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OverJohn t1_j2swp18 wrote

Rigidity and relativity is more complicated than you might think.

Firstly, relativity constrains the speed of sound in an object. This means for example you cannot have a rigid pole where pushing one end causes the other end to move instantaneously.

Secondly, relativity constrains rigidity even further. We could conspire to apply forces across an object at the same time in its instantaneous rest frame such that the object never experiences deformation in its rest frame. When we do this the object is called "Born rigid" (after Max Born). However it turns out it is impossible to for an object to be Born rigid under all types of motion. The motion in your son's hypothetical experiment would be an example of a type of motion where it is impossible to even maintain Born rigidity.

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rootofallworlds t1_j3207ah wrote

In classical mechanics, if the stiffness (ie the relevant elastic moduli for the wave type) tends to infinity or the density tends to zero then the speed of sound tends to infinity. Am I correct to think that when you apply special relativity, the speed of sound would tend to c and not infinity in those limits?

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PennyG t1_j3kfbh8 wrote

Nice explanation. If an object (like a very long steel rod) could be infinitely rigid, you could communicate information faster than the speed of light, which is obviously not gonna happen.

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