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Thought experiment: the light-second rod.

5 Jul 2008
Progress: Solved

Consider the following. A metal rod, one light-second in length, free to move through space. You stand at one end, and point a telescope at the other. You push your end of the rod. How long does it take you to see the other end move?

Again, forgetting outside factors and the fact you'd need an incredible amount of force to overcome the inertia, most people answer this question with "One second". Others argue it would take two seconds, as "data cannot travel faster than the speed of light". My answer is: several minutes.

It depends what the rod was created from, but this stems from the ideas of electromagnetic waves and physical vibrations travelling at diffent speeds through different mediums inversely. The denser the material, the slower the speed of light. But also, the denser the material, the faster the speed of sound.

If the rod was of infinite density, it would take two seconds. Any other material and it would take considerably longer, more specifically, at the speed of sound through that medium, plus one second.

The point of this experiment is to demonstrate how all movement can be expressed as a single, low frequency, high amplitude, longitudinal wave. I don't know if my answer is correct, and I'm not educated enough to see how this ties in with other aspects of physics. I think it's interesting though that everyone assumes motion is instant. There's probably a lot more factors to consider in this experiment, such as the elasticity of the material, which would absorb the energy of the wave. Also, what would happen if you had a horseshoe shaped rod? If both ends were next to you, and the overall circumference several light-seconds, what would happen when you push one end? It's likely that the rod would behave like a whip - how would a transverse wave travel?

If anyone has any thoughts to add to this, feel free to contact me.