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Physics of Particles and Nuclei

Quantum erasure and the locality problem

D. A. Slavnov

Published Jun 29, 2017• 1 citation
Publisher

Abstract

The problem of locality arising in connection with the quantum-erasure experiments is considered using the algebraic approach. We demonstrate that, contrary to a widespread opinion, the results of these experiments can be reconciled with the existence of a local physical reality determining the results of local measurements. A clear physical interpretation of the quantum-erasure experiments, that is consistent with the classical concepts, is given.

DOI
10.1134/s1063779617040062

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The problem of locality arising in connection with the quantum-erasure experiments is considered using the algebraic approach. We demonstrate that, contrary to a widespread opinion, the results of these experiments can be reconciled with the existence of a local physical reality determining the results of local measurements. A clear physical interpretation of the quantum-erasure experiments, that is consistent with the classical concepts, is given.
The locality problem of quantum measurements is considered in the framework of the algebraic approach. It is shown that contrary to the currently widespread opinion one can reconcile the mathematical formalism of the quantum theory with the assumption of the existence of a local physical reality determining the results of local measurements. The key quantum experiments: double-slit experiment on electron scattering, Wheeler’s delayed-choice experiment, the Einstein-Podolsky-Rosen paradox, and quantum teleportation are discussed from the locality-problem point of view. A clear physical interpretation for these experiments, which does not contradict the classical ideas, is given.
The article considers the epistemology of quantum phenomena and the quantum eraser experiments as reflecting certain essential features of these phenomena, and uses these experiments to introduce a new concept, that of ‘erasure’. This concept is defined by the fact that a given quantum measurement destroys, ‘erases’, the usefulness of actual or even possible information associated with a given quantum system prior to this measurement, for the purposes of predictions concerning the experiments performed on this system after this measurement. The concept of ‘erasure’ allows one to capture certain fundamental aspects of quantum phenomena more sharply than previously, and to differentiate classical and quantum phenomena, and theories in a new way.
In this chapter we are going to address the famous ‘problem of time’ which has become the headline for all the physical interpretational problems of the mathematical formalism. Roughly speaking the problem of time is that there is none in GR: at least in the spatially compact case without boundaries the Hamiltonian vanishes on the physical, constraint surface. This is physically relevant because we seem to live in a universe with precisely that spatial topology. Since the Hamiltonian generates time translations in any canonical theory we arrive at the conclusion that ‘nothing moves’ in GR, which is in obvious contradiction to experiment. Since there is no time also the usual interpretation of quantum mechanical measurements at given moments of time breaks down. One can fill books about this issue and we will not even try to cover a substantial amount of the existing literature. A superb source of information on these conceptual problems is Carlo Rovelli's book [3]. Rather, what we will do in what follows is to collect various proposals for solutions to the problem of time taken from other authors, especially Rovelli's relational approach to classical and quantum physics and Hartle et al. 's consistent history interpretation, and combine them into a consistent picture. We do not want to suggest that the resulting picture is to be accepted, rather we want to draw attention to the problems involved and to develop a working hypothesis. The discussion on the interpretation of quantum mechanics is very alive and some authors such as Penrose [243] not only propose to alter the interpretational aspect of quantum mechanics but also the mathematical framework.
Many experimental results and theoretical reasonings on gedanken experiments suggest that quantum entities behave in a non-local . In order to make the discussion more precise, we propose an operational definition of non-locality . We discuss two examples of spin superposition experiments which illustrate the use of this definition. They show that quantum entities like a neutron or an atom are non-local. We make an analysis of the difficulty to imagine such non-local entities and to conciliate this non-locality with the locality of classical entities
The problem of wave-particle duality is considered within the framework of the algebraic approach. Contrary to the widespread belief, we demonstrate that wave-particle duality can be reconciled with the assumption that there exists some local physical reality determining the results of local measurements. A number of quantum experiments—double-slit electron scattering, Wheeler’s delayed choice experiment, the past of photons passed through the interferometer—are discussed using the concept of locality. A clear physical interpretation of these experiments that does not contradict classical concepts is provided.