Gravity vs. infinitely rigid bar

[Karl Coryat]

Hey folks. I was reading this odd explanation for why the bottom of a hanging Slinky appears to defy gravity when the top is released. As the comments note, there is a simpler explanation involving how the spring under tension reacts when it becomes a free-falling object. But the attempt at an informational explanation made me think of a question I'm not sure how to answer:

Instead of a hanging slinky, consider a vertically hanging metal bar of infinite rigidity, length=l. It is released from the top at t=0. Does the bottom begin to move at t=0? I'm guessing it would not, because this would involve superluminal information transfer from the top to the bottom. If I am right, then the soonest it could move would be at t=l/c. But then the falling bar would be longitudinally compressed, which -- combined with its infinite rigidity -- seems to produce a paradox.

Is this just the universe's way of saying that the finite speed of light forbids infinitely rigid bodies?

 

[mrspeedybob]

Is this just the universe's way of saying that the finite speed of light forbids infinitely rigid bodies?

Yes.

 

[Karl Coryat]

If a material's rigidity is constrained to a finite value by the speed of light, we must then have a known upper bound on the elastic modulus of neutron matter, and perhaps even black hole matter - do we not?

 

[K^2]

Not really. The elastic modulus can be arbitrarily high. The object still isn't going to be perfectly rigid. Once you take into account the fact that force that makes object rigid is electrostatic, or if you go to limit of neutron matter, strong nuclear, and that carriers of these forces propagate at the speed of light, you get the condition that no matter how high the elastic modulus is, the compression wave will still propagate no faster than speed of light.

 

[Karl Coryat]

Excellent, thanks.