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arXiv:0806.3970

Quantum interference interpreted classically through application of Berry's phase

M. J. Rave

Published Jun 24, 2008• 0 citations
arXivHTMLPDF

Abstract

We show that quantum interference can be classically interpreted in terms of a phase invariant quantity, not unlike the Berry's phase. Under this interpretation, closed loops in time become fundamental quantum entities, and all quantum states become periodic. Decoherence is then seen to occur naturally as a consequence. This formalism, although counterintuitive, provides a useful way of assigning ``classical'' meaning to quantum probabilities.

DOI
10.48550/arxiv.0806.3970

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We show that quantum interference can be classically interpreted in terms of a phase invariant quantity, not unlike the Berry's phase. Under this interpretation, closed loops in time become fundamental quantum entities, and all quantum states become periodic. Decoherence is then seen to occur naturally as a consequence. This formalism, although counterintuitive, provides a useful way of assigning ``classical'' meaning to quantum probabilities.
In previous work (Rave, 2008) it was proposed that closed loops should be treated as fundamental quantum entities, and such loops were presented in a quasi-probability framework. We demonstrate that the closed-loop decomposition of quantum probabilities is a direct consequence of unitarity, and that Bargmann invariants arise naturally as the phase-invariant quantities associated with these loops, rather than being introduced independently. This identifies interference not as mysterious cross terms, but as contributions from distinct classes of closed loops weighted by their associated Bargmann phases. Additionally, the Born rule is seen to reflect the fundamental quadratic structure arising from the product of forward and reverse amplitudes, which together define such loops.
An alternative interpretation of the quantum adiabatic approximation is presented. This interpretation is based on the ideas originally advocated by David Bohm in his quest for establishing a hidden variable alternative to quantum mechanics. It indicates that the validity of the quantum adiabatic approximation is a sufficient condition for the separability of the quantum action function in the time variable. The implications of this interpretation for Berry’s adiabatic phase and its semi-classical limit are also discussed. Probably one of the best recognized applications of the quantum adiabatic approximation [1, 2] is in Berry’s derivation of the adiabatic geometrical phases [3]. Following Berry’s, by now, classical article on the adiabatic geometric phase [3], Hannay proposed a classical analogue of Berry’s phase [4] and Berry [5] and Anandan [6] explored the semiclassical limit of Berry’s phase and the classical analogue of the general, non-adiabatic geometric phase [7], respectively. The purpose of this note is to provide an alternative interpretation of the quantum adiabatic approximation which yields a natural approach to study the semi-classical limit of this approximation and consequently Berry’s phase.
Decoherence theory has played a central role in explaining the suppression of interference and the emergence of classicality in quantum systems. However, it remains unclear whether decoherence alone can universally account for the origin of quantum probabilities themselves. In the present work, we examine the consequences of interpreting decoherence not merely as an interference-suppression mechanism, but as the fundamental generator of probabilistic measurement outcomes. If quantum probabilities are produced through system–apparatus–environment interactions, the resulting probabilities would generally be expected to depend on the detailed structure of those interactions. Such dependence would imply the possibility of interaction-dependent corrections to the Born-rule probabilities. However, the experimentally observed universality and robustness of the Born rule strongly constrain such a possibility. We therefore argue that decoherence successfully explains the effective suppression of interference terms, but does not by itself universally determine quantum probabilities without additional principles ensuring probability invariance. Based on this distinction, we propose that the origin of quantum probabilities should be conceptually separated from decoherence-induced classicality. Within the Intrinsic Observability Framework (IOF), this separation arises naturally through structural limitations on observability rather than through environment-generated probability formation. The present analysis suggests a conceptual reorganization of the role of decoherence in the quantum measurement problem.
This study discusses the quantum behavior of a particle, which is controlled by fluctuations in the physical space-time (ST) variables, rather than provides a novel interpretation of quantum theory. The fluctuations, i.e., inhomogeneities in a homogeneous phase ST, are prescribed by their probability. They determine the reciprocal space and correlate with the correlation entropy different from zero. Alongside with the minimum entropy, action, and the presence of the Winn-Ehrenfest adiabatic invariant (AI), the fluctuations require the Gilbert information (probabilistic) space linking the physical and the reciprocal ST. Physical quantities in the information space are represented by linear Hermitian operators, which is due to the entropy production in the presence of an AI. Evolution of a quantum system is described by the wave functions having the meaning of information concerning all virtually possible states of a quantum particle. The wave functions are the solutions to the Schrodinger equation and represent a navigation 'roadmap' for the particle to follow. A quantum system is in fact a classical Hamiltonian system in the space of coefficients of the wave function decomposition with respect to the operator eigenfunctions. It is the linearity and the Hermitian nature of the operators which determine the trajectory and the superposition principle in case of the wave behavior of fluctuations. The uncertainty principle, reflects correlation of the fluctuations and, hence, their nonlocality. This study discusses the wave function phase, the Berry phase and its relationship to quantization, discriminability of states and macroscopic quantum effects caused by localization of the particle, followed by a possible entropy change during its transition into a new thermodynamic state.
An interpretative framework is proposed in which the loss of quantum superpositions in the macroscopic world is explained as wave dilation: a stretching of interference caused by the mismatch between the time scale of quantum dynamics and the time scale of the interaction with detectors or the environment. When an interaction is sufficiently strong and brief compared to the system's oscillation period, the wave structure stretches until it becomes imperceptible and resembles a classical straight line —a "taut extended string." The picture is fully compatible with established quantum physics through temporal averaging, decoherence, and the classical limit of the Feynman path integral. The theory introduces no new physical entities; it unifies these mechanisms under a single geometric intuition and provides an explanation for sixteen quantum phenomena.
A pedagogical introduction is given to the quantum mechanics of closed systems, most generally the universe as a whole. Quantum mechanics aims at predicting the probabilities of alternative coarse-grained time histories of a closed system. Not every set of alternative coarse-grained histories that can be described may be consistently assigned probabilities because of quantum mechanical interference between individual histories of the set. In “Copenhagen ” quantum mechanics, probabilities can be assigned to histories of a subsystem that have been “measured”. In the quantum mechanics of closed systems, containing both observer and observed, probabilities are assigned to those sets of alternative histories for which there is negligible interference between individual histories as a consequence of the system’s initial condition and dynamics. Such sets of histories are said to decohere. We define decoherence for closed systems in the simplified case when quantum gravity can be neglected and the initial state is pure. Typical mechanisms of decoherence that are widespread in our universe are illustrated. Copenhagen quantum mechanics is an approximation to the more general quantum framework of closed subsystems. It is appropriate when there is an approximately isolated subsystem that is a participant in a measurement situation in which (among other things) the decoherence of alternative registrations of the apparatus can be idealized as exact. Since the quantum mechanics of closed systems does not posit the existence of the quasiclassical domain of everyday experience, the domain of the approximate aplicability of classical physics must be explained. We describe how a quasiclassical domain described by averages of densities of approximately conserved quantities could be an emergent feature of an initial condition of the universe that implies the approximate classical behavior of spacetime on accessible scales.