Contemporary Whitehead Studies

Foundations of Relational Realism: Quantum Mechanics, Category Theory, and the Philosophy of Alfred North Whitehead

Forthcoming 2013

Authors

Abstract

In Process and Reality, as well as in other works, Alfred North Whitehead proposed a novel event-ontological scheme wherein the material objects of classical physics are redefined as system-histories of internally related quantum events. His goal was a metaphysical framework that would be compatible with the new science of quantum mechanics. Several decades later, eminent physicists including Nobel laureate Murray Gell-Mann, Roland Omnès, and Robert Griffiths would develop a family of interpretations of quantum mechanics based on the concept of decoherent histories of quantum events—a family of interpretations whose conceptual structure correlates precisely with the metaphysical framework proposed by Whitehead. This correlation was identified and explored in detail by Michael Epperson in Quantum Mechanics and the Philosophy of Alfred North Whitehead (Fordham University Press, 2004). 

Since that time, the decoherence-based interpretations of quantum mechanics have evolved to become among the most popular conventional approaches, and the phenomenon of quantum decoherence is currently a central experimental focus. For both physicists and scholars of philosophy, then, the quantum theoretic exemplification of Whitehead’s process metaphysical scheme is proving to be crucial to the ontological interpretation of quantum mechanics. More important, as a result of the increasing popularity of the decoherence-based interpretations, various associated conceptual difficulties have become better understood, particularly with respect to [1] the emergence of the ‘classical’ features of nature from the more fundamental quantum mechanical features; and [2] the problem of relating the local to the global in an extensive continuum—e.g., the infamous problem of relating quantum theory and general relativity. Remarkably, these are the same conceptual difficulties Whitehead himself had struggled with in his attempt to relate his Theory of Prehension to his Theory of Extension. This unique confluence presents a rare opportunity for both physicists and philosophers seeking a coherent ontological interpretation of quantum mechanics, in that efforts to resolve these difficulties within the domain of theoretical physics on the one side, and the domain of philosophical inquiry on the other, have proven to be mutually illuminative.

This is evinced by the present work—a collaboration between physicist and mathematician Elias Zafiris and philosopher Michael Epperson, who argue that any ontological interpretation of quantum mechanics requires an internal-relational framework of logical causality by which local measurement outcome events (i.e., predicative facts) can be coherently and consistently internally related globally. The key impediment to this end, for both quantum mechanics and Whiteheadian metaphysics, is that their respective formulations of spatiotemporal extension are grounded in a set-theoretic structure, where extension is fundamentally metrical—i.e., such that objects are fundamental to relations. The solution proposed by the authors is to delve beneath this set-theoretic framework to the more substrative category theoretic framework where extension is fundamentally topological, such that the fundamental quanta are defined as units of relation. By this framework, objects and relations are mutually implicative.

In this unique two-part volume, designed to be comprehensible by both specialists and non-specialists, the authors demonstrate that the decoherent histories interpretation of quantum mechanics, structured within a category theoretic topological formalism, provides a coherent and consistent Whiteheadian internal-relational framework by which local quantum events can be globally related both causally and logically. Further, this framework allows for a quantum mechanical description of spatiotemporal extension that is highly compatible with the mereotopological model of spatiotemporal extension proposed by Whitehead—one that refines and enhances the latter by elevating it from a set-theoretic basis to a category theoretic one. This provides a uniquely powerful approach to the critical problem of integrating quantum theory and general relativity within a coherent ontology, as well as providing a unified mathematical formalism by which this ontology can be applied practically to the physical sciences.