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Journal of Optics B Quantum and Semiclassical Optics

The quantum physics of observers

Bruce Mills

Published Aug 1, 2002• 0 citations
Publisher

Abstract

The observer is herein studied as an aspect of laboratory physics. It is generally accepted that our status as observers is mediated by our material aspects: our body and brain. But, observers are typically equated with classical coordinate systems. An alternative, modelling the observer as a quantum entity, is considered. The corresponding transformations between two quantum observers affect the computed wavefunctions of other quantum entities in a physically meaningful manner.

DOI
10.1088/1464-4266/4/4/311

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The observer is herein studied as an aspect of laboratory physics. It is generally accepted that our status as observers is mediated by our material aspects: our body and brain. But, observers are typically equated with classical coordinate systems. An alternative, modelling the observer as a quantum entity, is considered. The corresponding transformations between two quantum observers affect the computed wavefunctions of other quantum entities in a physically meaningful manner.
This study presents an alternating coordinate-momentum representation for propagation and transition of associated wave function, based on Bopp operators and on a certain symbolic determinant corresponding to a set of two linear equations with null free terms. It is shown that this alternating representation can justify in a good manner the patterns created through reflection/refraction of waves on nonperfectly smooth interfaces and phase correspondence of diffracted beams without the need of supplementary support functions. Correlations with Lorentz transformation of wave functions by interaction with a certain material medium (the space-time origin of a wave-train being adjusted) are also presented, and supplementary aspects regarding the use of electromagnetic scalar and vector potentials for modelling evolution within this alternating representation are added.
We consider symmetries and reduction in non-relativistic many-body quantum mechanics, with the aim of identifying physically meaningful observables in systems such as molecules and crystalline solids. To this end, we propose a unified framework based on two additional postulates supplementing the standard quantum-mechanical formalism. For stable systems, the physically relevant states are normalizable stationary states, while physically meaningful observables are required to be invariant under a selected subgroup of the symmetry group and under Galilean boosts. In addition, we postulate the existence of a map from the set of all observables allowed by quantum mechanics to the corresponding invariant physically meaningful observables. The originality of the present work does not lie in specific reductions, but in the unified framework that connects symmetry reduction and relational many-body quantum theory. We interpret entities like superselection rules and quantum reference frames as important parts of the postulated process of obtaining the physically meaningful relational description. In particular, the requirement of Galilean-boost invariance added strengthens the criterion for physical observability by excluding quantities that depend on the choice of inertial frame. An important consequence of the postulates is that in the considered cases every physically meaningful observable necessarily depends on more than one non-invariant observable, the latter being typically associated with degrees of freedom assigned to a single particle. The postulates thus lead to theories that are well aligned with the literature on reduction and the description of molecules, while at the same time being consistent with the relational interpretation of quantum mechanics, according to which the complete physical description of a system is defined only relative to other systems.
We consider symmetries and reduction in non-relativistic many-body quantum mechanics, with the aim of identifying physically meaningful observables in systems such as molecules and crystalline solids. To this end, we propose a unified framework based on two additional postulates supplementing the standard quantum-mechanical formalism. For stable systems, the physically relevant states are normalizable stationary states, while physically meaningful observables are required to be invariant under a selected subgroup of the symmetry group and under Galilean boosts. In addition, we postulate the existence of a map from the set of all observables allowed by quantum mechanics to the corresponding invariant physically meaningful observables. The originality of the present work does not lie in specific reductions, but in the unified framework that connects symmetry reduction and relational many-body quantum theory. We interpret entities like superselection rules and quantum reference frames as important parts of the postulated process of obtaining the physically meaningful relational description. In particular, the requirement of Galilean-boost invariance added strengthens the criterion for physical observability by excluding quantities that depend on the choice of inertial frame. An important consequence of the postulates is that in the considered cases every physically meaningful observable necessarily depends on more than one non-invariant observable, the latter being typically associated with degrees of freedom assigned to a single particle. The postulates thus lead to theories that are well aligned with the literature on reduction and the description of molecules, while at the same time being consistent with the relational interpretation of quantum mechanics, according to which the complete physical description of a system is defined only relative to other systems.