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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?

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    $\begingroup$ Question for you: do the scenarios in which people talk about photons in a QM context ever do any dynamics for the photon? $\endgroup$ – dmckee Aug 15 '16 at 5:09
  • $\begingroup$ 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. $\endgroup$ – CuriousOne Aug 15 '16 at 5:53
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    $\begingroup$ @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. $\endgroup$ – HolgerFiedler Aug 15 '16 at 6:09
  • $\begingroup$ @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. $\endgroup$ – CuriousOne Aug 15 '16 at 8:51
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    $\begingroup$ @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. $\endgroup$ – Sean Aug 15 '16 at 11:11
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Quantum mechanics is much more general than the Schrodinger equation, which first introduced the wave function concepts . The postulates of quantum mechanics are much more general, and different wave equations are used for different situations.

For relativistic wave functions one uses Klein Gordon for bosons, Dirac for fermions and a quantized version of Maxwell's equation for photons. The last is not very often stressed because, as you note, photons are relativistic and quantum field theory is used directly, without elaborating how the ground state function of the photon field is obtained. Here is a presentations on how the photon wave function is. Even at low energy experiments, as the double slit, the photon is described by its appropriate wave function .

Quantum field theory is a mathematical method of dealing with many body interactions in the quantum mechanical regime, but it is based on the postulates of quantum mechanics. It defines particle fields in all of spacetime and creation and annihilation operators for all these fields which act on the ground state wave function of the field, taken from the solution of the free equations mentioned above . The photon is treated in the same way as all the other particle/fields in the elementary particle table .

The interaction crossections written in the QFT formalism allow for the calculation of observables in experiments in the relativistic regime.

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  • $\begingroup$ So this treatment goes beyond Schrödinger. Is this paper you linked to in the QED regime or what would be the rough field for this Photon-Maxwell-QM treatment? $\endgroup$ – Thomas Elliot Aug 16 '16 at 5:12
  • $\begingroup$ In QFD one takes the solution of the free particle wave function, a sinusoidal function, a plane wave, as the ground state on which creation and annihilation operators generate the state function of the particle as its location changes in space time. For the photon it would be the solution of the quantized maxwell equation. For the electron the Dirac etc $\endgroup$ – anna v Aug 16 '16 at 5:55

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