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arXiv:1608.04805 · Physical Review A

Quantum reality via late-time photodetection

Adrian Kent

Published Dec 18, 2017• 35 citations
arXivHTMLPDF

Abstract

We further investigate postulates for realist versions of relativistic quantum theory and quantum field theory in Minkowski space and other background spacetimes. According to these postulates, quantum theory is supplemented by local variables that depend on possible outcomes of hypothetical measurements on the late-time electromagnetic field in spacelike separated regions. We illustrate the implications in simple examples by using photon wave mechanics and discuss possible extensions to quantum field theory.

DOI
10.1103/physreva.96.062121

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We further investigate postulates for realist versions of relativistic quantum theory and quantum field theory in Minkowski space and other background spacetimes. According to these postulates, quantum theory is supplemented by local variables that depend on possible outcomes of hypothetical measurements on the late-time electromagnetic field in spacelike separated regions. We illustrate the implications in simple examples by using photon wave mechanics and discuss possible extensions to quantum field theory.
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The implications of the relativistic space-time structure for a physical description by quantum mechanical wave-functions are investigated. On the basis of a detailed analysis of Bell's concept of local causality, which is violated in quantum theory, we argue that this is a subtle, as well as an important effort. A central requirement appearing in relativistic quantum mechanics, namely local commutativity, is analyzed in detail and possible justifications are given and discussed. The complexity of the implications of wave function reduction in connection with Minkowski space-time are illustrated by a quantum mechanical measurement procedure which was proposed by Aharonov and Albert. This procedure and its relativistic implications are explicitly analyzed and discussed in terms of state evolution. This analysis shows that the usual notion of state evolution fails in relativistic quantum theory. Two possible solutions of this problem are given. In particular, it is shown that also a theory with a distinguished foliation of space-time into space-like leafs - accounting for nonlocality - makes the right predictions for the Aharonov-Albert experiment. We will repeatedly encounter that an analysis of the wave-function alone does not suffice to answer the question of relativistic compatibility of the theory, but that the actual events in space time, which are predicted and described by the theory, are crucial. Relativistic versions of quantum mechanical theories which precisely describe actual processes in space-time are briefly described and discussed in the appendix.
Modern quantum information theory deals with an idealized situation when the spacetime dependence of quantum phenomena is neglected. However the transmission and processing of (quantum) information is a physical process in spacetime. Therefore such basic notions in quantum information theory as qubit, channel, composite systems and entangled states should be formulated in space and time. In particlular we suggest that instead of a two level system (qubit) the basic notion in a relativistic quantum information theory should be a notion of an elementary quantum system, i.e. an infinite dimensional Hilbert space HHH invariant under an irreducible representation of the Poincare group labeled by [m,s][m,s][m,s] where m≥0m\geq 0m≥0 is mass and s=0,1/2,1,...s=0,1/2,1,...s=0,1/2,1,... is spin. We emphasize an importance of consideration of quantum information theory from the point of view of quantum field theory. We point out and discuss a fundamental fact that in quantum field theory there is a statistical dependence between two regions in spacetime even if they are spacelike separated. A classical probabilistic representation for a family of correlation functions in quantum field theory is obtained. Entangled states in space and time are considered. It is shown that any reasonable state in relativistic quantum field theory becomes disentangled (factorizable) at large spacelike distances if one makes local observations. As a result a violation of Bell`s inequalities can be observed without inconsistency with principles of relativistic quantum theory only if the distance between detectors is rather small. We suggest a further experimental study of entangled states in spacetime by studying the dependence of the correlation functions on the distance between detectors.
The quantum reality problem is that of finding a mathematically precise definition of a sample space of configurations of beables, events, histories, paths, or other mathematical objects, and a corresponding probability distribution, for any given closed quantum system. Given a solution, we can postulate that physical reality is described by one randomly chosen configuration drawn from the sample space. For a physically sensible solution, this postulate should imply quasiclassical physics in realistic models. In particular, it should imply the validity of Copenhagen quantum theory and classical dynamics in their respective domains. A Lorentzian solution applies to relativistic quantum theory or quantum field theory in Minkowski space and is defined in a way that respects Lorentz symmetry. We outline a solution to the nonrelativistic and Lorentzian quantum reality problems and associated generalizations of quantum theory.