Imagine an infinitely small particle that keeps perfect time. Let’s call this particle a clocklet. We don’t have such particles, but they’re useful for considering the following.

Make a disc of clocklets about and start it spinning. Clocklet C0 is at the centre of the disc, C2 is on the edge, and C1 is half way in between. When the disc is spinning slowly, all three clocks agree on the time. C2 moves at twice the speed of C1. C0 spins, but does not otherwise move.

As we spin our disc faster and faster, the clocklets begin to differ due to an effect known as time dilation. Furthermore, C2 can never go faster than the speed of light even if C1 is moving faster than half the speed of light.

So what happens if it does? Assume that the disc spins fast enough such that C1 moves at 51% the speed of light. If the disc stops spinning, would C1 still be half way in between C0 and C2? Furthermore, does C0 differ at all from an independent clocklet outside of this disc?

I don’t have the background to answer these questions, but it’s certainly entertaining to think about.