Consistent Quantum Theory

Quantum mechanics is one of the most fundamental yet difficult subjects in physics. Nonrelativistic quantum theory is presented here in a clear and systematic fashion, integrating Born's probabilistic interpretation with Schrödinger dynamics. Basic quantum principles are illustrated with simple examples requiring no mathematics beyond linear algebra and elementary probability theory. The quantum measurement process is consistently analyzed using fundamental quantum principles without referring to measurement. These same principles are used to resolve several of the paradoxes that have long perplexed physicists, including the double slit and Schrödinger's cat. The consistent histories formalism used here was first introduced by the author, and extended by M. Gell-Mann, J. Hartle and R. Omnès. Essential for researchers yet accessible to advanced undergraduate students in physics, chemistry, mathematics, and computer science, this book is supplementary to standard textbooks. It will also be of interest to physicists and philosophers working on the foundations of quantum mechanics.

The principal intent of this monograph is to present in a systematic and self-con tained fashion the basic tenets, ideas and results of a framework for the consistent unification of relativity and quantum theory based on a quantum concept of spacetime, and incorporating the basic principles of the theory of stochastic spaces in combination with those of Born's reciprocity theory. In this context, by the physicial consistency of the present framework we mean that the advocated approach to relativistic quantum theory relies on a consistent probabilistic interpretation, which is proven to be a direct extrapolation of the conventional interpretation of nonrelativistic quantum mechanics. The central issue here is that we can derive conserved and relativistically convariant probability currents, which are shown to merge into their nonrelativistic counterparts in the nonrelativistic limit, and which at the same time explain the physical and mathe matical reasons behind the basic fact that no probability currents that consistently describe pointlike particle localizability exist in conventional relativistic quantum mechanics. Thus, it is not that we dispense with the concept oflocality, but rather the advanced central thesis is that the classical concept of locality based on point like localizability is inconsistent in the realm of relativistic quantum theory, and should be replaced by a concept of quantum locality based on stochastically formulated systems of covariance and related to the aforementioned currents.

The principal intent of this monograph is to present in a systematic and self-con tained fashion the basic tenets, ideas and results of a framework for the consistent unification of relativity and quantum theory based on a quantum concept of spacetime, and incorporating the basic principles of the theory of stochastic spaces in combination with those of Born's reciprocity theory. In this context, by the physicial consistency of the present framework we mean that the advocated approach to relativistic quantum theory relies on a consistent probabilistic interpretation, which is proven to be a direct extrapolation of the conventional interpretation of nonrelativistic quantum mechanics. The central issue here is that we can derive conserved and relativistically convariant probability currents, which are shown to merge into their nonrelativistic counterparts in the nonrelativistic limit, and which at the same time explain the physical and mathe matical reasons behind the basic fact that no probability currents that consistently describe pointlike particle localizability exist in conventional relativistic quantum mechanics. Thus, it is not that we dispense with the concept oflocality, but rather the advanced central thesis is that the classical concept of locality based on point like localizability is inconsistent in the realm of relativistic quantum theory, and should be replaced by a concept of quantum locality based on stochastically formulated systems of covariance and related to the aforementioned currents.

New ideas on the mathematical foundations of quantum mechanics, related to the theory of quantum measurement, as well as the emergence of quantum optics, quantum electronics and optical communications have shown that the statistical structure of quantum mechanics deserves special investigation. In the meantime it has become a mature subject. In this book, the author, himself a leading researcher in this field, surveys the basic principles and results of the theory, concentrating on mathematically precise formulations. Special attention is given to the measurement dynamics. The presentation is pragmatic, concentrating on the ideas and their motivation. For detailed proofs, the readers, researchers and graduate students, are referred to the extensively documented literature.

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.

The clearest, most accessible explanation yet of the amazing world of quantum mechanics. How can matter behave both like a particle and a wave? Does a particle exist before we look at it or does the very act of looking bring it into reality? Are there hidden elements to reality missing from the orthodox view of quantum physics? And is there a place where the quantum world ends and our perceivable world begins? Many of science's greatest minds have grappled with these questions embodied by the simple yet elusive "double-slit" experiment. Thomas Young devised it in the early 1800s to show that light behaves like a wave, and in doing so opposed Isaac Newton’s theories. Nearly a century later, Albert Einstein showed that light comes in particles, and the experiment became key to a fierce debate with Niels Bohr over the nature of reality. Richard Feynman held that the double slit embodies the central mystery of the quantum world. Hypothesis after hypothesis, scientists have returned to this ingenious experiment to help them answer the deep questions about the fabric of our universe. With his extraordinary gift for making the complicated comprehensible, Anil Ananthaswamy travels around the world and through history, down to the smallest scales of physical reality we have yet fathomed for the answers. ***PRAISE FOR THROUGH TWO DOORS AT ONCE*** A Physics Book of the Year A Forbes Best Book of the Year A Kirkus Best Book of the Year A Smithsonian Favourite Book of the Year Publisher's Weekly Best Books of Autumn 'A fascinating read and a must for anyone who would like to find out the latest experimental advances made in this most fundamental of quantum experiments.' Physics World 'Ananthaswamy cleverly comes at quantum physics from a different direction... An excellent addition to the 'Quantum physics for the rest of us' shelf.' Brian Clegg, author of Are Numbers Real? and The Quantum Age 'A challenging and rewarding survey of how scientists are grappling with nature’s deepest, strangest secrets.' Wall Street Journal 'A fascinating tour through the cutting-edge physics the experiment keeps on spawning.' Scientific American 'Ananthaswamy gives an absolutely mind-boggling tour of how quantum physicists try to explain this “reality” that one of the most powerful scientific models of our era.' Smithsonian 'Offers beginners the tools they need to seriously engage with the philosophical questions that likely drew them to quantum mechanics.' Science 'At a time when popular physics writing so valorizes theory, a quietly welcome strength of Ananthaswamy’s book is how much human construction comes into focus here. This is not “nature” showing us, but us pressing “nature” for answers to our increasingly obsessional questions.' Washington Post 'Ananthaswamy's book is simply an outstanding exploration of the double slit experiment and what makes it so weird.' Forbes 'A thrilling survey of the most famous, enduring, and enigmatic experiment in the history of science.' Kirkus, starred review

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws.