Photons certainly appear to have a real physical location with 1e9 FPS imaging capabilities:

"Visualizing video at the speed of light — one trillion frames per second" (2012) https://youtube.com/watch?v=EtsXgODHMWk&

But is there an identity function for a photon(s), and is "time-polarization" necessary for defining an identity function for photons?

> > > Mathematically a photon is defined as a state of the EM field (which has been quantised into a set of harmonic oscillators called "normal modes") in which there is exactly one quantum of excitation of a specific normal mode (with given wavevector and frequency). Depending on which kind of modes you consider, a photon could be a gaussian beam, or even a plane wave, so not something localised like you would say of a particle.

> Think of it like this: From the perspective of the photon, it lives and dies in the same instant. Even if it traveled across the entire universe.

Would an appropriate analogy be a "glider" from Conway's Game of Life? "Lives and dies in the same instant" isn't exactly the same, but I'm thinking of how no parts of the glider move while the glider as a whole "moves" across the board.