I recently read Arnold Neumaier's lectures on uncovering classical aspects of quantum mechanics:
- Classical and quantum field aspects of light
- Optical models for quantum mechanics
- I can't find the third lecture, probably it doesn't exist yet. I guess it will elaborate more on the thermal interpretation, but it's easy enough to find published material on this.
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...