Introduction: A Summary of Mathematical and Physical Background for One-Particle Quantum Mechanics

Gregory L. Naber

R. Bonventre

Peter D. Collins

Anthony Sudbery 1986 Cambridge: Cambridge University Press xiii + 358 pp price £40 (£1 5 paperback) ISBN 0 521 25891 X Hdbk, 0 521 27765 5 Pbk An unusual book this, since it tries to provide a basic introduction to quantum theory, together with the elements of modern particle physics, but is aimed not at physicists (who need to learn how to apply quantum mechanics to real physical problems) but at undergraduate mathematicians. The latter, it is supposed, will expect (or tolerate) greater mathematical rigour than the former, but may have little background knowledge of physics and would be more interested in the logical structure of the subject than in how to make use of it.

Arno Böhm, Haydar Uncu, Soliman R. Komy

Alyssa Ney

The aim of this volume is to develop and evaluate the suggestion that if one adopts the interpretation of quantum mechanics initially proposed by Hugh Everett, today frequently referred to as the “many-worlds interpretation,” then one can avoid the kind of nonlocality that is often thought to be a consequence of quantum entanglement according to other approaches, and thus permit the compatibility of these two pillars of modern physics: quantum mechanics and special relativity. Although this is an idea that seems to have been recognized by Everett and is sometimes touted as a reason to prefer his approach to interpreting quantum mechanics over others, the precise way in which Everett’s interpretation achieves this locality, indeed whether it even does achieve locality, has been debated, including among the interpretation’s proponents. The aim of this introductory chapter is to provide readers with a background of this debate concerning the locality of Everettian quantum mechanics. We begin with a brief historical introduction to Everett’s proposed interpretation of quantum mechanics and its later development into the many-worlds interpretation. The following section discusses how the by now well-established phenomenon of quantum entanglement seems to imply what Albert Einstein, in a 1947 letter to Max Born, called “spooky action at a distance,” and a tension with special relativity. We then discuss why one might think that the many-worlds interpretation allows one to avoid nonlocality in this sense. The next sections bring the reader up to date with how the locality of Everettian quantum mechanics has been debated both by critics and proponents of the interpretation. As we will see, the desire to understand Everettian quantum mechanics as an interpretation that avoids nonlocality has opened up some interesting debates concerning both what it means to say an interpretation of quantum mechanics is local and over the metaphysical and mathematical interpretation of Everettian quantum mechanics itself. This introductory chapter concludes with a summary of the contributions to the present volume in the context of this ongoing debate.

Andrii Iurov