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arXiv:physics/0605068

Quantum mechanics from a universal action reservoir

A. Garrett Lisi

Published May 8, 2006• 24 citations
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Abstract

A heuristic derivation of quantum mechanics using information theory requires a foundational physical principle: the existence of a universal action reservoir, analogous to the energy reservoir of a canonical ensemble.
DOI
10.48550/arxiv.physics/0605068

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In this paper we construct a theory of quantum mechanics based on Shannon information theory. We define a few principles regarding information-based frames of reference, including explicitly the concept of information covariance, and show how an ensemble of all possible physical states can be setup on the basis of the accessible information in the local frame of reference. In the next step the Bayesian principle of maximum entropy is utilized in order to constrain the dynamics. We then show, with the aid of Lisi's universal action reservoir approach, that the dynamics is equivalent to that of quantum mechanics. Thereby we show that quantum mechanics emerges when classical physics is subject to incomplete information. We also show that the proposed theory is relational and that it in fact is a path integral version of Rovelli's relational quantum mechanics. Furthermore we give a discussion on the relation between the proposed theory and quantum mechanics, in particular the role of observation and correspondence to classical physics is addressed. In addition to this we derive a general form of entropy associated with the information covariance of the local reference frame. Finally we give a discussion and some open problems.
The quantization of action, discrete energy levels, and finite phase-space resolution are among the most fundamental yet conceptually opaque features of quantum physics. In standard theory, the universal constant is introduced empirically, and canonical quantization rules are postulated without deeper ontological justification. In this work we present a first-principles derivation of quantization based on the Structural Unified Field (SUF) framework. By treating physical entities as layered “existence objects” characterized by a boundary parameter and an existence function , we argue that structural identity requires a minimal nonzero layer separation . This structural irreducibility implies a universal minimal distinguishability in all attribute domains, which, when projected into phase space, yields a minimal phase-space cell and thus a universal minimal action unit. Upon mapping to physical units, this structural minimal action corresponds to Planck’s constant . The SUF interpretation thereby promotes quantization from an empirical postulate to a necessary consequence of the ontological geometry of existence. The resulting framework naturally accounts for discrete spectra, uncertainty relations, action quantization, canonical commutation relations, topological quantization phenomena, and the universality of . We discuss broader implications for the foundations of quantum theory, the quantum–gravity interface, and potential avenues for testing structural deviations.
I present a reconstruction of general Hamiltonian action mechanics that eliminates all foundational problems of quantum mechanics. The key advance is the completion of Hamiltonian mechanics to the universal mechanics of particles based on action-waves, consistent with the inclusive validity of the principle of stationary action. It is found that irreducible indeterminism is intrinsic and universal at all scales of dynamics. The new action-wave equation is the complete description of single dynamical histories, dissolving the classical-quantum divide. The statistical theory of quantum mechanics emerges as the ensemble average of modified action dynamics. The ensemble average of the new action mechanics leads to a hybrid function consisting of the action-waves and the probability density of the ensemble. This hybrid wavefunction obeys the Schrödinger equation, which is not a single particle dynamical equation. The reconstructed mechanics without matter waves is free of the cardinal problem known as the collapse of the wavefunction and with that, the vexing issue of quantum measurement is resolved. Another significant advance is the correct decoding of quantum entanglement and purging of nonseparability and nonlocality in quantum correlations. The action-waves do not carry the burden of divergent zero-point energy. The reconstructed mechanics is in complete agreement with all empirical requirements and in harmony with credible physical ontology.