Is it possible for information to be transmitted faster than light?
Consider the following thought experiment. You have a long perfectly rigid beam (for the sake of simplicity, suppose it is one light-second long) which is placed on a fulcrum in the middle, so it is like an extremely long see-saw. There are two participants on either side of the beam.
Suppose participant A flips a coin and, based on the flip, chooses to place either a light or heavy boulder on his end of the beam. Participant B, one light-second away, sits down on his end of the beam.
What happens to participant B for the first second of his sit? If participant A randomly decided to place a light boulder on his end, then participant B would lower the beam with his weight; conversely, if there's a heavy boulder on the other end, he'll stay up in the air. Either way, he will know in that first second what the outcome of participant A's coin flip was, and therefore gain one bit of information faster than the speed of light! This is, of course, patently impossible.
My guess, as you can probably tell from the title of the question, is that this entire hypothetical situation cannot happen because there is not really such a thing as a "perfectly rigid body". The reason that one end of a lever moves at all in relation to the other is because the electromagnetic forces between the atoms in the beam push each other up. But what does this "look like" for absurd lengths like one light-second? Does the upward motion travel like a wave through the beam? Does the speed of this wave depend on the material, the magnitude of the forces involved, or something else entirely? Is there a name for it? And what, if anything, does participant B feel in that first second, and what would the beam "look like" to an external observer who can see the whole beam at once? I can't intuitively visualize any of this at all.
Standard disclaimer: I only know high-school level physics, if that helps when aiming answers.