Nonlocality and Relativity in Various Interpretations of Quantum Mechanics

Aleksandr V. Belinsky, Michael H. Shulman

Tim Oliver Eynck, Holger Lyre, Nicolai von Rummell

Since its discovery in 1959 the Aharonov-Bohm effect has continuously been the cause for controversial discussions of various topics in modern physics, e.g. the reality of gauge potentials, topological effects and nonlocalities. In the present paper we juxtapose the two rival interpretations of the Aharonov-Bohm effect. We show that the conception of nonlocality encountered in the Aharonov-Bohm effect is closely related to the nonseparability which is common in quantum mechanics albeit distinct from it due to its topological nature. We propose a third alternative interpretation based on the loop space of holonomies which serves to solve some of the problems and we trace back the topological nonlocality and thereby the Aharonov-Bohm effect to their quantum mechanical origin. All three discussed interpretations are, of course, empirically equivalent. In fact, they present us with an instructive case study for the thesis of theory underdetermination by empirical data.

Abner Shimony

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.

Susan Schneider, Mark Bailey

We propose the Prototime Interpretation of quantum mechanics, which claims that quantum entanglement occurs in a “prototemporal” realm which underlies spacetime. We claim that the Prototime Interpretation (PI) is worthy of further consideration as a superior explanation for perplexing quantum phenomena such as delayed choice, superposition, the wave-particle duality and nonlocality. In Section 11.2 , we introduce the Prototime Interpretation. Section 11.3 identifies its advantages. Section 11.4 discusses several implications of the view, such as its deterministic nature and relation to the simulation hypothesis.

Sandu Popescu