At the heart of quantum mechanics lies the wave function, a powerful but mysterious mathematical object which has been a hot topic of debate from its earliest stages. Covering much of the recent debate and providing a comprehensive and critical review of competing approaches, this ambitious text provides new, decisive proof of the reality of the wave function.

Aiming to make sense of the wave function in quantum mechanics and to find the ontological content of the theory, this book explores new ontological interpretations of the wave function in terms of random discontinuous motion of particles. Finally, the book investigates whether the suggested quantum ontology is complete in solving the measurement problem and if it should be revised in the relativistic domain.

A timely addition to the literature on the foundations of quantum mechanics, this book is of value to students and researchers with an interest in the philosophy of physics.

Review

‘A thoughtful survey of the many issues arising from the question: does the quantum mechanical wave function represent physical reality? Gao's book will provoke stimulating discussions among physicists and philosophers of science.' Stephen L. Adler, Institute for Advanced Study, Princeton, New Jersey

‘A profound book for a deep question.' Nicolas Gisin, Université de Genève

‘The meaning of the wave function is a problem encountered by all students of quantum mechanics. The wave function is usually attributed just a probabilistic significance but might it have other characteristics - could it be a physical field? Gao's admirable book is the first to present a comprehensive analysis of this fundamental topic. Drawing upon recent thinking, the author presents a readable up-to-the-minute assessment of the various viewpoints on the significance of the wave function. The book provides an excellent introduction to this key area in the foundations of physics.' Peter Holland, University of Oxford

'This book discusses in great detail the fundamental problem of the conceptual and philosophical status of the quantum wave function. The remarkable deepness and completeness of the analysis and the objective style of the author when discussing divergent positions render the book a useful tool of investigation. I unrestrictedly recommend this work to all people interested in contributing to the most intriguing aspects of the measurement problem and the various obscure and debated aspects of quantum mechanics.' GianCarlo Ghirardi, Università degli Studi di Trieste and International Centre for Theoretical Physics, Trieste

'The reality or unreality of the quantum wave function is a topic of lively debate in the foundations of quantum mechanics. In this thoughtful and thought-provoking book, Shan Gao offers nothing less than a novel realist interpretation of the wave function, as describing the propensities of particles undergoing random discontinuous motion. It is a book that everyone interested in the ongoing debates will want to take a look at.' Wayne Myrvold, University of Western Ontario

'Gao's book is particularly important for researchers in the foundations and metaphysics of quantum mechanics. Physicists and philosophers alike will find plenty of material for further development. The focus on protective measurements and on randomly jumping particles brings new input for unravelling the ontology of the wave-function - and of relativistic quantum theories. Gao has shown us a promising path well worth following.' Mario Hubert, Notre Dame Philosophical Reviews

'Does the wave function directly represent a state of reality, or merely a state of (incomplete) knowledge of it, or something else? This question is the starting point of this book, in which the author - a professor of philosophy - aims to make sense of the wave function in quantum mechanics and investigate the ontological content of the theory. A very powerful mathematical object, the wave function has always been the focus of a debate that goes beyond physics and mathematics to the philosophy of science … Aimed at readers familiar with the basics of quantum mechanics, the book could also appeal to students and researchers interested in the philosophical aspects of modern science theories.' Virginia Greco, CERN Courier

'This is a fascinating and important book about how to interpret the wave function of quantum theory. It is clearly written, up to date, and has a wealth of interesting things to say … The Meaning of the Wave Function makes a courageous and fascinating contribution to understanding the quantum domain. I hope it provokes research from others along similar lines.' Nicholas Maxwell, Metascience

'Shan Gao has written an exemplary book on the nature of the wave function - its theoretical role, the ontology it represents, and how understanding this ontology can contribute to solving the measurement problem. These themes are connected by a single line of argument that runs through the book from beginning to end. The argument is presented clearly and concisely, and the relevant philosophical and physical background is explained with admirable clarity and precision, without either excessive verbiage or unnecessary technicality. Gao’s proposed solutions to the foundational problems of quantum mechanics are clear, novel, and well-motivated … But there is a lot more in the book that is worth thinking about, too, including many incisive criticisms of competing views concerning the nature of the wave function and how to solve the measurement problem. I highly recommend taking the time to engage with Gao’s arguments.' Peter J. Lewis, International Journal of Quantum Foundations

'For some time, Gao has been developing an original perspective on quantum mechanics, based on the idea that the wave function describes the random discontinuous motion of real particles: … [The author] gives a detailed and meticulous illustration of this view, and the arguments supporting it, engaging in a careful discussion with many arguments present in the literature. Up to discriminating empirical results, or proven logical inconsistencies, 'interpretations' of quantum mechanics cannot be truly proven or disproven. They give us a way to think about the theory, and about nature in general, they can orient scientific research, and they interact strongly with our general philosophical orientations … One of the best aspects of Gao’s book, actually, is the punctilious account of many arguments and counterarguments given in the literature; as such, the book is also a useful source and an overview of number of debates around the interpretation of quantum theory.' Carlo Rovelli, Foundations of Physics

'… offers a readable and comprehensive discussion on the everlasting debate about the reality of the mathematical object that is used to represent states of quantum systems. With a profound influence on ontological interpretations, the measurement problem is faced in a very original form that, I believe, will provoke renewed discussions on the matter. The text, consisting of eight chapters, is an ambitious attempt to relieve one of the worst features of quantum mechanics textbooks: the exclusion of all historical and philosophical grounds. It includes well-founded concepts to interpret experiments and avoids the purely calculation problems … In summary, I found the present book well-written and organised, with very stimulating discussions on the meaning of the wave function. This monograph represents an excellent resource for students and researchers interested in the foundations and philosophy of quantum mechanics.' Oscar Rosas-Ortiz, Contemporary Physics

'Shan Gao has now written a book that will serve as a valuable resource for everybody interested in the subject and advance the debate by new and bold ideas. That he manages to do this in a mere 170 pages is due not least to the fact that he avoids the temptation to play the classics. He does not try to entertain (or bore) us with yet another discussion of the double-slit experiment but dives right into recent developments in quantum foundations.' Dustin Lazarovici, International Studies in the Philosophy of Science.

About the Author

Shan Gao is Professor of Philosophy at the Research Center for Philosophy of Science and Technology, Shanxi University, and Visiting Professor at the University of Chinese Academy of Sciences. He is the founder and managing editor of the International Journal of Quantum Foundations, and is the author of several books and the editor of the recent anthology Protective Measurement and Quantum Reality: Towards a New Understanding of Quantum Mechanics (Cambridge, 2015). His research focuses on the foundations of quantum mechanics and the history of modern physics.