That's an interesting paper. It does not, however, support markie's belief that Mills has come up with a classical reformulation of quantum mechanics. Aharonov et al. explicitly state that their deterministic account is based upon "nonlocal interactions"/"dynamical nonlocality"/"nonlocal equations of motion", which is an even stronger violation of classical physics than the "the more familiar kinematical nonlocality [implicit in entangled states...]" markie rejects as "woo".
The purpose of showing that paper was to show, as I said, that it should not be assumed that all interpretations of the double slit experiment are the same. Aharonov and company are making progress, but that they have to invoke non locality shows they haven't yet arrived.
It should also be noted that Bell's inequalities, whose relevance markie rejects because Mills can't explain why they are violated in all of the many experimental tests conducted so far, are a purely mathematical fact about probabilities, easily understood and proved without any mention of quantum mechanics or (markie's favorite) hidden variables.
As I've said before, there are no hidden variables in the way Mills describes the EPR results.
The purely mathematical nature of Bell's inequalities is obscured by expositions based on the history of quantum mechanics and the famous Einstein/Podolsky/Rosen (EPR) paper suggesting that a deterministic account of the strikingly non-classical phenomena predicted (and observed!) by quantum mechanics might be obtained by supposing quantum mechanics is somehow "incomplete"; in particular, EPR suggested a deterministic version of quantum mechanics might become possible if there were "hidden variables". The EPR paper certainly inspired Bell to prove his theorem, and Bell's own exposition referred to the EPR paper and to hidden variables, but the theorem and its proof is just a calculation involving probabilities.
All proposed theories that are consistent with classical physics obey Bell's inequalities. Experiments do not obey Bell's inequalities, so all theories based on classical physics are inconsistent with experiment. New theories continue to be proposed, but the interesting question nowadays is not whether those new theories are based on classical physics, but which principles of classical physics do they abandon?
Not all 'proposed theories that are consistent with classical physics obey Bell's inequalities', since, after all, Mills has such a theory. I don't think you've actually looked at Mills' reasoning about why classical attempts failed (as he critiques Horne), nor how he obtains the correct expectation values.
In particular, markie's oft-repeated claim that Randell Mills has given a purely classical explanation for quantum phenomena is hogwash, and markie's attempts to support that claim are slapstick comedy. ("The photon exchange would be described classically with Maxwell's equations.")
Read the first page of chapter 8 dealing with diffraction and the double slit experiment. It starts off with Maxwells equations which leads to the Hemholtz wave equation. Also Huygen's principle and Diracs delta function are invoked. So of course it goes beyond Maxwell's equations per se, but it starts there.
