Michael Epperson

The very fact that the totality of our sense experiences is such that by means of thinking (operations with concepts, and the creation and use of definite functional relations between them, and the coordination of sense experiences to these concepts) it can be put in order, this fact is one which leaves us in awe. One may say, " The eternal mystery of the world is its comprehensibility. " The fact that it is comprehensible is a miracle. ~ Albert Einstein, " Physics and Reality, " 1936 1 After nearly a century of attempted integration, the deep and enduring incompatibility of quantum mechanics and the general theory of relativity is today increasingly portrayed as a crisis in physics. What was once characterized as a stubbornly persistent technical problem now signifies, for many physicists, a crisis of incomprehensibility. Without a formal means of quantum mechanically depicting local-global relations in an extensive continuum, our earned confidence in physics' ability to provide a coherent, unified description of nature has, for the growing number of physicists calling attention to this crisis, begun to falter. To make matters worse, both quantum mechanics and general relativity have their own individual crises of incomprehensibility which add even deeper levels of complication in any attempted integration. The problems of dark matter and dark energy are infamously emblematic of observational inconsistencies with general relativity, so much so that for many cosmologists, dark matter and energy in recent decades have been costumed and recast as conventional features of modern physics. Likewise, in quantum mechanics, there is perhaps no more obvious manifestation of a crisis of incomprehensibility—in this case, one that inspires the total abandonment of the idea of a coherent, unified understanding of nature—than the Many Worlds Interpretation 2 (MWI) where, for any given quantum measurement, every potential

It is argued that quantum theory is best understood as requiring an
ontological duality of res extensa and res potentia, where the latter is
understood per Heisenberg's original proposal, and the former is roughly
equivalent to Descartes' 'extended substance.' However, this is not a dualism
of mutually exclusive substances in the classical Cartesian sense, and
therefore does not inherit the infamous 'mind-body' problem. Rather, res
potentia and res extensa are proposed as mutually implicative ontological
extants that serve to explain the key conceptual challenges of quantum theory;
in particular, nonlocality, entanglement, null measurements, and wave function
collapse. It is shown that a natural account of these quantum perplexities
emerges, along with a need to reassess our usual ontological commitments
involving the nature of space and time.

Through both a historical and philosophical analysis of the concept of possibility, we show how including both potentiality and actuality as part of the real is both compatible with experience and contributes to solving key problems of fundamental process and emergence. The book is organized into four main sections that incorporate our routes to potentiality: (1) potentiality in modern science [history and philosophy; quantum physics and complexity]; (2) Relational Realism [ontological interpretation of quantum physics; philosophy and logic]; (3) Process Physics [ontological interpretation of relativity theory; physics and philosophy]; (4) on speculative philosophy and physics [limitations and approximations; process philosophy]. We conclude that certain fundamental problems in modern physics require complementary analyses of certain philosophical and metaphysical issues and that such scholarship reveals intrinsic features and limits of determinism, potentiality, and emergence that enable, among others, important progress on the quantum theory of measurement problem and new understandings of emergence.

Through both a historical and philosophical analysis of the concept of possibility, we show how including both potentiality and actuality as part of the real is both compatible with experience and contributes to solving key problems of fundamental process and emergence. The book is organized into four main sections that incorporate our routes to potentiality: (1) potentiality in modern science [history and philosophy; quantum physics and complexity]; (2) Relational Realism [ontological interpretation of quantum physics; philosophy and logic]; (3) Process Physics [ontological interpretation of relativity theory; physics and philosophy]; (4) on speculative philosophy and physics [limitations and approximations; process philosophy]. We conclude that certain fundamental problems in modern physics require complementary analyses of certain philosophical and metaphysical issues, and that such scholarship reveals intrinsic features and limits of determinism, potentiality, and emergence that enable, among others, important progress on the quantum theory of measurement problem and new understandings of emergence.

Among the many exotic interpretations of quantum theory—those entailing ‘multiverse’ cosmologies, 'time reversal,' ‘retro-causality,’ and physical superpositions of alternative actual system states—lies a single core principle: That quantum theory’s most emblematic feature is its invalidation of classical logic—the very foundation of intuitive, critical reasoning—at the level of fundamental physics. As a result, quantum mechanics has become widely popularized, and in many cases, marketed, as mystifying and essentially incomprehensible to non-specialists.

Yet at the heart of this popularization lies a paradox: The rules of classical logic purportedly invalidated by quantum mechanics are, at the same time, necessarily presupposed by quantum mechanics; indeed, they are the very rules used to formalize quantum mechanics in the first place.

In Foundations of Relational Realism: A Topological Approach to Quantum Mechanics and the Philosophy of Nature (Rowman & Littlefield, 2013), Michael Epperson and Elias Zafiris provide a powerful new solution to this paradox by upgrading quantum theory’s presupposed set theoretic, metrical structure, grounded in object elements, to a category theoretic, topological structure grounded in object relations. To this end, the book presents a novel, intuitive interpretation of quantum mechanics, based on a revised decoherent histories interpretation, structured within a category theoretic topological formalism.

In this unique two-part volume, designed to be comprehensible to both specialists and non-specialists, the authors chart out a pathway forward by identifying the central deficiency in most interpretations of quantum mechanics, and indeed, in modern philosophy more generally: That in the conventional, metrical depiction of extension, inherited from the Enlightenment, objects are characterized as fundamental to relations—i.e., such that relations presuppose objects but objects do not presuppose relations. The authors, by contrast, argue that in quantum mechanics physical extensiveness fundamentally entails not only relations of objects, but also relations of relations. In this way, quantum mechanics exemplifies a concept of extensive connection that it is fundamentally topological rather than metrical, and thus requires a logico-mathematical framework grounded in category theory rather than set theory.

By this thesis, the fundamental quanta of quantum physics are properly defined as units of logico-physical relation rather than merely units of physical relata as is the current convention. Objects are always understood as relata, and likewise relations are always understood objectively. Objects and relations are thus coherently defined as mutually implicative. The conventional notion of a history as ‘a story about fundamental objects’ is thereby reversed, such that the classical ‘objects’ become the story by which we understand physical systems that are fundamentally histories of quantum events. These are just a few of the novel critical claims explored in this volume—claims whose exemplification in quantum mechanics will, the authors argue, serve more broadly as foundational principles for the philosophy of nature as it evolves through the 21st century and beyond.

Reviews

“Recommended reading for graduate students and researchers/faculty. 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. Here, Epperson and Zafiris 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.”

~ CHOICE

"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

Professor Emeritus of Theoretical Physics

University of Paris

Author of The Interpretation of Quantum Mechanics and

Converging Realities (both Princeton University Press).

“Leveraging rigorously-tested core quantum physics, in combination with careful philosophical distinctions and new mathematical developments (topology and category theory), Drs. Epperson and Zafiris have achieved a uniquely viable interpretation of all known quantum experiments (including many rigorously-checked Bell inequality tests) in a way that is intuitively reasonable and avoids the usual exotica. In addition, their predictions on non-local quantum correlations associated with global topological phases have been confirmed in recent experiments. Epperson provides very readable yet in-depth philosophical and interpretive foundations (210 pages) followed by Zafiris' rigorous treatment of mathematical foundations (177 pages). This work is a must read for all those interested in the philosophy of physics, as well as those concerned with foundational philosophical questions.”

~TIMOTHY E. EASTMAN, PH.D.

Senior Physicist (ret.)

Sciences and Exploration Directorate

NASA Goddard Space Flight Center

"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

Professor Emeritus of Mathematics

Department of Mathematics

University of Athens

Author of Geometry of Vector Sheaves (Springer) and

Modern Differential Geometry in Gauge Theories (Birkhäuser).

Spośród wielu prac traktujących o filozoficznych konsekwencjach

mechaniki kwantowej, znaczna część starała się wyjaśnić paradoksalne

efekty pojawiające się, gdy próbuje się połączyć teorię

kwantową z klasycznym, mechanistyczno-materialistycznym światopoglądem.

Ostatnie wyniki z zakresu fizyki teoretycznej, pochodzące

m.in. od Roberta Griffithsa, Rolanda Omnesa, Wojciecha Zurka

i Murraya Gell-Manna, sprowokowały powstanie nowej rodziny

interpretacji mechaniki kwantowej, które skutecznie łagodzą te

paradoksalne niezgodności - jednak nie poprzez ingerencję w formalizm

kopenhaski, lecz poprzez rozwój nowego schematu ontologicznego,

w którym opis klasyczny wyprowadzany jest z bardziej

fundamentalnego opisu kwantowo-mechanicznego na drodze pojęciowego

abstrahowania przy użyciu pojęcia „dekoherencji kwantowej".

By the relational realist interpretation of wave function collapse, the quantum mechanical actualization of potentia is defined as a decoherence-driven process by which each actualization (in “orthodox” terms, each measurement outcome) is conditioned both by physical and logical relations with the actualities conventionally demarked as “environmental” or external to that particular outcome. But by the relational realist interpretation, the actualization-in-process is understood as internally related to these “enironmental” data per the formalism of quantum decoherence. The concept of “actualization via wave function collapse” is accounted for solely by virtue of these presupposed logical relations—the same logical relations otherwise presupposed by the scientific method itself—and thus requires no “external” physical-dynamical trigger: e.g., the Gaussian hits of GRW, acts of conscious observation, etc. By the relational realist interpretation, it is the physical and logical relations among quantum actualities (quantum “final real things”) that drives the process of decoherence and, via the latter, the logically conditioned actualization of potentia. In this regard, the relational realist interpretation of quantum mechanics is a praxiological interpretation; that is, these physical and logical relations are ontologically active relations, contributing not just to the epistemic coordination of quantum actualizations, but to the process of actualization itself.