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The Thermodynamic Origins and Dynamical Foundations of Quantum Discontinuity

Diana Taschetto

Published Feb 9, 2024• 0 citations
Publisher

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 viewthat the existence of the energy quantawas 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 fromWave Mechanics; (iv) a discussion, that improves on F. A. Muller\'s work, about the theoretical equivalence of Matrix andWave 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

DOI
10.11606/t.8.2024.tde-16092024-163523

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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 viewthat the existence of the energy quantawas 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 fromWave Mechanics; (iv) a discussion, that improves on F. A. Muller's work, about the theoretical equivalence of Matrix andWave 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
This paper combines mathematical, philosophical, and historical analyses in a comprehensive investigation of the dynamical foundations of the formalism of orthodox quantum mechanics. The results obtained include: (i) A deduction of the canonical commutation relations (CCR) from the tenets of Matrix Mechanics; (ii) A discussion of the meaning of Schrödinger's first derivation of the wave equation that not only improves on Joas and Lehner's 2009 investigation on the subject, but also demonstrates that the CCR follow of necessity from Schrödinger's first derivation of the wave equation, thus correcting the common misconception that the CCR were only posited by Schrödinger to pursue equivalence with Matrix Mechanics; (iii) A discussion of the mathematical facts and requirements involved in the equivalence of Matrix and Wave Mechanics that improves on F. A. Muller's classical treatment of the subject; (iv) A proof that the equivalence of Matrix and Wave Mechanics is necessitated by the formal requirements of a dual action functional from which both the dynamical postulates of orthodox quantum mechanics, von Neumann's process 1 and process 2, follow; (v) A critical assessment, based on (iii) and (iv), of von Neumann's construction of unified quantum mechanics over Hilbert space. Point (iv) is our main result. It brings to the open the important, but hitherto ignored, fact that orthodox quantum mechanics is no exception to the golden rule of physics that the dynamics of a physical theory must follow from the action functional. If orthodox quantum mechanics, based as it is on the assumption of the equivalence of Matrix and Wave Mechanics, has this "peculiar dual dynamics," as von Neumann called it, then this is so because by assuming the equivalence one has been assuming a peculiar dual action.
Abstract Following the path by which humanity learned quantum mechanics can lead to an improved understanding of the theory and the origins of its perceived limitations. Our goal is to retrace the development by investigating primary sources, including original published papers and letters, with attention to their timing and influence. Quantum mechanics began in 1900 with the introduction of Planck’s constant, which lead to the “old” quantum theory and Bohr’s model of the atom. With the introduction of matter waves in 1924, a second more intense period began. By 1928 the complete fundamental structure of quantum mechanics was established with the introduction of the Schrödinger equation, the proof of its equivalence to Heisenberg’s matrix mechanics, and the introduction of the relativistic Dirac equation. The theory retains the same essential form today, fueling the technological revolution that began in the last century. We culminate with an introduction to quantum information and computing. This completely new physical scientific paradigm was developed largely in Germany during a period of enormous social, economic, and political upheaval—in a hostile intellectual environment—that parallels the overturning of classical physics. It is striking that all the problems debated today were immediately recognized by the founders of the theory and instructive to see how they dealt with the various issues. We emphasize the centrality of the often neglected second quantization form of the theory for questions of interpretation and give a detailed examination of von Neumann’s widely misunderstood hidden variable theorem.
This article is the first part of a three-part series developing Ontological Field Theory (OFT), a unified framework grounding quantum mechanics in foundational ontological principles. The trilogy is structured as follows: Part I — Conceptual Necessity:Why Quantum Mechanics Is Inevitable: Ontological Continuity and the Necessity of Quantum Dynamics establishes that quantum mechanics follows necessarily from minimal requirements on coherent being, independently of specific physical postulates. Part II — Technical Realization:Derivation of the Schrödinger Equation from Ontological Field Theory provides the explicit field-theoretic derivation showing how the Schrödinger equation emerges as the non-relativistic limit of a covariant ontological field. Part III — Critical Context:Why Classical Physics Is an Approximation: Decoherence, Coarse-Graining, and the Limits of Determinism explains why classical determinism and trajectories arise only as emergent, approximate descriptions of fundamentally quantum and relational dynamics. Each article is logically self-contained, but the full argument is distributed across the three contributions. The conceptual analysis motivates the mathematics; the mathematics grounds the physics; and the critical examination situates classical intuition as a limiting case rather than a foundation. The papers are intended to be read as a coherent whole. We argue that quantum mechanics is not an arbitrary empirical framework but an inevitable consequence of minimal ontological requirements. Assuming only that being must exist necessarily, remain consistent, be relational, and admit self-reference, we show that classical deterministic physics is structurally insufficient. Quantum dynamics emerges as the unique low-energy realization of coherent ontological continuity. This work complements explicit field-theoretic derivations by clarifying why quantum mechanics could not have been otherwise.
Some aspects of the interpretation of microscopic physics in terms of quantum theory are discussed. It is first emphasized that quantum theory is formulated in a Cartesian coordinate system; in other coordinates the result obtained with the help of the Hamiltonian formalism and commutation relations between ''canonically conjugated'' coordinate and momentum operators leads to a wrong version of quantum mechanics. In this connection the Feynman integral formalism is also discussed. In this formalism the measure is not well defined, and there is no idea how to distinguish between the true version of quantum mechanics and an incorrect one. In this respect, the Feynman approach consists of a mnemonic rule to generate perturbation series from an undefined zero-order term. The origin of time in the quantum framework is then analyzed in detail and illustrated by the example of atomic collisions. It is shown that the time-dependent Schr ¨ odinger equation for the closed three-body (two nuclei + electron) system has no physical meaning because in the high-impact energy limit it transforms into an equation with two independent time-like variables; time naturally appears in the stationary Schr ¨ odinger equation as a result of extraction of a classical subsystem (two nuclei) from a closed three-body system. Finally, following the well-known Einstein-Rosen-Podolsky experiment and Bell's inequality, we reiterate that the wave function must be interpreted as an actual field of information, in a form as elementary as the usual material particles and electromagnetic fields. In fact, experimental measurements transfer this quantum information field into the classical world, which is directly discernable. In my conclusion, the relation between physical reality and its mathematical formulation is discussed. 2012 Physics Essays Publication. (DOI: 10.4006/0836-1398-25.1.27) R ´
Some aspects of the interpretation of quantum theory are discussed.It is emphasized that quantum theory is formulated in a Cartesian coordinate system; in other coordinates the result obtained with the help of the Hamiltonian formalism and commutator relations between 'canonically conjugated' coordinate and momentum operators leads to a wrong version of quantum mechanics.In this connection the Feynman integral formalism is also discussed.In this formalism the measure is not well-defined and there is no idea how to distinguish between the true version of quantum mechanics and an incorrect one; it is rather a mnemonic rule to generate perturbation series from an undefined zero order term.The origin of time is analyzed in detail by the example of atomic collisions.It is shown that the time-dependent Schrödinger equation for the closed three-body (two nuclei + electron) system has no physical meaning since in the high impact energy limit it transforms into an equation with two independent time-like variables; the time appears in the stationary Schrödinger equation as a result of extraction of a classical subsystem (two nuclei) from a closed three-body system.Following the Einstein-Rosen-Podolsky experiment and Bell's inequality the wave function is interpreted as an actual field of information in the elementary form.The relation between physics and mathematics is also discussed.
Planck's introduction of the quantum of action in 1900 was followed by 25 years of trial and error in quest of the understanding of the quantum world; different ideas and directions had to be pursued until the path leading to the elementary quantum theory was discovered. Radical changes away from traditional perceptions about natural phenomena were necessary, the entire system of basic concepts in classical physics had to be abandoned and replaced by a new mode of thought. Continuity and determinism of classical laws were no longer applicable on the quantum scale, where dynamical behaviour proceeds by discontinuous and statistical quantum transitions. Albert Einstein laid the essential foundations for the new concept; Max Born made the decisive step further leading to the breakthrough in 1925. The development of the ideas, which eventually resulted in the elementary quantum theory in 1925/26, will be described, relying on original publications and letters written during that period in time by the major contributors. The fundamental laws of Quantum Theory derived by Max Born and Pascual Jordan may mathematically be represented in many different ways, and particular emphasis is given to the distinction between physical content and mathematical representation.