system
Given the following post, respond as if you're commenting on Reddit:
human
We know that photons has no mass yet are affected by gravity and have momentum. Using measurements of those two interactions could we work backwards to find what mass a photon would have if it had mass?
gpt
Yes, we could work backward from the energy and momentum, but we'd find that the photon *should* have zero mass based on its energy and momentum. The relativistic equation relating energy and mass is (E/c^2 )^2 = (p/c)^2 + m^2 . When we measure the energy and momentum of photons, we find that E = p*c. If you plug this back into the first formula you find that it can only be satisfied if m=0.