If you were able to construct a rigid beam 25 million miles long wouldn't you be able to transmit data (push a button) on the other end faster than the speed of light?
It is impossible to construct a perfectly rigid beam, in the sense that you are thinking of. A "rigid beam" would be made up of matter and, as you push on one end, you would trigger a wave that would propagate from neighbour to neighbour until it reaches the other end.
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.
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.
Even if you create a rigid beam (ignoring the fact that it isn't possible), once you start turning it with a certain speed, its end will start reaching speed of light and start acquiring mass. As the speed aproaches speed of light, the mass of the beam will be approaching infinity.
To think about it, if you have a sufficiently long beam you won't be able to give it any angular momentum at all, regardless of how much force you apply. It will be fixed in space. Perfect starting point if your hobby is moving stars with a combination of chains and pulleys.
It is possible to conceive of violating the known laws of physics if you start by conceiving of an object that violates the known laws of physics. A perfectly rigid beam 25 million miles long would be such an object.
A beam made of matter is not rigid (as we think of the word) on that scale, as others in the thread have pointed out.
I think that's going a little too far. If you can construct a "rigid beam" five feet long, I see no way that relativity countermands a "rigid beam" 25 million miles long. It's just that "rigid" doesn't mean what grandparent thinks it means -- info still travels through the beam via pressure waves.
The pressure waves are ultimately manifestations of the exclusion principle, expressed through forces that are constrained to travel at or below c.
So yes, relativity dictates that you can't create a rigid beam 25 molecules long, much less 25 million miles long. There can be no such thing as a perfectly rigid beam of any length.
Exactly, you can only construct beams at any scale that seem rigid at some scale. A 2 foot long piece of re-bar looks pretty rigid, until you look closer.