Research

FOUNDATIONS OF RELATIONAL REALISM

The Evolution of Set Theoretic External Relations to Category Theoretic Internal Relations Toward an Event-Ontological, Topological Approach to Quantum Mechanics

This project reconstructs quantum theory’s conventional set theoretic metrical formalism, grounded in object elements, as a category theoretic topological formalism grounded in object relations. The result is an intuitive Whiteheadian event-ontological, mereotopological interpretation of quantum mechanics formalized via the mathematics of sheaf theory. We apply this framework to two fundamental challenges: [1] the understanding of non-dissipative decoherence, and [2] the coherent relationship of quantum mechanics and the General Theory of Relativity.

Principal Investigator: Michael Epperson. Co-Investigators: Elias Zafiris, Senior Research Fellow in Theoretical and Mathematical Physics, University of Athens; Stuart Kauffman, Research Professor, Complex Systems Center, University of Vermont; Timothy Eastman, NASA-Goddard; Phillip Stamp, Professor of Physics, University of British Columbia; Karim Bschir, ETH Zurich; David Finkelstein, Professor Emeritus of Physics, Georgia Institute of Technology; Roland Omnès, Laboratoire de Physique Théorique Université de Paris XI, (Unité Mixte de Recherche, CNRS). Supported by a grant from the Fetzer-Franklin Fund (Grant D21C62)

PROJECT CAPSTONE VOLUME

M. Epperson & E. Zafiris. Foundations of Relational Realism: A Topological Approach to Quantum Mechanics and the Philosophy of Nature. Lexington Books / Rowman & Littlefield, New York, 2013.

PROJECT SUPPLEMENTAL BOOKS

M. Epperson. Quantum Mechanics and the Philosophy of Alfred North Whitehead. (2nd ed.) Fordham University Press, 2012.

A. Mallios & E. Zafiris. Differential Sheaves and Connections: A Natural Approach to Physical Geometry. World Scientific, 2015.

Project Peer Reviewed Articles

Zafiris, E. "The Equiareal Archimedean Synchronization Method of the Quantum Symplectic Phase Space: I. Spinorial Amplitudes, Transition Probability, and Areal Measure of Time" and "II. Circle-Valued Moment Map, Integrality, and Symplectic Abelian Shadows." Foundations of Physics 52, 44 (2022)

Epperson, M. “Relational Realism and the Ontogenetic Universe: Subject, Object, and Ontological Process in Quantum Mechanics.” Angelaki 25:3 (2020)

R. Kastner, S. Kauffman, M. Epperson, "Taking Heisenberg's Potentia Seriously" International Journal of Quantum Foundations, 4:2 (2018) 158-172 (See also Tom Siegfried's review article on this paper in Science News)

M. Epperson, “Event-Ontological Quantum Mechanics: A Process Theoretic Approach” in Physics and Speculative Philosophy: Potentiality and Modern Science. Eds. Timothy Eastman, Michael Epperson, and David Ray Griffin. Berlin: De Gruyter (2016)

E. Zafiris, "The Global Symmetry Group of Quantum Spectral Beams and Geometric Phase Factors," Advances in Mathematical Physics (2015)

Epperson, M. “The Common Sense of Quantum Theory: Exploring the Internal Relational Structure of Self-Organization in Nature,” Coding as Literacy, Metalithicum 5. Ed. Vera Bühlmann and Ludger Hovestadt. Birkhäuser (2015)

E. Zafiris, V. Karakostas, “A Categorial Semantic Representation of Quantum Event Structures,” Foundations of Physics 43 (2013)

K. Bschir, M. Epperson, E. Zafiris, “Decoherence: A View from Topology,” Center for Philosophy and the Natural Sciences, California State University Sacramento (2014)

M. Epperson, “Quantum Mechanics and Relational Realism: Logical Causality and Wavefunction Collapse,” Process Studies, 38:2 (2009)

E. Zafiris, A. Mallios, “The Homological Kähler-De Rham Differential Mechanism, Part I: Application in General Theory of Relativity,” Advances in Mathematical Physics (2011)

E. Zafiris, A. Mallios, “The Homological Kähler-de Rham Differential Mechanism, Part II. Sheaf-Theoretic Localization of Quantum Dynamics,” Advances in Mathematical Physics (2011)

P. Stamp, S. Takahashi, et al. “Decoherence in crystals of quantum molecular magnets.” Nature 476.7358 (2011): 76-79

E. Zafiris, "Boolean information sieves: a local-to-global approach to quantum information," International Journal of General Systems 39, No. 8 (2010): 873–895

M. Epperson, "Relational Realism: The Evolution of Ontology to Praxiology in the Philosophy of Nature." World Futures, 65:1, Routledge (2009): 19-41

M. Epperson, “The Mechanics of Concrescence: Quantum Theory and Process Metaphysics,” Studia Whiteheadiana, Vol 4 (2010): 159-190

EXPLORE FURTHER

Project Description

Foundations of Relational Realism: The Evolution of Set Theoretic External Relations to Category Theoretic Internal Relations Toward an Event-Ontological, Topological Approach to Quantum Mechanics

This project reconstructs quantum theory’s conventional set theoretic metrical formalism, grounded in object elements, as a category theoretic topological formalism grounded in object relations. The result is an intuitive Whiteheadian event-ontological, mereotopological interpretation of quantum mechanics formalized via the mathematics of sheaf theory. We apply this framework to two fundamental challenges: [1] the understanding of non-dissipative decoherence, and [2] the coherent relationship of quantum mechanics and the General Theory of Relativity.

Project Experiment

We explore the concept of 'intrinsic' sources of decoherence in Nature—i.e., sources that cannot be accounted for, in an experimental setting, solely via any of the known decoherence mechanisms. Experimental investigation of the hypothesis of intrinsic decoherence is as crucial to the enterprise of philosophy as it is to the enterprise of physics; for the implication is that decoherence, and the associated logical conditioning of physical causality by which the effects of decoherence are recognized, is inevitable. The experimental component of this project culminated in the publication of Stamp, P., Takahashi, S. et al. “Decoherence in crystals of quantum molecular magnets.” Nature 476.7358 (2011): 76-79.

Project Applications

We apply our sheaf-theoretic, mereotopological formalization of quantum mechanics to the following goal areas: [1] A sheaf-theoretic mereotopological model of quantum spacetime that coherently integrates quantum mechanics and general relativity (see E. Zafiris, A. Mallios, “The Homological Kähler-De Rham Differential Mechanism, Part I: Application in General Theory of Relativity” and “The Homological Kähler-de Rham Differential Mechanism, Part II. Sheaf-Theoretic Localization of Quantum Dynamics,” Advances in Mathematical Physics (2011), and [2] A sheaf-theoretic explication of quantum geometric (topological) phases (see CPNS White Paper on the Topological Approach to Quantum Geometric Phases).

PREVIOUS PROJECTS

Logical Causality in Quantum Mechanics: Relational Realism and the Evolution of Ontology to Praxiology in the Philosophy of Nature

Principal Investigator: Michael Epperson. Co-Investigators: David Finkelstein, Professor, Department of Physics, Georgia Institute of Technology; Henry P. Stapp, Lawrence Berkeley National Laboratory; Timothy Eastman, NASA-Goddard. Click here for Project Description. Supported by a grant from the Fetzer-Franklin Fund (Grant D11C36). Project Capstone: T. Eastman, M. Epperson, D. Griffin, eds. Physics and Speculative Philosophy: Potentiality in Modern Science. De Gruyter, 2016

Quantum Mechanical Investigations into the Causal and Logical Orders and the Physical Basis of Potentiality

Principal Investigator: Michael Epperson. Co-Investigators: David Finkelstein, Professor, Department of Physics, Georgia Institute of Technology; Henry P. Stapp, Lawrence Berkeley National Laboratory; Timothy Eastman, NASA-Goddard; Mohsen Shiri-Garakani, Department of Physics, Pace University; William Kallfelz, Foundations of Physics Group, University of Maryland. Supported by a grant from the John Templeton Foundation.