The original question was: If I had a really long (about 500,000 km) and really stiff stick would I be able to send information faster than light by moving it quickly by 1 cm and poking someone on the other side or pushing a button?
Physicist: This is a classic thought experiment! If you had an infinitely rigid stick, then you could definitely send poking information faster than light. In fact, this is one argument for why you’ll never find perfectly rigid materials.
However, in any real material the “push” information travels from atom to atom at the speed of light or slower. That is, there are electromagnetic forces holding the pole’s atoms together, and the fastest that changes in those forces can be felt is the speed of light (this is true for any force).
So, you push on one atom, it moves, then the next atom notices after a while (as much time as it would take light to cover the distance between them, or longer) and then it moves, then a little later the next atom…
The best you can do is push suddenly, and create a compression wave that travels down the pole at nearly light speed (or more likely, just split the pole). There’s nothing special about pokin’ sticks, by the way. Every time anything gets pushed the “push information” has to travel through the object, generally at a rate much slower than light speed, but still pretty fast. I mean, outside of Jello, it’s hard to notice.