Transcribed record of Paul Dirac's talk at Lindau about the requirements of fundamental physical theory

Asım Orhan Barut, Alwyn van der Merwe

Helge Kragh

Julian Schwinger, Berthold‐Georg Englert

This review is the updated and enlarged version of a talk delivered by J. S. on the occasion of the 1982 meeting of Nobel laureates at Lindau, and of talks given by B.-G. E. at several West German universities and Max Planck institutes in 1984.

P A M Dirac

The author discusses Heisenberg's approach to quantum theory and the associated Hamiltonian.

N. David Mermin

A little while ago I was asked to give a lecture at the very elegant Weisman Art Museum in Minneapolis on an assigned title: “Elegance in Physics.” As I get older, the things I'm asked to do get stranger, so I wasn't surprised. Alarmingly, the older I get, the stronger is my inclination to do the peculiar ones. So I accepted the invitation, and soon found myself brooding, not, as I had imagined, about the glory of the eternal verities, but about the highly contentious nature of elegance in physics. Here is the first such difference of opinion I came upon. In a lecture at Fermilab with a title similar to the one I was given, Subrahmanyan Chandrasekhar talked about “harmoniously organizing a domain of science with order, pattern, and coherence.” He cited five examples of such pinnacles of exposition, one of them being Paul Dirac's celebrated book, Principles of Quantum Mechanics. “The translucence of the eternal splendor through material phenomena,” Chandrasekhar remarked, “[is] made iridescent in these books.” Keeping that iridescent translucence firmly in mind, consider the following remarks of the eminent mathematician Jean Dieudonné: When one arrives at the mathematical theories on which quantum mechanics is based, one realizes that the attitude of certain physicists in the handling of these theories truly borders on delirium … One has to ask oneself what remains in the mind of a student who has absorbed this unbelievable accumulation of nonsense, real hogwash! It would appear that today's physicists are only at ease in the vague, the obscure, and the contradictory [1]. What is Dieudonné talking about? He is addressing the approach to quantum mechanics laid out in Dirac's book. Elegance in physics is as much in the eye of the beholder as it is in any other field of human endeavor. Dirac's formulation appeals to physicists because, by being a little vague and ambiguous about its precise mathematical structure, it enables them to grasp and manipulate the physical content of the theory with a clarity and power that would be greatly diminished if one were distracted by certain complicating but fundamentally uninteresting mathematical technicalities. But for mathematicians, those minor technical matters lie at the heart of the subject. Quantum mechanics becomes ill-formulated and grotesque if it does not properly rest on impeccable mathematical foundations.

Jonathan Tennyson

In 1929 Paul Dirac pronounced that "the underlying physical laws necessary for the mathematical theory for a large part of physics and the whole of chemistry are...completely known". While the fundamental aspects of non-relativistic quantum mechanics have remained essentially unchanged ever since, physics and chemistry have been driven largely by experiment. Dirac had the answer to that too. To his comment he added a rider: "The difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble."