Causality Violation in Extended Newton's Cradle?

[jrab227]

I wanted to post a small thought experiment that has been really bugging me.

Let's say you could build a Newton's cradle the length of 1 AU, all the balls are elastic, there is no loss of energy due to friction, and you are standing at one end and your friend is standing at the other. At the start, your friend picks up the ball and releases it, with angular velocity in the classical mechanics realm, sending momentum down the balls.

Now we know because of the speed of light, it would take about 8 minutes for you to actually see your friend pick up the ball and release it, but when would the ball on your end actually be knocked?

My vote is when you see your friend hits the ball, you will strangely see the ball on your end be knocked instantly in your perspective because the momentum transfer on the atomic scale is moved atom-by-atom by the EM force, which is certainly governed by the laws of relativity.

This problem is just very strange because we obviously have non-relativistic speeds on the small scale, but its over very long lengths, so it most likely causes a relativistic response, AND there's non-relativistic speeds on the large scale.

 

[ghwellsjr]

You would not see the ball on your end be knocked at the same time that you see your friend hit the ball at the other end. It would take a very long time because the speed of the propagation of an impact through a solid object is very slow compared to the speed of light.

 

[mfb]

The propagation of the momentum is sound, and therefore moves with the speed of sound. With ~5km/s (depending on the material), sound needs about 1 year for this. 8 minutes after your friend releases the ball, you see your friend's ball hitting the others, and 1 year later a ball at your side will get a kick, assuming perfect propagation of the momentum (this includes "no dispersion").