The Dual Dynamical Foundation of Orthodox Quantum Mechanics

• URL: http://arxiv.org/abs/2402.15031v2
• Date: Sat, 07 Dec 2024 19:54:08 GMT
• Title: The Dual Dynamical Foundation of Orthodox Quantum Mechanics
• Authors: Diana Taschetto, Ricardo Correa da Silva,
• Abstract summary: A deduction of the canonical commutation relations ( CCR) from the tenets of Matrix Mechanics. A discussion of the meaning of Schr"odinger's first derivation of the wave equation. A critical assessment of von Neumann's construction of unified quantum mechanics over Hilbert space.
• Score: 0.0
• License:
• Abstract: 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 Schr\"odinger'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 Schr\"odinger's first derivation of the wave equation, thus correcting the common misconception that the CCR were only posited by Schr\"odinger 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, this is so because by assuming the equivalence one has been assuming a peculiar dual action.

Related papers

• Tensorial Quantum Mechanics: Back to Heisenberg and Beyond [0.0]
  We will argue that while Heisenberg's approach was consistently developed, Dirac's axiomatic re-formulation was, instead, developed. We will present a new tensorial proposal which -- taking as a standpoint Heisenberg's original approach -- will prove capable.
  arXiv  Detail & Related papers  (2024-10-12T13:52:26Z)
• A Theory of Quantum Jumps [44.99833362998488]
  We study fluorescence and the phenomenon of quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field. Our results amount to a derivation of the fundamental randomness in the quantum-mechanical description of microscopic systems.
  arXiv  Detail & Related papers  (2024-04-16T11:00:46Z)
• Quantum Principle of Least Action in Dynamic Theories With Higher Derivatives [44.99833362998488]
  This form is the initial point for the construction of quantum theory. The correspondence between the new form of quantum theory and "ordinary" quantum mechanics has been established in the local limit.
  arXiv  Detail & Related papers  (2024-04-15T09:29:58Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Fluctuation theorems for genuine quantum mechanical regimes [0.0]
  We look for corrections to work fluctuations theorems when the acting system is allowed to enter the quantum domain. For some specific processes, we derive several fluctuation theorems within both the quantum and classical statistical arenas.
  arXiv  Detail & Related papers  (2022-11-29T13:14:30Z)
• Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
  In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
  arXiv  Detail & Related papers  (2022-05-24T20:51:03Z)
• Bohm's quantum "non-mechanics": An alternative quantum theory with its own ontology? [0.0]
  Bohmian mechanics allows us to establish a direct link between the dynamics exhibited by quantum systems and the local variations of the quantum phase associated with their state. This goes beyond the passive role typically assigned to this field in Bohmian mechanics, where traditionally trajectories and quantum potentials have received more attention instead.
  arXiv  Detail & Related papers  (2021-05-13T09:31:02Z)
• Self-adjointness in Quantum Mechanics: a pedagogical path [77.34726150561087]
  This paper aims to make quantum observables emerge as necessarily self-adjoint, and not merely hermitian operators. Next to the central core of our line of reasoning, the necessity of a non-trivial declaration of a domain to associate with the formal action of an observable.
  arXiv  Detail & Related papers  (2020-12-28T21:19:33Z)
• Experimental Validation of Fully Quantum Fluctuation Theorems Using Dynamic Bayesian Networks [48.7576911714538]
  Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small systems. We experimentally verify detailed and integral fully quantum fluctuation theorems for heat exchange using two quantum-correlated thermal spins-1/2 in a nuclear magnetic resonance setup.
  arXiv  Detail & Related papers  (2020-12-11T12:55:17Z)
• The Entropic Dynamics of Quantum Scalar Fields Coupled to Gravity [0.0]
  We propose a model for a quantum scalar field propagating in a dynamical space-time. Rather than modelling the dynamics of the fields, ED models the dynamics of their probabilities. A particularly significant prediction of this ED model is that the coupling of quantum fields to gravity implies violations of the quantum superposition principle.
  arXiv  Detail & Related papers  (2020-06-09T03:44:36Z)
• A quantum system with a non-Hermitian Hamiltonian [0.0]
  relevance in Physics of non-Hermitian operators with real eigenvalues is being widely recognized. In this note, a quantum system described by a non-Hermitian Hamiltonian is investigated.
  arXiv  Detail & Related papers  (2020-04-15T17:03:45Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.