Francis Perey (2018). The Collected Works of Francis Perey on Probability Theory. RESEARCHERS.ONE, https://www.researchers.one/article/2018-10-6.

Francis Perey, of the Engineering Physics Division of Oak Ridge National Lab, left a number of unpublished papers upon his death in 2017. They circulate around the idea of probabilities arising naturally from basic physical laws. One of his papers, Application of Group Theory to Data Reduction, was published as an ORNL white paper in 1982. This collection includes two earlier works and two that came later, as well as a relevant presentation. They are being published now so that the ideas in them will be available to interested parties.

November 2, 2018 10:42 am

I read Greenwood's article in the Atlantic and since I have an interested in the conduct of scientific discourse, I was interested in reading the supposed "out-there" texts of Perey. I was surprised at how coherent his writing is. I am by no means an expert, just a curious hobbyist sufficiently far outside my field, but Perey's approach to Von Mises' Water and Wine Problem is nearly equivalent to Mikkelson's proposed "symmetry," discussed in this review, with an additional justification for the specific functional form (denoted by phi in the review, which Perey and Mikkelson separately argue is simply x) based on his solution to the "non-informative problem."

Perey's Quantum Mechanics manuscript is a little bit harder to get through but it seems to me that it's very much in line with the ensemble interpretation of quantum mechanics. This interpretation is best developed by Leslie Ballentine. As far as I know, Ballentine also was inspired by Jaynes and extended Jaynes' approach to Quantum theory. In my opinion, Ballentine's textbook, "Quantum Mechanics: A Modern Development," is the best resource for this interpretation.

November 3, 2018 1:50 pm

His "Why Quantum Mechanics is Not a Local Relativistic Theory" is absolutely in the Copenhagen interpretation camp. He is saying the wavefunction is not real, it is literally a superposition of complex, imaginary values that become real once a measurement is made. He argues that the wavefunction can be nonlocal and satisfy Bell’s inequalities because a real wavefunction would be local. In other words he is saying the Copenhagen interpretation satisfies Bell’s inequalities.

He is arguing that the eigenvalue cannot be found through statistics because we do not know how many possible values there are for that measurement. My rebuttal would be the sum of the states must be equal to 1 (something must happen, a value must be measured), this is called normalization. The boundary conditions of the problem would set the possible values. He was trying to solve the Schrodinger equation to get the possible values by using Bayesian probability.

I would have asked him why he did not consider using the entropy of mixing in his water and wine problem. But I think he took this approach because he wanted to eliminate the ensemble interpretation and nonlocal hidden variable theories from quantum mechanics and satisfy the Copenhagen interpretation. The combinatorics of entropy show a symmetry that would resolve the contradictions. I would have liked to have read his counterargument.

He is also arguing that the solutions to the wavefunction evolve according to the schrodinger equation and are the set of solution found in group theory by Galois. I like the Galois part but it does not explicitly rule out a nonlocal hidden variable theory. To summarize, he believes Bayesian probability with a complex wavefunction is in perfect agreement with the Copenhagen interpretation and Bell’s inequalities. This is the dominant viewpoint.

If Veronique wants closure then she should know that her grandfather was satisfying his need to know why quantum is the way it is and he wanted to share that insight with others who may have been equally frustrated by the theory. The probability exercises were done to convince himself that Bayesian probability works in the real world and that it can be applied to quantum mechanics. The slides on uncertainty shows he was arguing the uncertainty in quantum is not systemic or statistical, but a fundamental part of the theory. This is a true statement.

Everything he is arguing is based on the our current understanding of the ontology. To most physicists quantum is just plucked out of the air without preparing anyone to understand the mathematics. He may have been trying to axiomatize physics which is Hilbert’s sixth problem.

https://en.wikipedia.org/wiki/Hilbert%27s_sixth_problem

I hope this helps. I am sorry other physicists did not understand him.

Thanks for posting. Should be read alongside this piece: https://www.theatlantic.com/amp/article/574573/?__twitter_impression=true