Quote by Edi
I understand the system where the photon is replaced with .. something. A particle. System where the particle would simply have kinetic energy in another direction.. but can the same be for a photon? It would kinda have to move faster than c in order to cover that increased distance when summing the two vectors.

This is not correct. Let's simply work this out from the
Lorentz Transforms.
If a pulse of light is moving at c in the +y' direction then the equation for its worldline is:
[tex]y'=ct'[/tex]
If we substitute in the Lorentz transform expressions and simplify we get:
[tex]\frac{v}{c} x + \sqrt{1\frac{v^2}{c^2}} y = c t[/tex]
Noting that:
[tex]\left(\frac{v}{c}\right)^2 + \left(\sqrt{1\frac{v^2}{c^2}} \right)^2 = 1[/tex]
we immediately see that the speed is c in both frames.