Bohmian Mechanics

Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. This book provides a systematic introduction to Bohmian mechanics and to the mathematical abstractions of quantum mechanics, which range from the self-adjointness of the Schrödinger operator to scattering theory. It explains how the quantum formalism emerges when Boltzmann's ideas about statistical mechanics are applied to Bohmian mechanics. The book is self-contained, mathematically rigorous and an ideal starting point for a fundamental approach to quantum mechanics. It will appeal to students and newcomers to the field, as well as to established scientists seeking a clear exposition of the theory.

Most textbooks explain quantum mechanics as a story where each step follows naturally from the one preceding it. However, the development of quantum mechanics was exactly the opposite. It was a zigzag route, full of personal disputes where scientists were forced to abandon well-established classical concepts and to explore new and imaginative pathways. Some of the explored routes were successful in providing new mathematical formalisms capable of predicting experiments at the atomic scale. However, even such successful routes were painful enough, so that relevant scientists like Albert Einstein and Erwin Schrödinger decided not to support them. In this book, the authors demonstrate the huge practical utility of another of these routes in explaining quantum phenomena in many different research fields. Bohmian mechanics, the formulation of the quantum theory pioneered by Louis de Broglie and David Bohm, offers an alternative mathematical formulation of quantum phenomena in terms of quantum trajectories. Novel computational tools to explore physical scenarios that are currently computationally inaccessible, such as many-particle solutions of the Schrödinger equation, can be developed from it.

We are often told that quantum phenomena demand radical revisions of our scientific world view and that no physical theory describing well defined objects, such as particles described by their positions, evolving in a well defined way, let alone deterministically, can account for such phenomena. The great majority of physicists continue to subscribe to this view, despite the fact that just such a deterministic theory, accounting for all of the phe nomena of nonrelativistic quantum mechanics, was proposed by David Bohm more than four decades ago and has arguably been around almost since the inception of quantum mechanics itself. Our purpose in asking colleagues to write the essays for this volume has not been to produce a Festschrift in honor of David Bohm (worthy an undertaking as that would have been) or to gather together a collection of papers simply stating uncritically Bohm's views on quantum mechanics. The central theme around which the essays in this volume are arranged is David Bohm's version of quantum mechanics. It has by now become fairly standard practice to refer to his theory as Bohmian mechanics and to the larger conceptual framework within which this is located as the causal quantum theory program. While it is true that one can have reservations about the appropriateness of these specific labels, both do elicit distinc tive images characteristic of the key concepts of these approaches and such terminology does serve effectively to contrast this class of theories with more standard formulations of quantum theory.

Emergent quantum mechanics explores the possibility of an ontology for quantum mechanics. The resurgence of interest in "deeper-level" theories for quantum phenomena challenges the standard, textbook interpretation. The book presents expert views that critically evaluate the significance—for 21st century physics—of ontological quantum mechanics, an approach that David Bohm helped pioneer. The possibility of a deterministic quantum theory was first introduced with the original de Broglie-Bohm theory, which has also been developed as Bohmian mechanics. The wide range of perspectives that were contributed to this book on the occasion of David Bohm’s centennial celebration provide ample evidence for the physical consistency of ontological quantum mechanics. The book addresses deeper-level questions such as the following: Is reality intrinsically random or fundamentally interconnected? Is the universe local or nonlocal? Might a radically new conception of reality include a form of quantum causality or quantum ontology? What is the role of the experimenter agent? As the book demonstrates, the advancement of ‘quantum ontology’—as a scientific concept—marks a clear break with classical reality. The search for quantum reality entails unconventional causal structures and non-classical ontology, which can be fully consistent with the known record of quantum observations in the laboratory.

This book shows how Bohmian mechanics overcomes the need for a measurement postulate involving wave function collapse. The measuring process plays a very important role in quantum mechanics. It has been widely analyzed within the Copenhagen approach through the Born and von Neumann postulates, with later extension due to Lüders. In contrast, much less effort has been invested in the measurement theory within the Bohmian mechanics framework. The continuous measurement (sharp and fuzzy, or strong and weak) problem is considered here in this framework. The authors begin by generalizing the so-called Mensky approach, which is based on restricted path integral through quantum corridors. The measuring system is then considered to be an open quantum system following a stochastic Schrödinger equation. Quantum stochastic trajectories (in the Bohmian sense) and their role in basic quantum processes are discussed in detail. The decoherence process is thereby described in terms of classical trajectories issuing from the violation of the noncrossing rule of quantum trajectories.

It has often been claimed that without drastic conceptual innovations a genuine explanation of quantum interference effects and quantum randomness is impossible. This book concerns Bohmian mechanics, a simple particle theory that is a counterexample to such claims. The gentle introduction and other contributions collected here show how the phenomena of non-relativistic quantum mechanics, from Heisenberg's uncertainty principle to non-commuting observables, emerge from the Bohmian motion of particles, the natural particle motion associated with Schrödinger's equation. This book will be of value to all students and researchers in physics with an interest in the meaning of quantum theory as well as to philosophers of science.

Most textbooks explain quantum mechanics as a story where each step follows naturally from the one preceding it. However, the development of quantum mechanics was exactly the opposite. It was a zigzag route, full of personal disputes where scientists were forced to abandon well-established classical concepts and to explore new and imaginative pathways. Some of the explored routes were successful in providing new mathematical formalisms capable of predicting experiments at the atomic scale. However, even such successful routes were painful enough, so that relevant scientists like Albert Einstein and Erwin Schrödinger decided not to support them. In this book, the authors demonstrate the huge practical utility of another of these routes in explaining quantum phenomena in many different research fields. Bohmian mechanics, the formulation of the quantum theory pioneered by Louis de Broglie and David Bohm, offers an alternative mathematical formulation of quantum phenomena in terms of quantum trajectories. Novel computational tools to explore physical scenarios that are currently computationally inaccessible, such as many-particle solutions of the Schrödinger equation, can be developed from it.

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.