# Proving that $c$ is constant in multiple directions

I was lightly tickled by Veritasium video Why no one has measured the speed of light in which the author says that a one-way measurement of speed of light is impossible (or, rather, that $$c$$ could vary depending on direction).

So riddle me this:

You have a mirror (M), light source (LS) and light detector (LD) at a certain distance apart (either d/2 or d).

M ←d/2→ LS ←d→ LD

Let's periodically shoot two photons from the light source in two directions:

1. one towards the detector
2. one towards the mirror

In first case, it travels distance 'd' (LS to LD). In second case it travels distance 2d (LS to M, M to LS, LS to LD).

If lightspeed is isotropic, you will see the photons that traveled directly arrive with some frequency, and the others bouncing off the mirror with half of that frequency. If it isn't isotropic, they will de-sync (since it traveled 0.5d in one direction and 1.5d in the other).

Measurement is done by a single device at a single place, no sync needed. No moving parts either.

So what am I missing?

• the energy levels depend on $c$, or on $\epsilon_0$, does this change when c is not a constant?, or are they a function of the averaged $c$?