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Nope. Pushing on the end of the beam sends a pressure wave through the beam. The button gets pushed when the wave reaches the other end. Wave travels significantly slower than light.

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If you push on the beam and the other end does not move right away doesn't that imply that the beam has compressed and is not rigid?

What you're proposing is an effect mediated by physical forces. Specifically, on a fundamental, atomic level your beam is made up of atoms. And when you push it, you're bringing atoms closer together, that feel an electrostatic repulsion. And the beam moves.

So, in the best case, this method of communication is equivalent to communicating with electromagnetic waves. And they have a speed limit: the speed of light :)

So this wouldn't be faster than light communication.

> doesn't that imply that the beam has compressed and is not rigid?

Yes it does. And in fact that is the case: The beam has compressed. A fully rigid beam is impossible.

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