I was reading Jacob Bronowski’s The Ascent of Man this morning and came across a lovely thought experiment that gives intuition into time dilation that probably goes back to Einstein himself. It goes something like this. Imagine there is a clock. You see the second hand move around the face as light continuously streams from the clock to your eyes. Now imagine that you suddenly travel at the speed of light away from the clock. You would be riding with the last photons from the clock face to reach your eyes. Your vision would be filled with a frozen image of the clock because no other light would be able to reach you. Hence the second hand does not move and time stands still.
One can derive the full special relativistic time dilation expression from this kind of argument and a simple spacetime diagram.
This analogy does raise interesting questions. Imagine we were fish and that we put our clock under water. The speed of light in water is about 1.3 times smaller than in vacuum and it would be possible (although difficult) to move at the speed of light in water. So if a fish could travel at the speed of light in water away from our now-submerged clock, they would also see the clock frozen in time.
But would that be the correct interpretation of the relative rates of the ticking of the clock and a watch on the fish’s fin?