I just had a thought and I'm wondering if anyone could take a look at it and see if there are any problems with it. According to Einstein, information cannot travel faster than the speed of light. But imagine that there are two stationary planets 1 light year separated. Then imagine I build a rod between them so that it it touching each planet. Realistically, of course this is impossible, but isn't it theoretically possible that people on one end could move the rod back and forth, tapping the other planet and transmitting instantaneous information via Morse code?

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This thought experiment has been explored before. Assuming that you were able to set up the situation as you described, it seems as though one could transmit instantaneous information along the rod. Unfortunately, we are assuming that the rod behaves as a "rigid body." A rigid body is an object that is perfectly solid, such that any force applied is felt by the entire object at once, with rotations behaving similarly. Simply put, a rigid body does not deform (bend, stretch or twist) at all.

Treating objects as rigid bodies works well in everyday life (indeed, that's really how most humans perceive solid objects). When we are dealing with non-complicated collisions on Human size scales, objects behave very much like they are perfectly rigid. However, real solids do deform on small time and distance scales as an applied force propagates through the body.

For example, consider a car crashing into a telephone pole at a high speed. When viewed in slow-motion, it is clear that initially the front of the car crumbles while the back of the car is still intact - the rear of the car is essentially "unaware" of the collision. Eventually, the "information" of the collision reaches the rear of the car, and it breaks apart.

The long-distance rod would behave similar to the car. When planet #1 "taps" its end of the rod, it is actually creating pressure waves within the solid structure of the rod. These pressure waves propagate along the rod at or below (usually far below) the speed of light. Assuming no loss of energy, planet #2 will only "see" the tapped message when those pressure waves finally travel all the way along the rod.

I've been fascinated by this kind of problem for some time. In engineering circles I think the phenomena is called "pogoing". Consider the Saturn V at the moment of takeoff. The five F-1 engines are at full power and the hold-down clamps are released. At that moment in time the bottom (or rear) of the rocket begins to accelerate, slowly at first. The top of the rocket where the astronauts are sitting is momentarily at a standstill while the rear of the rocket has started upward with the main body of the rocket compressing slightly. Then the top of the rocket "catches up" with the rear of the rocket and begins it's acceleration, but rather than simply catching up with the forward motion the top of the rocket overshoots slightly, by only a few inches at first then snaps back to it's original dimension but slightly overshooting there as well.

To the astronauts, it's like they're bouncing up and down in line with the direction of motion. This is actually the entire rocket stack compressing and decompressing in the direction of motion due to that first moment of acceleration at the base and the slight delay before that motion is "felt" at the top. At ~365 feet in length the Saturn V was impressively large and the pogoing effect, although expected, was somewhat extreme compared to any other manned rocket. I believe this pogoing effect is a normal and expected phenomena of just about every rocket.

My post here is designed to make it easier to visualize what exactly would happen with that theoretical rod connecting two planets. A mostly hollow 365 foot rocket vs. a perfectly solid rod 1 light year long is maybe a poor comparison but is the best I can do.

To you rocket scientists out there who are tearing your hair out at my explanation: I gave up some accuracy for two reasons. A) I'm going by three-decades old memories as to how this worked and B) Sometimes it's easier to visualize how something works without the accuracy. When explaining how something works to a novice (think about describing how hard drive defragmentation works to a senior who's new to computers) sometimes accuracy gets in the way of clarity. Sorry!