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Title: Common Axioms for Inferring Classical Ensemble Dynamics and Quantum Theory

Abstract

The same set of physically motivated axioms can be used to construct both the classical ensemble Hamilton-Jacobi equation and Schroedingers equation. Crucial roles are played by the assumptions of universality and simplicity (Occam's Razor) which restrict the number and type of of arbitrary constants that appear in the equations of motion. In this approach, non-relativistic quantum theory is seen as the unique single parameter extension of the classical ensemble dynamics. The method is contrasted with other related constructions in the literature and some consequences of relaxing the axioms are also discussed: for example, the appearance of nonlinear higher-derivative corrections possibly related to gravity and spacetime fluctuations. Finally, some open research problems within this approach are highlighted.

Authors:
 [1];  [2]
  1. Department of Physics, National University of Singapore, Kent Ridge (Singapore)
  2. (Singapore)
Publication Date:
OSTI Identifier:
20787710
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 810; Journal Issue: 1; Conference: Vaxjo conference on quantum theory: Reconsideration of foundations - 3, Vaxjo (Sweden), 6-11 Jun 2005; Other Information: DOI: 10.1063/1.2158745; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CORRECTIONS; EQUATIONS OF MOTION; FLUCTUATIONS; GRAVITATION; HAMILTON-JACOBI EQUATIONS; NONLINEAR PROBLEMS; QUANTUM FIELD THEORY; RELATIVISTIC RANGE; SCHROEDINGER EQUATION; SPACE-TIME

Citation Formats

Parwani, Rajesh R., and University Scholars Programme, National University of Singapore, Kent Ridge. Common Axioms for Inferring Classical Ensemble Dynamics and Quantum Theory. United States: N. p., 2006. Web. doi:10.1063/1.2158745.
Parwani, Rajesh R., & University Scholars Programme, National University of Singapore, Kent Ridge. Common Axioms for Inferring Classical Ensemble Dynamics and Quantum Theory. United States. doi:10.1063/1.2158745.
Parwani, Rajesh R., and University Scholars Programme, National University of Singapore, Kent Ridge. Wed . "Common Axioms for Inferring Classical Ensemble Dynamics and Quantum Theory". United States. doi:10.1063/1.2158745.
@article{osti_20787710,
title = {Common Axioms for Inferring Classical Ensemble Dynamics and Quantum Theory},
author = {Parwani, Rajesh R. and University Scholars Programme, National University of Singapore, Kent Ridge},
abstractNote = {The same set of physically motivated axioms can be used to construct both the classical ensemble Hamilton-Jacobi equation and Schroedingers equation. Crucial roles are played by the assumptions of universality and simplicity (Occam's Razor) which restrict the number and type of of arbitrary constants that appear in the equations of motion. In this approach, non-relativistic quantum theory is seen as the unique single parameter extension of the classical ensemble dynamics. The method is contrasted with other related constructions in the literature and some consequences of relaxing the axioms are also discussed: for example, the appearance of nonlinear higher-derivative corrections possibly related to gravity and spacetime fluctuations. Finally, some open research problems within this approach are highlighted.},
doi = {10.1063/1.2158745},
journal = {AIP Conference Proceedings},
number = 1,
volume = 810,
place = {United States},
year = {Wed Jan 04 00:00:00 EST 2006},
month = {Wed Jan 04 00:00:00 EST 2006}
}
  • The first three of these axioms describe quantum theory and classical mechanics as statistical theories from the very beginning. With these, it can be shown in which sense a more general than the conventional measure theoretic probability theory is used in quantum theory. One gets this generalization defining transition probabilities on pairs of events (not sets of pairs) as a fundamental, not derived, concept. A comparison with standard theories of stochastic processes gives a very general formulation of the non existence of quantum theories with hidden variables. The Cartesian product of probability spaces can be given a natural algebraic structure,more » the structure of an orthocomplemented, orthomodular, quasimodular, not modular, not distributive lattice, which can be compared with the quantum logic (lattice of all closed subspaces of an infinite dimensional Hilbert space). It is shown how our given system of axioms suggests generalized quantum theories, especially Schroedinger equations, for phase space amplitudes. 38 refs., 3 figs., 1 tab.« less
  • A group of axioms for quantum field theory are discussed. This group varies in some respects from that of Lehmann, Symanzik, and Zimmermann, but it retains Lorentz-invariance, asymptotic conditions, and causality. The starting point in the development of these axioms is the nonrelativistic canonical field theory, which is applied in a restricted sense to the relativistic case. As a consequence of the Theorem of Haag, the concept of local, causal fields must be generalized. (tr-auth)