How does a relativistic particle perceive a non-relativistic particle?

I would just like to point out again (to myself) that velocity is just a unitless number, since time carries the same units as distance in 4-dimensional spacetime, and the speed of light  just a conversion factor of seconds into meters, both of which are arbitrary units.

So what implications does this have to the question “what is a universe with only spacetime and photons”? In an exclusively radiation filled universe, can space and/or time exist? If so, how? Can/does empty space exist in between the photons? How can a photon exist as a (point) particle when it exists everywhere along its path simultaneously (i.e., what does it really mean to exist as a particle and a wave simultaneously)?

So I think I concluded that time only exists for non-relativistic particles and therefore does not exist for relativistic particles in the previous spacetime post so it makes no sense to talk about motion or moving for a universe with only photons since that entails rates of distance per unit time. Or rather, all motion in whatever universe is just a ratio in the photon’s perspective. We non-relativistic particles perceive relativistic particles as “moving” but they perceive us as “ratios”. What does that mean? What does it mean to “perceive something as a ratio”? I think that the photon (or neutrino or whatever) would be just as clueless about what velocity means as we are about what this ratio thing means..

Well, Einstein asks “what happens when we catch up with a beam of light” but what he really asks is “what happens to the perception of a non-relativistic particle when it reaches the same velocity as a relativistic particle”. What happens to the second half of the question “what happens to the perception of a relativistic particle when a non-relativistic particle suddenly acquires the same distance/time ratio as the relativistic particle”? Wasn’t that part of the deal too since in relativity everything is relative and so you shouldn’t just be questioning things from the absolute perspective of a non-relativistic particle? Did that second question get answered along the way/was I just not paying attention??? Uh…?