Paul Dirac revisited.

Basil J. Hiley

In this paper we revisit the controversy that arose between Paul Dirac and Joe Moyal.Our motivation is provided by the fact that the algebraic aspects of both their approaches are becoming more appreciated as interest in the development of non-commutative geometry's attempt to "geometrise" quantum mechanics grows.Both were seeking to understand the role of non-commutativity, Moyal from a consideration of the differences between classical and quantum statistics, while Dirac was exploring its implications for the dynamics.The disagreement arose essentially over which should be given priority, the dynamics or the statistics.We will provide the background to show that both are essential aspects of the same overall mathematical structure. IntroductionN this paper I want to focus on the controversy that arose between Paul Dirac and Joe Moyal as a consequence of their different proposals for developing a phase space approach to quantum theory.This controversy gets to the heart of the fundamental problems in the description of quantum phenomena.Interestingly Dirac and Moyal were both "outsiders" in the sense that they started out as engineers, more so Moyal because of the way he entered academia, a story beautifully told in a biography penned by his wife Ann Moyal (2006).! We pick up the story when Moyal was working in the Meteorological branch of the Ministére de |'Air in Paris at the outbreak of World War IJ.In the ensuing chaos, he managed to escape to England and was eventually given a job at the de Havilland Aircraft Company where he became the Assistant Director of the wartime Vibrations Department.After the war Moyal wanted to work in quantum physics when fortunately an opportunity arose for him to enter academia by becoming an assistant lecturer in the Department of Mathematical Physics at Queen's University Belfast.It was there in 1949 that he published his classic paper which is the focus of his disagreement with Dirac.This disagreement involves the question as how best to develop a (p, x,t) phase space formulation for quantum phenomena, the well-recognised difficulty arising from the non-commutativity of the quantum observables for momentum and position.In other words, if we replace the classical variables, (p,x), by operators, or rather 1. See also Moyal (2017).[Ed.]

James L. Pinfold

Alisa Bokulich

… in apprehension, how like a god! The beauty of the world … Shakespeare , Hamlet, Act 2 Scene 2 Open theories When it comes to the issues of reductionism, scientific methodology, and theory change, the views of Werner Heisenberg and Paul Dirac diverge in fundamental and interesting ways. They revisited their disagreements over these philosophical issues many times throughout their careers, and their disagreements can be most succinctly described as a debate over whether physical theories are “open” or “closed.” As we saw in the last chapter, Heisenberg's belief that classical and quantum mechanics are closed leads him to view these theories as perfectly accurate within their domains, inalterable, and correct for all time. Although Dirac never uses the term, his own views on classical and quantum mechanics can be fruitfully understood as a rival account of “open theories.” Dirac argues that even the most well-established parts of quantum theory are open to future revision; indeed he takes no part of physics to be a permanent achievement, correct for all time. Instead of viewing classical mechanics as a theory that had been replaced, he sees it as a theory that should continue to be developed, modified, and extended. Unlike Heisenberg, who views physics as a set of consistent axiomatic systems, Dirac sees physics as a discipline much closer to engineering.

Viktor Trkal

William Carter