Where Time Breaks Down.
Einstein’s Equivalence Principle tells us that the frame in a gravitational field is indistinguishable from an accelerating frame.
And so, clocks also must tick slower the deeper they are in their gravitational field. This is the gravitational time dilation of General Relativity.
So, what does this odd example have to do with real time and real matter?
Well, if our photon clock behaves this way, then so does our photon box. In a fast moving photon box, we perceive that its internal particles have further to travel to bounce off the walls compared to an identical stationary box.
Note that, this is not the same thing as an accelerating box which gives the feeling of mass.
Here, we are talking about something moving at a high but constant speed.
And we know, atoms and their nucleons are all kind of like photon boxes. They are made up of things that would move at the speed of light, except that they are confined.
Quarks and electrons are confined first by their coupling with the Higgs field, and then by the forces binding them into atoms.
So, as an atom races past you at high speed, you would see all its internal bits ticking slower, just like the photon clock.