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Is it possible that two photons move in parallel, on the same trajectory - having the same wavelength, but differ in phase?

  • Is it fundamentally possible on the level of quantum mechanics?
  • Is it potentially possible to build an experiment demonstrating it?
  • Was such an experiment actually done?
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  • $\begingroup$ Photons don't move at all, they are just local field measurements. If you need an interpretation of quantum mechanics that have semi-classical "particles" moving around, the Feynman path integral would be it. In that case every "particle photon" moves everywhere in the entire universe (within the emitters future light cone, of course). It can be mathematically and experimentally demonstrated that this is so (within the ontological limits of the interpretation, of course). In effect this means that "particle photons" can not move parallel, they are just moving randomly all over the place. $\endgroup$ – CuriousOne Jul 9 '16 at 1:01
  • $\begingroup$ But could one see it as the maximum of the wave function moving around? $\endgroup$ – Volker Siegel Jul 9 '16 at 1:32
  • $\begingroup$ That's why you have to condition on some initial and final data. What scattering is all about. $\endgroup$ – AHusain Jul 9 '16 at 1:34
  • $\begingroup$ The wave function is a formula on paper. Nobody has ever seen it in the wild. $\endgroup$ – CuriousOne Jul 9 '16 at 2:29
  • $\begingroup$ I thought you were just addressing the subtlety about plane-waves vs wave-packet solutions. $\endgroup$ – AHusain Jul 9 '16 at 5:09
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Is it possible that two photons move in parallel, on the same trajectory - having the same wavelength, but differ in phase?

Photons are quantum mechanical entities/particles listed in the elementary particle table which is the basis of the standard model of particle physics.

When measured individually, it just gives an (x,y,z,t) , by interacting with some other particles and an energy can be measured equal to h*nu , where nu is the frequency of the macroscopic classical electromagnetic wave that can be built up out of an enormous number of same energy photons.

As a quantum mechanical entity it has a wave function, although it is not often thought about, since classical electromagnetism describes so well the behavior of light. It is the wavefunction which will answer whether two photons can be on the same trajectory . The wavefunction of a single photon is a complex function and the electric and magnetic fields appear in the phases of this complex function. In an ensemble of photons, a light beam, they build up the E nd B fields of the classical light wave. The quantum field theoretical framework is used for the calculations, where creation and annihilation operators operate on the free photon wavefunction.

For two photons:

Photon photon interactions are so small they can be ignored for frequencies less than gamma ray frequencies. Therefore it is only the superposition of the two photon wavefunctions that will have an effect. The square of this superposition will give the probability density for finding the two photons in (x1,y1,z1,t1) and (x2,y2,z2,t2)

interference

Standing wave interference pattern (showing the optical intensity) from the superposition of two elliptical Gaussian beams under some angle.

italics mine

This by definition is the probability distribution of adding two photons with the spatial and temporal phases of the laser beams.

Is it fundamentally possible on the level of quantum mechanics?

Yes.

Is it potentially possible to build an experiment demonstrating it?

There have been a number of experiments with single photons hitting a double slit. Conceptually one might design an experiment on the lines of the figure above where the beams are controlled two photons at the time.

Was such an experiment actually done?

It seems that people have been looking at two single photon interference patterns

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