system
Given the following post, respond as if you're commenting on Reddit:
human
C in all reference frames?

I'm aware that the speed of light is the same in all reference frames, but, what would a passing photon look like to another photon travelling in the opposite direction?
gpt
Sadly, special relativity does not define reference frames for photons or anything else propagating at ~~zero~~ c. So we cannot answer what a photon sees. This manifests in the mathematics of a spacetime interval,  

> ds^2 = (cdt)^2 - dr^2

which for light, the null interval has ds=0,  

> 0 = (cdt)^2 - dr^2  

which reveals,  

> dr/dt = c

Here we can interpret ds=0 as dτ=0 or the proper time of the trajectory. We we directly see that time is not defined for light. We can describe the motion of light in relativity, but we cannot describe the motion of the universe while sitting on a light beam.