, the ends would start to fall before the center. $\endgroup$– Zo the RelativistCommented Aug 10, 2023 at 20:50
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1$\begingroup$ Thanks very much, that is fascinating! $\endgroup$– TigerCommented Aug 11, 2023 at 7:18
2 Answers
This is essentially a variant of the idea of using a rigid pole to transmit information. The key point is that stresses in a material are only transmitted at the speed of sound in the material, which is necessarily slower than the speed of light, and typically much slower. The central parts of your bridge would not start to fall until long after the observer in the center sees the ends get severed.
It may appear that the bridge is different from the pole because the gravitational force that causes the bridge to collapse is already present. But that force was counteracted by forces within the bridge, and will continue to be counteracted until the collapse finally "transmits" through the material.
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$\begingroup$ Thank you. Does this mean that someone watching through a telescope from a long way away would see the ends snap, then the ends start to drop, then the middle drop later on? Or if rigid enough, the ends snap and then a pause before it fell at all, seemingly levitating? $\endgroup$– TigerCommented Aug 10, 2023 at 20:29
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2$\begingroup$ @Tiger The ends would start to drop, and the middle later, in the scenario where both ends are severed instantly. Since the speed of sound is so low, I would not be surprised if you could find a video demonstrating this, but am not in a position to search right now. $\endgroup$– StenCommented Aug 10, 2023 at 20:38
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$\begingroup$ That's great, thanks very much for your help! $\endgroup$– TigerCommented Aug 10, 2023 at 20:40
You may be interested in this experiment. The bridge, however long (it doesn't have to be light seconds) will collapse in the same way. This is not even a relativistic scenario, as the governing speed is the speed of sound, ~3000 m/s for most solids.
The speed of sound in solid governs how fast changes in intermolecular forces propagate. The effective speed of sound in the slinky is very slow, allowing us to see it happen. As the narrator notes, different wave modes (such as twisting, shear, compression) can have different sound speeds.
