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I have heard that pilot wave theory adequately explains all quantum phenomenon and is an alternative to the more mainstream Copenhagen interpretation.

We have an experiment called the delayed choice quantum eraser.

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Pilot wave theory expalins a similar phenomenon, the double slit experiment by saying that the wave which is guiding the particle is split into two parts by the double slit and interacts with each other to produce the interference pattern.

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But how does this expalin the dealyed choice quantum eraser experiment? Is the pilot wave split and then recombined? How does this work mechanically?

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The double slit as well as the quantum eraser experiments can also be explained with virtual photons/forces .... similar to the Bohm pilot wave.

Even before the real photon is created by the excited electron, the excited electron itself is already generating virtual forces in the EM field .... the forces will eventually yield a "path" for the photon. The EM field is very dynamic full of virtual as well as real photons.

Richard Feynman proposed the path integral (PI) theory .... by calculating and totalling all the phases for many paths (use a computer loop) most likely paths will be predicted. The PI shows interestingly that photons like to travel paths that have length equal to an integer multiple of the wavelength.

In the eraser setup the typical paths are from the source to the slit to the crystal and then either the detectors that reveal path or not. It appears as though the path is known from the source ... as the real photons' paths are sometimes influenced by both slits (interference) and sometimes not (no interference/one slit).

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  • $\begingroup$ There are no virtual photons in linear optics. Those perturbation theory terms only exist in quantum electrodynamics if there is a non-linear process involved that changes the energy of quanta. Generally speaking all of linear optics is such a degenerate system that it can not be used to teach actual quantum mechanics... and it hasn't been used that way until Feynman wrote some really crappy undergrad textbooks. Even today QM 101 professors who know better avoid the Feynman fallacy in their classes. Mine certainly did. $\endgroup$ Commented Nov 5, 2022 at 1:13
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    $\begingroup$ @FlatterMann I would say there are virtual photons everywhere .... or better said there are EM forces everywhere .... especially in excited electrons in atoms that are about to emit a real photon. Yes Feynman struggled with the undergrad stuff but the path integral was found to be fundamental in QED and QED is more concerned with subatomic interactions ... it doesn't have time for the DSE. $\endgroup$ Commented Nov 5, 2022 at 22:28
  • $\begingroup$ You are welcome to measure a virtual photon. I am looking forward to the paper. No offense, but there is an actual difference between math and reality. $\endgroup$ Commented Nov 5, 2022 at 22:30
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    $\begingroup$ @FlatterMann Yes that would be a great paper ..... no offense taken. $\endgroup$ Commented Nov 5, 2022 at 22:40
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The double slit is not a quantum mechanical experiment. It can be (and has been) explained perfectly well with Maxwell. The only place in the double slit where a quantum mechanical effect takes place is in the detector, where the probability of an irreversible energy exchange (which we call "a photon") is proportional to the classical intensity at that point. Why is this important? Because the solution theory of Maxwell tells us that the intensity at the detector is fully determined by the boundary value problem of the linear wave equation, i.e. the shape of the slit. There are absolutely no interactions happening in the volume (this is what linearity and the word "interference" mean). This is fully backed up by the proper theory for photons, which is quantum electrodynamics. It tells us that the interaction probability for optical photons is vanishingly small (even if it is finite, but the lowest order photon-photon scattering processes can only be observed at very high energies).

In the delayed choice quantum eraser we have quantum effects both in the source as well as in the detectors, but again we have absolutely no interaction in the volume between them. All of the physics along the light path is exactly as predicted by Maxwell's equations. However, since we are feeding a correlated photon pair in, quantum correlations can not be avoid any longer as in the simple double slit.

If you want to model such a multi-quantum system mathematically, then you have to go into the product space of the single quanta systems. This means that the original idea of Bohm that there is a guide wave in actual physical space dies right away. The guide wave is now an abstract multi-dimensional phenomenon in the abstract product space rather than a magical (it has no physical properties like energy, momentum etc. of its own) but somehow still "physical" phenomenon in physical space. This kind of removes the advertised ontological "advantages" of Bohm's theory. It basically calculates the very same thing as Copenhagen in a more complicated way but loses its ontological edge as a "classical" explanation of QM.

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