Let's say I have a metal bar (which does not expand or contract at all) that's 1 light-second long which is connected to a block at the end. I am in space holding the other end of the bar. If I pull on the bar, what happens?
If the block moves instantly, then shouldn't the bar appear to get longer, because I don't see the end move until one second later?
On the other hand, if the block takes one second to move, does the bar actually expand, as my end has moved but the block's end hasn't?
As mentioned in the comments, there is no such thing as a perfectly rigid body in the context of relativity. As for what you would see, the other end of the rod would not move the instant you pulled it. The effect actually would propagate at the speed of sound in the material. Therefore, not only would the bar appear longer, it actually would be longer. On the other hand, the Lorentz length contraction of the bar is given by $$L=L_{0}\sqrt{1-\frac{v^{2}}{c^{2}}}.$$ Depending on how fast you are pulling the bar, it could also appear shorter.
