Taschetto, Diana
(2024)
The Thermodynamic Origins and Dynamical Foundations of Quantum Discontinuity.
[Preprint]
Abstract
Doubts and misconceptions about the origin and justification of a physical theory’s most fundamental concept are bound to spill over into doubts and misconceptions about the origin and foundation of the theory as a whole: such is the case, in point of fact, of the concept of quantum discontinuity of orthodox quantum mechanics. This work, which comprises three chapters, each of which is an independent paper, is a comprehensive investigation of the origin and nature of the concept of quantum discontinuity. The first paper, entitled “Rewriting the Quantum ‘Revolution’,” gives a novel account of the origin of quantum theory. It refutes, by direct counter-example, Thomas Kuhn’s well-known thesis that revolutions in science do not happen on the basis of theory and experiment alone; the quantum revolution happened exactly in this way. The second paper, “On the Lawfulness of Quanta,” is a sequel to “Rewriting the Quantum ‘Revolution’.” It evinces that and how the existence of the energy quanta is a principled result; it refutes the traditional view that the existence of the energy quanta was originally introduced in physics as an ad hoc hypothesis in a self-contradictory argument by showing that it is instead a necessary consequence of the laws of thermodynamics of black-bodies. This result affects our understanding of what is actually involved in the classical-to-quantum paradigm-shift, of scientific method, and of the specific nature of the quantum hypothesis which was carried over into contemporary physics in the course of the quantum revolution. The third paper, “The Dual Dynamical Foundation of Orthodox Quantum Mechanics,” was written in collaboration with the mathematical physicist Dr. Ricardo Correa da Silva. It is a detailed critical study of the dynamical foundations of orthodox quantum mechanics; it contains several original results of mathematical, historical, and theoretical interest. The most important of them is the discovery of a dual action functional from which both of the dynamical postulates of von Neumann’s quantum mechanics, process 1 and process 2, necessarily follow. It also contains the following results that have interest on their own: (i) a derivation of the canonical commutation relations from Matrix Mechanics; (ii) an analysis of Schrödinger’s first derivation of the wave equation that improves on the understanding of it that is now current in the literature; (iii) a demonstration of how the canonical commutation relations follow from Wave Mechanics; (iv) a discussion, that improves on F. A. Muller’s work, about the theoretical equivalence of Matrix and Wave Mechanics; (v) a revaluation of von Neumann’s statement of the measurement problem. Broadly speaking, the three papers, taken together, drive home the lesson that the concept of quantum discontinuity stands on a more solid foundation than the scholarship on the foundations of quantum mechanics has hitherto acknowledged.
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