Lexington Books

Pages: 422
•
Trim: 6¼ x 9¼

978-0-7391-8032-7 • Hardback • June 2013 • $162.00 • (£125.00)

978-1-4985-1622-8 • Paperback • March 2015 • $73.99 • (£57.00)

978-0-7391-8033-4 • eBook • June 2013 • $66.00 • (£51.00)

**Michael Epperson** is director of the Center for Philosophy and the Natural Sciences in the College of Natural Sciences and Mathematics at California State University, Sacramento, where he is a research professor and principal investigator. He is the author of *Quantum Mechanics and the Philosophy of Alfred North Whitehead*.

**Elias Zafiris**is research professor in theoretical and mathematical physics at the Institute of Mathematics at the University of Athens, and is currently a visiting professor in the Department of Logic, Institute of Philosophy, Eötvös Loránd University in Budapest. He is also a senior research fellow and principal investigator at the Center for Philosophy and the Natural Sciences in the College of Natural Sciences and Mathematics at California State University, Sacramento.

Preface

Part I: Philosophical Foundations of Quantum Relational Realism

Chapter 1: Introduction: Relational Realism: A Program in Speculative Philosophy

Chapter 2: Substance and Logic in Quantum Mechanics

Chapter 3: Predication in Quantum Mechanics

Chapter 4: Logical Causality in Quantum Mechanics: A Relational Realist Ontology

Chapter 5: Integrating Logical Relation and Extensive Relation: Mereotopology and Quantum Mechanics

Interlude: Part II: Mathematical Foundations of Quantum Relational Realism

Chapter 6: Notion of Localization Processes

Chapter 7: Sheaves of Germs: The Topological Case

Chapter 8: Sheaves of Boolean Germs: The Quantum Topological Case

Chapter 9: Functorial Entanglement and Logical Classification

Chapter 10: Quantum Localization in a Broader Conceptual Perspective

Chapter 11: Recapitulation: A Semantic Bridge Between Process Metaphysics and Quantum Theory via Sheaves

Bibliography

Index

About the Authors

One of the driving contentions in modern physics has been the inability to reconcile the dominance of classical thought in the theory of relativity with the indeterminate nature of quantum mechanics. Some would argue that one such attempt at a compromise had arrived in the form of quantum field theories, with multiple ideas for resolving the asymmetrical features between relativity and ordinary quantum mechanics. Here, Epperson and Zafiris (both, California State Univ., Sacramento) decide to return to ordinary quantum mechanics and propose sheaf theory, a theory that grew out of the abstract algebra of topology and set theory, as a solution to the stubborn paradoxes found in quantization attempts. They then compare the theory's interpretive value to the category scheme found in Whitehead's *Process and Reality* (1929). Epperson's earlier work, *Quantum Mechanics and the Philosophy of Alfred North Whitehead* (2004), is a good predecessor to the current book. The authors begin with the famous 1935 paper on quantum theory and reality by Einstein, Podolsky, and Rosen. . . . Part of the 'Contemporary Whitehead Studies' series. Summing Up: Recommended. Graduate students and researchers/faculty.

**— ****Choice Reviews**

[*Foundations of Relational Realism*] contributes to a body of literature which seeks to apply sheaf theory (and in many cases, topos theory in particular) to the discussion of quantum non-locality. Particularly noteworthy are the research programs initiated by Butterfield and Isham, Doering and Isham, and Landsman et al., respectively, which seek (modulo subtle differences) to develop a sheaf-theoretic account of quantum mechanics, as well as recent work by Abramsky et al. which brings various types of quantum nonlocality and contextuality under a sheaf-theoretic rubric (but without absorbing the entire structure of quantum mechanics).

**— ****Metascience**

A startling development in the last century has been the overflowing of theoretical and observational sciences into the fields of philosophy, particularly by quantum mechanics and cosmology. The present book is twice valuable on this fascinating subject in my opinion: on one hand for its clear and lucid exposition and application of Whitehead's ontology as a most attractive framework for this kind of query, and on the other hand, for its extension of the dialectics of ontology through an original use of advanced concepts from modern mathematics.

**— ****Roland Omnès, University of Paris XI**

This is a unique book in its scope, approach and method. A novel physical and philosophical interpretation of sheaf theory sheds new light on the quantum measurement problem, entanglement, locality and truth. A new systematic and rigorous relational realistic paradigm for natural philosophy has emerged, rooted on the same principles with Abstract (Modern) Differential Geometry that transmutes the above into a fully fledged dynamical theory.

**— ****Anastasios Mallios, University of Athens**