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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!





  4. Physics maths Symbols keyboard requires copy and pasting

    easier to use but less symbols.




    "This article summarizes the Quantum Bayesian [1–7] point
    of view of quantum mechanics, with special emphasis on the
    view’s outer edges—dubbed QBism.1 QBism has its roots
    in personalist Bayesian probability theory, is crucially dependent upon the tools of quantum information theory, and most
    recently, has set out to investigate whether the physical world
    might be of a type sketched by some false-started philosophies
    of 100 years ago (pragmatism, pluralism, nonreductionism,
    and meliorism). Beyond conceptual issues, work at Perimeter
    Institute is focussed on the hard technical problem of finding
    a good representation of quantum mechanics purely in terms
    of probabilities, without amplitudes or Hilbert-space operators. The best candidate representation involves a mysterious
    entity called a symmetric informationally complete quantum
    measurement. Contemplation of it gives a way of thinking
    of the Born Rule as an addition to the rules of probability theory, applicable when an agent considers gambling on
    the consequences of his interactions with a newly recognized
    universal capacity: Hilbert-space dimension. (The word “capacity” should conjure up an image of something like gravitational mass—a body’s mass measures its capacity to attract
    other bodies when nothing impedes. With hindsight one can
    say that the founders of quantum mechanics discovered another universal capacity, “dimension.”) The article ends by
    showing that the egocentric elements in QBism represent no
    impediment to pursuing quantum cosmology and outlining
    some directions for future work."


    Review ofQBism: The Future of Quantum Physics
    Matthew S. Leifer

  9. "Is it all in my head?
    According to the Bayesian approach, quantum theory is not a law of Nature that
    physical systems ‘must obey.’ Rather, it is a theory that advises you about how
    you should decide your degree of confidence in predicting outcomes of future
    experiments, based on your prior knowledge and your latest observations of
    these systems.
    The Bayesian approach seems to be a consistent way to view quantum theory,
    and it will never make a prediction that contradicts any other valid ways of
    interpreting the theory. Independent of which philosophy might be preferred by
    users of quantum theory, they calculate and use the same probabilities. Yet many
    physicists are not comfortable with the Bayesian approach when taken to its
    limits, wherein quantum theory represents beliefs rather than representing the
    physical world. One of its proponents, Ruediger Schack, acknowledges that the
    philosophy of Quantum Bayesianism, also called QBism for short, can be a hard
    pill to swallow for many physicists. He said, “When QBism holds that science is
    as much about the scientist as it is about the world external to the scientist, it
    challenges one of the most deeply held prejudices that most physicists subscribe
    Some physicists have criticized the Bayesian approach by claiming it equates
    a person’s degree of confidence with a mere arbitrary belief. A counter to such
    criticism is to point out that, of course, this theory should reflect deeply Nature’s
    ways of behaving so your degree of confidence is based on sound reasoning.
    This is where the detailed physics comes in, constraining what a person
    following the Bayesian approach will choose to believe. In other words, a careful
    use of the Bayesian approach will not lead one to predict one thousand fairies
    dancing on the head of a pin. Yet there is still a lingering awkwardness in
    Quantum Bayesianism, according to many physicists. Physicist Steven van Enk
    says, “Quantum Bayesians simply assume quantum mechanics does not describe
    the world, just what we know about it. But of course, then they still have to
    answer the question what the world is like.”
    13 That is, what is it about the
    physical world that makes it this way? Brukner writes about the problem in
    understanding how measurements happen:
    One possibility to address these questions would be to dismiss the measurement problem as a pseudoissue. … It seems to me that this path is taken by some proponents of … Quantum Bayesianism
    (QBists), for example when Fuchs and Schack write, “a measurement is an action an agent takes to
    elicit an experience. The measurement outcome is the experience so elicited.” Such a view is
    consistent and self-contained, but in my opinion, it is not the whole story. It is silent about the
    question: what makes a photon counter a better device for detecting photons than a beam splitter? Yet
    the question is scientifically well posed and has an unambiguous answer (which manufacturers of
    photo-detectors do know!)."
    (P.250-251, Quantum Physics What everyone should know, Michael Raymer).

    "Within the Quantum Bayesianism interpretation of quantum theory, the Born rule is seen as an extension of the standard Law of Total Probability, which takes into account the Hilbert space dimension of the physical system involved.[5] In the ambit of the so-called Hidden-Measurements Interpretation of quantum mechanics the Born rule can be derived by averaging over all possible measurement-interactions that can take place between the quantum entity and the measuring system.[6][7] It has been claimed that Pilot wave theory can also statistically derive Born's law.[8] While it has been claimed that Born's law can be derived from the many-worlds interpretation, the existing proofs have been criticized as circular.[9] Kastner claims that the transactional interpretation is unique in giving a physical explanation for the Born rule.[10]"