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HNPS Advances in Nuclear Physics

Local Theories and Bohmian Mechanics

C. Syros

Published Feb 19, 2020• 0 citations
Publisher

Abstract

One of the last develoonents in the research for extending the scope of the quantum theory is the recently appearing work on the Bohmian Mechanics. The motivation for an extension is provided by the conclusions of the EPR paradoxon and the famous alternative concerning the physical reality. Discussed are some properties of Bohmian Mechanics concerning the self-consistency of the theory.

DOI
10.12681/hnps.2885

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One of the last develoonents in the research for extending the scope of the quantum theory is the recently appearing work on the Bohmian Mechanics. The motivation for an extension is provided by the conclusions of the EPR paradoxon and the famous alternative concerning the physical reality. Discussed are some properties of Bohmian Mechanics concerning the self-consistency of the theory.
Many recent results suggest that quantum theory is about information, and that quantum theory is best understood as arising from principles concerning information and information processing. At the same time, by far the simplest version of quantum mechanics, Bohmian mechanics, is concerned, not with information but with the behavior of an objective microscopic reality given by particles and their positions. What I would like to do here is to examine whether, and to what extent, the importance of information, observation, and the like in quantum theory can be understood from a Bohmian perspective. I would like to explore the hypothesis that the idea that information plays a special role in physics naturally emerges in a Bohmian universe. 1 Introduction: The Status
The aim of this book is to provide a comprehensive guide to the metaphysics of Bohmian mechanics. Bohmian mechanics is a quantum theory that describes the motion of particles following trajectories that are determined by the quantum wave-function. The key question that the theory has to face relates to the ontological interpretation of the quantum wave-function. The main debate has mostly centered around two opposing views, wave-function realism on the one hand, and the nomological view on the other hand. The supporters of the former believe that the wave-function is a physical field living in a high-dimensional space; the supporters of the latter regard the wave-function as just an entity that appears in the laws of nature and lacks physical status. This monograph discusses both views open-mindedly, illuminating their tacit problems and providing new insight into how they can be overcome. Moreover, it discusses the structuralist view, which is often neglected and which can be regarded as a reconciliation of the two main opposing camps.
Abstract We consider how Bohmian mechanics characterizes the behavior of physical systems paying particular attention to what it means to make a measurement in the theory and how one should understand the empirical content of one’s records. We discuss the sense in which a measurement record selects a branch of the quantum-mechanical state and, hence, why the empirical content of the record is well-understood as being given by the effective wave function in configuration space. We conclude by considering the virtues and vices of Bohmian mechanics given how it accounts for our experience. This includes reflecting on how the theory explains surreal trajectories and EPR-Bell type nonlocal correlations.
Bohmian mechanics is the most naively obvious embedding imaginable of Schr\\"odinger's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function \\psi its configuration is typically random, with probability density \\rho given by |\\psi|^2, the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, is a consequence of Bohmian mechanics.
Since its inception Bohmian mechanics has been generally regarded as a hidden-variable theory aimed at providing an objective description of quantum phenomena. To date, this rather narrow conception of Bohm’s proposal has caused it more rejection than acceptance. Now, after 65 years of Bohmian mechanics, should still be such an interpretational aspect the prevailing appraisal? Why not favoring a more pragmatic view, as a legitimate picture of quantum mechanics, on equal footing in all respects with any other more conventional quantum picture? These questions are used here to introduce a discussion on an alternative way to deal with Bohmian mechanics at present, enhancing its aspect as an efficient and useful picture or formulation to tackle, explore, describe and explain quantum phenomena where phase and correlation ( entanglement ) are key elements. This discussion is presented through two complementary blocks. The first block is aimed at briefly revisiting the historical context that gave rise to the appearance of Bohmian mechanics, and how this approach or analogous ones have been used in different physical contexts. This discussion is used to emphasize a more pragmatic view to the detriment of the more conventional hidden-variable (ontological) approach that has been a leitmotif within the quantum foundations. The second block focuses on some particular formal aspects of Bohmian mechanics supporting the view presented here, with special emphasis on the physical meaning of the local phase field and the associated velocity field encoded within the wave function. As an illustration, a simple model of Young’s two-slit experiment is considered. The simplicity of this model allows to understand in an easy manner how the information conveyed by the Bohmian formulation relates to other more conventional concepts in quantum mechanics. This sort of pedagogical application is also aimed at showing the potential interest to introduce Bohmian mechanics in undergraduate quantum mechanics courses as a working tool rather than merely an alternative interpretation.
We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end.