I know that the Englert-Greenberger-Yasin (D^2+v^2=1 for a laser) duality relation is often considered an equation quantifying Wave-Particle Duality. However, when I was playing around with the equation I found that it could be derived from a classical perspective. For example, if the slits in a double slit experiment are not of the same width then the probability of finding the photon at a slit can be found from the slit widths. Furthermore, since the amplitude of the light passing through the slits is related to the width of the slits one can find the maximum and minimum intensities of the interference pattern in terms of the slit widths. Adding the squares of the probability and visibility then gives you the EDY duality relation equation. So, since the EGY relation can be derived from a classical perspective, is it really quantum after all?
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$\begingroup$ That's more of a pseudo-science interpretation than it is physics. Wave-particle duality does not exist and quanta are not taking classical paths. One can, of course, quantify the dependence of the formation of interference fringes on the intermediate measurement coupling strength, but none of that gets us back to a failed physical picture except in the minds of those who can't let go of an eighty year old bad idea. $\endgroup$– CuriousOneCommented Dec 23, 2015 at 0:20
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$\begingroup$ Your comment is a bit confusing. Wave-particle duality is an essential nature of not only light but all matter. How can you say that wave-particle duality does not exist, in any apparatus? $\endgroup$– Clement DeckerCommented Dec 23, 2015 at 4:20
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$\begingroup$ Because wave particle duality is an 80 year old scientific concept that was popular for some time while there was confusion about the foundations of quantum mechanics. That confusion is long over, but for some reason that is hard to understand some people keep holding on to it. There is absolutely no reason to keep perpetuating concepts that didn't work well back then and that still don't work. You can do quantum mechanics perfectly rationally without any confusion and without using this term even once. Things that are not necessary have no place in science. $\endgroup$– CuriousOneCommented Dec 23, 2015 at 4:49
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$\begingroup$ So you are saying that wave-particle duality is an incorrect theory, or at least that it is no longer accepted by the scientific community? You would have to give me evidence because there is still a lot of literature being published on the concept of wave particle duality and I can find no evidence that it is a disregarded theory. $\endgroup$– Clement DeckerCommented Dec 23, 2015 at 5:00
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1$\begingroup$ But wave particle duality says nothing of the sort. It states very plainly that all matter can exhibit both particle and wave properties. $\endgroup$– Clement DeckerCommented Dec 23, 2015 at 16:53
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