Why can we make statements about photons in QM?

Sometimes we talk about experiments with photons in quantum mechanics. Examples: double slit with photons, experiment with entangled photons etc.

Quantum mechanics is a non-relativistic theory (per design by Schrödinger). Photons are relativistic since they always travel with the speed of light.

Why can we use a non-relativistic theory do describe relativistic particles?

• Question for you: do the scenarios in which people talk about photons in a QM context ever do any dynamics for the photon? – dmckee Aug 15 '16 at 5:09
• The double slit experiment is not a quantum experiment, we can do it with surface waves on water and it still works the same. Photons don't travel, at all. They are local exchanges of energy, momentum and angular momentum between the electromagnetic field and matter. Both the electromagnetic field and matter only exist because of relativity, so it's not that describing the em field without it is any more wrong than a non-relativistic matter description. Truthfully, though, none of the experiments that you mention has anything to do with relativistic effects like pair production. – CuriousOne Aug 15 '16 at 5:53
• @CuriousOne The result of slit experiments with water waves are not the same. The fringes behind a slit from photons or electrons stand still, from water waves the intensity distribution is always in motion. Furthermore water waves have an amplitude associated with a dimension, for photons and electrons this is not defined by this way. Water waves behind an obstacle really dissipate behind the obstacle as circular wave, particles never do so, you are not able to detect them at 90° behind the slit. – HolgerFiedler Aug 15 '16 at 6:09
• @HolgerFiedler: The fringes in a the water wave experiment are also standing still, which you can see here: youtube.com/watch?v=J_xd9hUZ2AY. What you perceive as "motion" is the motion of the waves, which you can see in case of water and which stay invisible for light with a frequency of $10^{15}Hz$. If you did the interferometric phases resolves experiment, then you could reconstruct the motion of the light waves in the double slit experiment as well. It's just a matter of having a smarter detector than the pure intensity detector that we use for our students. – CuriousOne Aug 15 '16 at 8:51
• @HolgerFiedler - Electrons can also be used within the 2 slit experiment, and thus they too can demonstrate the particle/wave duality, thus they also demonstrate the collapse of the quantum wave. Can your question be applied to electrons as well ? I have not heard it said that electrons don't move at all. Electrons can be accelerated within a particle accelerator, thus if electrons don't move, then what is accelerating ? Overall, when bringing electrons into the game, relativistic particles are still in play. – Sean Aug 15 '16 at 11:11