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Foundations of Quantum Mechanics

Robert W. Spekkens

Published Jan 1, 2016• 0 citations
Publisher

Abstract

The field of quantum foundations seeks to answer questions such as: What do the elements of the mathematical formalism of quantum theory represent? From what physical principles can the formalism be derived? What are the precise ways in which a quantum world differs from a classical world and other possible worlds? These lectures will cover some important foundational topics which touch upon these questions, in particular, operational and realist interpretations of the formalism, the quantum measurement problem, nonlocality and contextuality.

DOI
10.14288/1.0040936

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The field of quantum foundations seeks to answer questions such as: What do the elements of the mathematical formalism of quantum theory represent? From what physical principles can the formalism be derived? What are the precise ways in which a quantum world differs from a classical world and other possible worlds? These lectures will cover some important foundational topics which touch upon these questions, in particular, operational and realist interpretations of the formalism, the quantum measurement problem, nonlocality and contextuality.
Quantum mechanics is an extraordinarily successful scientific theory. But more than 100 years after it was first introduced, the interpretation of the theory remains controversial. This Element introduces some of the most puzzling questions at the foundations of quantum mechanics and provides an up-to-date and forward-looking survey of the most prominent ways in which physicists and philosophers of physics have attempted to resolve them. Topics covered include nonlocality, contextuality, the reality of the wavefunction and the measurement problem. The discussion is supplemented with descriptions of some of the most important mathematical results from recent work in quantum foundations, including Bell's theorem, the Kochen-Specker theorem and the PBR theorem.
The foundations of quantum mechanics have been a subject of intense investigation and debate since the theory's inception. Recent developments in quantum technologies and theoretical frameworks have shed new light on foundational issues and raised intriguing questions about the nature of reality at the quantum level. recent advancements in our understanding of the foundational principles of quantum mechanics and discuss unresolved questions that continue to challenge our conceptual framework. Topics of interest include the measurement problem, quantum entanglement, the role of contextuality and nonlocality, interpretations of quantum theory, and the quest for a unified theory of quantum gravity. findings and ongoing debates in the field, we aim to provide a comprehensive overview of the current state of research in the foundations of quantum mechanics and stimulate further discussion and inquiry into these fundamental questions.
This novel text directly addresses common claims and misconceptions around quantum mechanics and presents a fresh and modern understanding of this fundamental and essential physical theory. It begins with a non-mathematical introduction to some of the more controversial topics in the foundations of quantum mechanics. For those more familiar with the theoretical framework of quantum mechanics, the text moves on to a general introduction to quantum field theory, followed by a detailed discussion of cutting-edge topics in this area such as decoherence and spontaneous coherence. Several important philosophical problems in quantum mechanics are considered, and their interpretations are compared, notably the Copenhagen and many-worlds interpretations. The inclusion of frequent real-world examples, such as superconductors and superfluids, ensures the book remains grounded in modern research. This book will be a valuable resource for students and researchers in both physics and the philosophy of science interested in the foundations of quantum mechanics.
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Conceptual Foundations of Quantum Mechanics provides a detailed view of the conceptual foundations and problems of quantum physics, and a clear and comprehensive account of the fundamental physical implications of the quantum formalism. This book deals with nonseparability, hidden variable theories, measurement theories and several related problems. Mathematical arguments are presented with an emphasis on simple but adequately representative cases. The conclusion incorporates a description of a set of relationships and concepts that could compose a legitimate view of the world.
Introduction: The Theory of Local Beables John Bell's most celebrated contribution to the foundations of physics is his famous theorem. The theorem demonstrates that any physical theory capable of generating the predictions of the standard quantum-mechanical algorithm, in particular the prediction of violations of Bell's inequality for experiments done at spacelike separation, cannot be local. The sense of “locality” used here is the same sense that Einstein had in mind when he pointed out that the standard interpretation of the quantum algorithm was committed to “spooky action at a distance” To this day, the import of Bell's theorem is not universally appreciated. I have written about this elsewhere [1], and others in this volume will take up that task. It is properly the main focus during this 50th anniversary of that great achievement. But it is also important to recall and celebrate Bell's other achievements. In many of his later writings, including “The Theory of Local Beables,” “Quantum Mechanics for Cosmologists,” “On the Impossible Pilot Wave,” “Beables for Quantum Field Theory,” “Six Possible Worlds of Quantum Mechanics,” “Are There Quantum Jumps?” and “Against ‘Measurement,”’ 1 Bell turned his attention to the more general problem of physically construing the mathematical formalism used to derive these predictions. This activity is often denominated “interpreting quantum theory” as if there were some precise physical theory that might somehow be supplemented with an “interpretation” Once the issue is framed this way it is easy to ask: But if I already have a theory in hand, what can be gained by supplementing it with an “interpretation”? Many physicists, at this juncture, are happy to conclude that “interpretations” are not a matter of physics at all – maybe they are only of interest to philosophers – and that therefore the whole enterprise of “interpreting quantum theory” is not within the purview of physics per se. What then is in the purviewof physics proper?One answer to this question goes under the banner “instrumentalism”: all physics as such, is concerned about is predicting the outcomes of experiments .