This is a companion piece to A9940052, Parallel Universes and Crossover Fiction.
There are two dimensions of time. Once you realise that, it all makes sense.
Normally we travel diagonally through time, but in a so-called “time machine”, we travel horizontally, as it were. When we stop, we continue along the diagonal as usual, but this is not the same diagonal we came from. You’re perfectly welcome to shoot your grandfather here, as it were. When you go back forward, you may arrive at the same time as you left, but on a third diagonal, you may arrive so that the time you were missing from your diagonal is the same as the length of time you were in the other, or something in-between. This explains how The Restaurant at the End of the Universe can have so many patrons, but they’re not all there together.
You know, this could probably do with some kind of diagram.