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Tuesday, 15 October 2019


A Challenge to Quantum Physicists

Tom Leonard

Retired Professor of Statistics

Universities of Wisconsin-Madison and Edinburgh


1.1. My Grand Scheme (13th September 2019)

This morning I gave a brief ministry to South Edinburgh Quakers on Morningside Road on the other side of Edinburgh, to a meeting in the plush basement of the more basic Open Door Café which I have attended for almost three years (though I am not a Quaker myself and struggle with the concept of a Creator God as well as the apparent irrationality of consensus decision making). I was responding to three previous ministries during our hour of, otherwise silent, contemplation. As I remember, I suddenly leapt to my feet with the help of my bright blue walking frame Freddie, and, sounding holier than thou, blethered something like:

Before 2017, I spent a couple of years driving around the Scottish countryside with Thomas, enjoying all the sorts of views of coastlines and sunsets which you have described. Now I no longer have a car, and I plan to spend the remainder of my old age studying the mathematics of Quantum theory, so that I can escape from reality. My flatmate has just given me a beginner's book, and I intend to research and generalise its contents, in the hope of also discovering more about nature, genetics, evolution, and so on and so forth.

Everybody had a good, silent, chuckle at that! As with all such ministries, my utterances were interpreted by the members present as the spontaneous' Word of the Living God'. What I said, out of my sub-conscious, might sound over-ambitious, but I am proudly Attention Deficit and neurodiverse, a highly eccentric septuagenarian, and eclectic enough to firmly believe that I will be able to use my old-fashioned skills in probability and frequentist and Bayesian statistics to discover mathematical methodologies which turn out to be earth shattering generalisations of quantum mechanics.

The book I am referring to is entitled Quantum Mechanics: The Theoretical Minimum, and it was written in quite amiable style by Leonard Sussman and Art Friedman (2014). I will mainly focus on this book for a while, and check any extensions for originality later

Along the way I will doubtlessly derive lots of things which are already well-known e.g. to the courageous quantum Bayesians who follow in the foot steps of my sadly deceased friend Ed Jaynes [It was Ed who encouraged me to use the idea of maximum entropy when representing incomplete information. These is one of the various themes discussed in my book Bayesian Methods (with John Hsu, 1999)]. At the very least I will learn a bit about the diverse approaches to quantum mechanics and provide my readership with a easy way of surveying them. Concepts like quantum cognition particularly appeal to me. Maybe this will produce ways of describing how we people on the spectrum of neurodiversity actually think.

What are my skills in Mathematical Physics? Pretty slim! While I obtained a grade one in Physics at G.C.E. ordinary level, and a grade B at advanced level, I scarcely remember any of the Physics I studied at High School, and wouldn't even be able to operate a Bunsen burner or describe a Wheatstone Bridge. However, my A grades at advanced level in Pure and Applied Mathematics helped me obtain lowly Gamma grades in my first and (repeated) second year Applied Maths courses at Imperial College London in 1967 and 1969. Fortunately I did better in Statistics, after a monumental disaster in 1968, and quickly progressed, after graduating with a very lucky first class honours degree, to obtain my M.Sc. and Ph.D. from University College London (supervised by Dennis V. Lindley) during 1971 and 1973.

The title of my Ph.D. thesis was Bayesian Methods for the Simultaneous Estimation of Several Parameters. I, for example, derived alternatives to the shrinkage estimators for multinomial probabilities which had been used by I.J. Good and Alan Turing, when developing cryptanalysis techniques to solve the Nazi Codes during the Second World War. My entertaining correspondences with Jack Good (who also published 25 papers entitled Partly Baked Ideas) helped to stimulate this and further research.

Maybe I'll be able to use some of my ideas from my Ph.D, thesis and my follow up articles to extend the quantum mechanics literature, for example by developing further probabilistic representations for a collection of entangled Qubits. This might be used to imply spatial correlations between electrons in different states of spin.

I must say that I'm extremely impressed by the superb theoretical level of mathematical physics, which epitomizes the amazing heights of human accomplishment. I have only come close to this level in three of my published papers, by Leonard (1978), Leonard and Hsu (1992), and Chiu, Leonard and Tsui(1996), and all of these utilised theory developed by the great applied mathematician Richard E. Bellman.

    Richard E. Bellman (1920-84)

I have more recently been impressed to learn that Roger Penrose thinks that an older Universe could have existed before the 'Big Bang', and that it might be possible to use Quantum Theory to explain human consciousness.

My flat is packed with books which my much more diversely intellectual flatmate orders on the Internet, and they come crashing through the door several times a week. We've recently discussed the amazing complexity of biochemistry, epigenetics, the human genome, and our biological, neurological and reproductive systems, and we' ve wondered how all of this has been produced so speedily by our evolutionary process, and how the geological systems, which affect the weather on the surface of our planets and thereby create a propensity for Life, could have existed before intelligent life forms came into being.

I also live in hope that a joint 'afterlife' can be predicted in some convincing scientific way. So immense mysteries remain, and these certainly shouldn't be blamed on some mythical divinity or other. How far Science will progress before our planet is destroyed by the return of the dinosaurs, or whatever, is another question.

In the morning, I will return to first principles and examine the properties of Qubits in greater detail. Maybe they will ultimately explain everything!