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I recently read Arnold Neumaier's lectures on uncovering classical aspects of quantum mechanics:

In "8. Simulating quantum mechanics", an optical model based on the second order coherence theory of the Maxwell equations is presented. Even so I can understand this model more or less, I would prefer simpler optical toy models for a start. Having explicit boundary conditions would be nice, and a restriction to (quasi-)monochromatic light could make it easier to intuitively understand such a system.

For example, I guess that a complex superposition of polarized monochromatic plane waves traveling up or down in z-direction could be used to create a faithful optical model of a 2-qubit quantum system. (The periodic boundary conditions used here cannot really be reproduced in an actual physical experiment, but that doesn't worry me at the moment.) The first qubit would be the complex degree to which the plane wave is traveling up or down, and the second qubit would be the complex degree to which the plane wave is x- or y-polarized. But which measurements are allowed in such a toy model? The average intensity can of course be measured, but can the average Poynting vector be measured as well? Are destructive measurements such as putting a polarization filter into the system allowed? Is there a way to add a stochastic element (Born rule) to the measurement process in such an optical model?

Of course I should be able to work out most of these questions myself, but I wonder whether people like Arnold Neumaier haven't already worked out such simple optical toy models, and put the details online somewhere...

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    $\begingroup$ this has not been done yet except maybe somewhat in a paper by neumaier, a simple hidden variable experiment. it is thought to be impossible (eg due to bell nonlocality) but probably an incorrect "barrier/ no-go" thm understanding/ interpretation due to a near-century-long misunderstanding of QM originating with Bohr/ Copenhagen interpretation. are sound models also ok with you? have some ideas on this & looking for math/ physics experts to flesh them out with eg in Physics Chat $\endgroup$
    – vzn
    Commented Jan 10, 2015 at 0:01
  • $\begingroup$ @vzn Indeed, that paper by Arnold Neumaier seems to answer my question. I have no problems with sound (acoustic) models either, why should I? $\endgroup$
    – Thomas Klimpel
    Commented Jan 10, 2015 at 12:05
  • $\begingroup$ @vzn As long as you are convinced that Arnold Neumaier's models (or your ideas) are revolutionary non-mainstream physics (which they are not, they are both mainstream and non-revolutionary), I would prefer not to discuss with you about them on physics.se (not even chat). The community here is opposed to non-mainstream physics, or to what they perceive to be non-mainstream physics. And if you keep claiming it is revolutionary, how could they not perceive it as "non-mainstream"? $\endgroup$
    – Thomas Klimpel
    Commented Jan 10, 2015 at 12:11
  • $\begingroup$ contd in chat $\endgroup$
    – vzn
    Commented Jan 15, 2015 at 6:15
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    $\begingroup$ I saw this post only now.... I never got around to the third lecture. But I wrote up an account of Stokes' 1852 classical view of the qubit in physicsforums.com/insights/a-classical-view-of-the-qubit This contains at the top a link to much more about the thermal interpretation. $\endgroup$
    – Arnold Neumaier
    Commented May 29, 2019 at 15:01

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But which measurements are allowed in such a toy model?

The basic assumption should be that oscillations in time are so quick that only averages over time can be measured. Because the speed of light is so big, measuring at different positions in space should be allowed nevertheless.

but can the average Poynting vector be measured as well?

Why not? It may be hard to describe a non-destructive measurement device for it, but it should be measurable in principle.

Are destructive measurements such as putting a polarization filter into the system allowed?

Definitively. Whether polarization can only be measured destructively is another question.

Is there a way to add a stochastic element (Born rule) to the measurement process in such an optical model?

There seems to be no natural way to do so, but maybe this is a good thing. It shows that there are systems satisfying all axioms and assumptions of the quantum mechanical formalism, without also satisfying the (stochastic version of the) Born rule. Similar to the situation for the parallel postulate in Euclidean geometry, this shows that the Born rule cannot be derived from the other axioms and assumptions alone.

One reason for this answer is that the missing stochastic element might actually be a good thing. The other reason is that the "restriction to (quasi-)monochromatic light" from the question is essentially equivalent to requiring that all quantum states have the same energy level. One motivation for looking at optical toy models was to get entanglement in an easily understandable model. Because my textbooks treat entanglement and quantum computing in a static setting without considering the energy levels, it was only natural that (quasi-)monochromatic light seemed preferable to me. But because the energy levels determine the time evolution of the phases, they might be an important limitation for quantum computing in practice, if it should be impossible to avoid multiple energy levels completely.

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Light IS the toy model for quantum mechanics. Maybe the technically most simple quantum mechanical experiment I know is the double slit experiment with light and it's extremely simple to replicate, even with household means (we can talk about potential experimental setups in an independent question).

As for Dr. Neumaier's very skewed perspective about physics... I would suggest that he should think VERY CAREFULLY about the reason why we call it QUANTUM mechanics and not PARTICLE mechanics. After reading part of these pamphlets, I am getting the definitive feeling, that he is not a good source for an introduction to QM. Those scripts are enormously confused about physics, and quite honestly, I think they are full of technical mistakes and misinterpretations. In effect, I think he is struggling with the demons of his misunderstanding of physics more in those documents than he is "teaching".

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  • $\begingroup$ These lectures are definitively not "introductions", but this doesn't mean that they are enormously confused. They use advanced technical language and tools without even trying to introduce them properly. For the tools with which I'm familiar, I can assert you that the lectures applied them correctly. The advanced tools he uses are the reason why I would prefer simpler models... Regarding Prof. Dr. Arnold Neumaier's perspectives, they may appear skewed from a physical perspective, but their mathematical content is good enough for all practical purposes... $\endgroup$
    – Thomas Klimpel
    Commented Sep 7, 2014 at 22:04
  • $\begingroup$ @ThomasKimpel: I won't get into a discussion with you about this. I said my piece. You can ask other physicists about the obvious confusion of a mathematician (?) about physics in these "lectures". Like I said, you can find the most simple "model systems" of QM in every real introductory textbook about QM. Please consult the library. If you want advice on how to repeat simple quantum mechanical experiments with light with simple means that everybody in the developed world has access to, I am more than happy to help you. $\endgroup$
    – CuriousOne
    Commented Sep 7, 2014 at 22:09
  • $\begingroup$ "we can talk about potential experimental setups in an independent question": What do you mean? I carefully wrote this question to describe what I would like to know, why I would like to know it, and at which point I'm stuck. So the points about which I would need help are the ones following "But which measurements are allowed in such a toy model?" Before writing this question, I consulted Jan-Markus Schwindt "Tutorium Quantenmechanik", Gernot Münster "Quantentheorie" and Jochen Pade "Quantenmechanik zu Fuß" in detail. I wasn't aware that these are not real textbooks. $\endgroup$
    – Thomas Klimpel
    Commented Sep 7, 2014 at 22:16
  • $\begingroup$ @ThomasKlimpel: I know what you wrote and I gave you the perspective of an experimentalist, who has spent his entire experimental career working on quantum mechanical systems. If you want to know what QM really is, get down and dirty with a light source and some objects scattering it. THAT is QM. Musing about whether photons are "localizable particles" or not is not QM. It's the thoughts of a man who, INHO, simply hasn't read the physics textbooks carefully. I can't comment on your choice of books. Again, if you want to "see" QM at work, that's easy. $\endgroup$
    – CuriousOne
    Commented Sep 7, 2014 at 22:34
  • $\begingroup$ -1 . Writing with uppercase letters does not make your claims more right. I think the first part of your reply is enough to provide some answer to the question (even if it is apparently not answering the original question). The following personal rant on Neumaier and his understanding of physics and what should physics be about, according to your own belief, seem out of place to me. $\endgroup$
    – gatsu
    Commented Dec 11, 2015 at 9:08

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