This is a thought experiment
, and a fun one in that most people will get the answer
wrong. Basically, it goes something like this
. Take a rigid
that is 1 light-year in length, and place it in a vacuum
(space would be a good bet...). Place an observer
on each end of the pole. Have one observer move the pole 1 inch. Assume it takes him 1/4 a second to move it 1 inch (yeah yeah, we're assuming remember). Now the question is, how far does the other end of the pole move and how long does it take it to move?
Most people will immediately answer that it will move 1 inch and it will move instantly. After all, the pole is only moving at a rate of 4 inches/second, so we are well below the speed of light. However, if this were the case, the information that the pole has been moved would have been transmitted instantly over a distance of 1 light-year, which is infinitely faster than the speed of light. So this begs the question, can information be conveyed faster than the speed of light?
The answer is no. The mistake here deals with the difference between our observations of objects in our daily lives, and extrapolating those observations to a different scale. In the case of a metal pole, the size which we have experience with is small enough that the pole can be observed to be perfectly rigid along its length (although it's not, we cannot detect it with our own senses). But, a pole with a length of 1 light-year would have a significant amount of flexibility.
Basically what happens when you displace the pole is that you start a compression wave. The force of pushing on it forces the atoms in the pole closer together near the end of the pole. This will increase the force on neighboring atoms due to the repulsion caused by forcing them out of equilibrium. Thus the atoms you displaced cause atoms next to them to displace, and so on and so on. Essentially, you have a region of compressed metal which will move down the pole, and will do so at less than the speed of light. In our experience however, it takes tiny fractions of a second for this to happen on smaller lengths so we observe it as being instantaneous (keep in mind light travels along a 1 foot pole in roughly .000000000008 seconds).
Now, theoretically if you had a perfectly rigid pole it would move instantaneously. But, it is impossible to have a perfectly rigid pole. This kinda makes you wonder though, is it impossible to have a perfectly rigid pole because it would allow you to violate the speed of light, sort of a microscopic speed limiter? An interesting thought...
Another point is how far it will actually move in the real word. I haven't quite figured out this one yet. My feeling is that it's not going to move very far at all and it would take some fancy equipment to measure how far it did move. I say this because the energy you put into it will gradually be converted into heat due to internal shear forces as it moves along the length (remember, we're in a vacuum so there's no drag). Of course, this means that by moving one end an inch, we have decreased the length of the pole. This may not seem right, but as we saw above, our observation of physical behaviour don't always scale well... One of these days I'll have to sit down and figure out how far it moves and how long it takes it...