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In the classic double slit experiment (not the single photon double slit experiment), an interference pattern emerges on whatever screen is being used. I've always heard this is because light has wave-like properties or because light is a wave.

Is the interference pattern in the double slit experinent caused by electromagnetic waves interfering or is it caused by probabiltiy waves interfering?

If it is caused by electromagnetic waves interfering, then is it fair to say that polarizing both slits differently to perform a "which-way" experiment only removes interference because light that is polarized differently

If it is caused by probability waves interfering, then is it fair to say that polarizing both slits differently to perform a "which-way" experiment isn't really measuring which way they went? It is only "setting up" for a measurement. Why does interference go away when polarized differently if this is the case?

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  • $\begingroup$ It's a probability wave. $\endgroup$ – user108787 Aug 13 '16 at 23:53
  • $\begingroup$ And polarization is not part of the probability wave function? Huh. $\endgroup$ – Jon Custer Aug 14 '16 at 1:22
  • $\begingroup$ There is no such thing as a probability wave. There is a QED wave function, but using quantum electrodynamics is total overkill for this experiment since we are not interested in the interaction of the electromagnetic field with matter here. The distinction between single photon and multi-photon interference is completely nonsensical. Photons do not interact with each other because at the energy and energy density of this experiment the em field is perfectly linear. The experiment itself is not a quantum experiment, at all. $\endgroup$ – CuriousOne Aug 14 '16 at 1:53
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    $\begingroup$ The conceptual content of the two is identical as well. The place you stumble is where you ask "which way [the photons] went", which is not a well-defined question. It's precisely as meaningless as asking which slit an electromagnetic wave went through -- it's neither one or the other, but rather a superposition of the two. $\endgroup$ – knzhou Aug 14 '16 at 2:15
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    $\begingroup$ @CuriousOne It is the one photon at a time double slit experiment that shows that the pattern on the screen can be interpreted as a probability density distribution for photon ( you know, those thingies that leave ONE point footprint on the screen) $\endgroup$ – anna v Aug 14 '16 at 3:37
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Focussing on just the one aspect of the question about the reason why polarization tagging of the slits would remove interference in the ``probability waves'' interpretation:

Firstly, as stated in the comments, one must be careful with this ``probability wave'' interpretation. It is really a probability amplitude and as such it carries all the degrees of freedom including the polarization of the state/field. When the part of the field from the different slits are tagged in terms of their polarization, the interference would go away. Effectively one `traces out' the unobserved degree of freedom, polarization. This really becomes clearer when you do the math. I can add that later, if you want (don't have the time now). Incidently, one can recover the interference with another polarizer behind the screen, if this polarizer selects out a common polarization from both fields.

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The underlying framework of the physical world we have studied with our experiments is definitely quantum mechanical. The classical particles and waves emerge from this quantum mechanical level in a mathematically smooth fashion.

If one wants to go to the basic framework for light, one has to use quantum mechanics. Quantum mechanics relies on postulates imposed on the self consistent mathematical functions in addition to the mathematical axioms, in order to connect measurements to the mathematics. Crucial to QM is the Born rule

is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born.

It can be shown that classical electromagnetic waves are built up by a confluence of photons, but this needs the formalism of quantum field theory, which is based on the quantum mechanical postulates . A photon's wavefunction is derived quantum mechanically by a quantized Maxwell's equation and it should not be surprising that the solutions merge at the classical limit.

Note, a single measurement. In the case of the double slit single photon experiment it is the probability of a point being seen at the screen's (x,y).

single photon ds

Viewed quantum mechanically that is what the interference pattern is, the distribution of photons builds up a probability density.

It is only "setting up" for a measurement.

as you say.

Why does interference go away when polarized differently if this is the case?

In principle this probability density is the solution of the quantum mechanical boundary value problem " photon scattering on two specific slits". As the solutions of quantum mechanical equations are mostly sinusoidal, and sines and cosines when functions are added or subtracted usually show interference patterns, it should not be surprising that when the probability of measurement depends on sinusoidal distributions, interference patterns may appear or go away , depending on the boundary conditions, in this case the ones imposing polarization.

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  • $\begingroup$ Can you show me experimental evidence for a double-slit two-photon experiment? $\endgroup$ – CuriousOne Aug 14 '16 at 4:28
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    $\begingroup$ @CuriousOne you are becoming funny in you monomania of "QFT uber alles". Can you show me experimental evidence of a two electron experiment? You should be the first to know about the HUP and the impossibility of setting up the exact same two particle wave function as initial condition in scatterin.g , which is important in order to be able to analyze the resulting distributions $\endgroup$ – anna v Aug 14 '16 at 5:21
  • $\begingroup$ All I am asking is that you show me a two-photon double slit experiment. Can I show you a two-electron experiment? Yes, that is what you did at LEP a while ago. I can even show you a many-quark/gluon experiment... it's what LHC scientists are doing when they are colliding lead on lead. $\endgroup$ – CuriousOne Aug 14 '16 at 5:34
  • $\begingroup$ @CuriousOne no, lep was scattering of one electron on one positron at center of mass, with known energy momentum vector. it is not a two electron experiment . lets stop this here. I have to cook for my family. $\endgroup$ – anna v Aug 14 '16 at 6:18
  • $\begingroup$ We should talk about this offline... I think you will get my point, one day. Just promise me to think about it a little. $\endgroup$ – CuriousOne Aug 14 '16 at 7:23

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