If energy is stored as size in subatomic particles, and the rate of time is related to the size of these same particles, then time can be expected to slow down for any particle that experiences an increase in energy.
This is because the “electron-clock” is bigger, and therefore slower.
Observed from outside, the natural processes associated with a speeding atom will appear to slow down.
This is exactly what we find. Radioactive particles travelling close to the speed of light decay less quickly than the same particles do when stationary.
However, there is more going on than just a swelling of matter in the open state. At the speed of light, time comes to a halt. If this is entirely due to a swelling of matter, then matter will have to be infinitely large at such speeds.
The solution to this lies in considering what it means for a photon to cross an electron. If this means a round-trip, either back and forth, or around the electron, we get the answer to the problem.
When a photon crosses an electron in motion, it does so faster in one direction than the other. The relative speed going against the electron is the speed of the photon plus the speed of the electron. The relative speed going with the electron is the speed of the photon minus the speed of the electron.
The overall round-trip slows down for particles in motion, even if there is no swelling. At the speed of light, time stops completely because the leg of the journey going with the electron takes for ever to complete.