Foundations of Relational Realism: A Topological Approach to Quantum Mechanics and the Philosophy of Nature
If there is a central conceptual framework that has reliably borne the weight of modern physics as it ascends into the twenty-first century, it is the framework of quantum mechanics. Because of its enduring stability in experimental application, physics has today reached heights that not only inspire wonder, but arguably exceed the limits of intuitive vision, if not intuitive comprehension. For many physicists and philosophers, however, the currently fashionable tendency toward exotic interpretation of the theoretical formalism is recognized not as a mark of ascent for the tower of physics, but rather an indicator of sway—one that must be dampened rather than encouraged if practical progress is to continue.
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: That in its 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 quantum mechanics exemplifies the fact that physical extensiveness is fundamentally topological rather than metrical, with its proper logico-mathematical framework being category theoretic rather than set theoretic.
By this thesis, extensiveness fundamentally entails not only relations of objects, but also relations of relations. Thus, 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. In this way, objects and relations are 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 twenty-first century and beyond.
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Part II Mathematical Foundations of Quantum Relational Realism
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Foundations of Relational Realism: A Topological Approach to Quantum ...
Michael Epperson,Elias Zafiris
Keine Leseprobe verfügbar - 2015
asymmetrical base category Boolean algebra Boolean contexts Boolean frames Boolean germ Boolean localization system Boolean logical Boolean reference frames Boolean subalgebras category theory causal chapter classical coarse-graining coherent concept constitutive correlations corresponding covering sieves decoherence deﬁned deﬁnition depicted detector Differential discussed equivalence classes event structure example extensive connection ﬁrst formalism framework function functor fundamental gluing Grothendieck topology Hilbert space induced inductive limit internally related interpretation of quantum isomorphism localization scheme locally contextualized logically conditioned Mallios mathematical measurement outcome mereotopological metrical morphisms mutually exclusive mutually implicative notion object ontological ontological interpretation philosophical potential outcome potential relations predicative fact presheaf presupposed presupposition probability Process and Reality quantum algebra quantum event algebra quantum measurement quantum mechanics quantum observables quantum system quantum theory reference contexts reﬂected relational realist representation represented respect restriction scientiﬁc set-theoretic sheaf sheaf-theoretic sheaves signiﬁcance speciﬁcation subsystems superposition tensor product theoretic tion topological space totality Whitehead Whiteheadian