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Complementarity Principle

Gennaro Auletta, Shang-Yung Wang

Published Jun 20, 2014• 0 citations
Publisher

Abstract

In this chapter we shall come back to the issue of the undulatory nature of matter. Interferometer experiments with a blocked path show that this character cannot be taken in a classical sense. Indeed, quantum probabilities are deeply affected by the presence of features. The possibility of measurements without interaction shows that such probabilities have in quantum mechanics an ontological import. We then state a complementarity between local events and non-local features. Delayed choice experiments sets these aspects in new and enlightening terms.

DOI
10.1201/b17083-10

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In this chapter we shall come back to the issue of the undulatory nature of matter. Interferometer experiments with a blocked path show that this character cannot be taken in a classical sense. Indeed, quantum probabilities are deeply affected by the presence of features. The possibility of measurements without interaction shows that such probabilities have in quantum mechanics an ontological import. We then state a complementarity between local events and non-local features. Delayed choice experiments sets these aspects in new and enlightening terms.
Abstract The results of the experiments described in the last chapter all point fairly unambiguously to a reality that is decidedly non-local in nature, at least in the quantum domain. Of course, these are results that come as no surprise to those willing to accept one of the most fundamental principles of the Copenhagen interpretation — that quantum phenomena are describable only in terms of the dual classical physical concepts of waves and particles. The wave properties of quantum entities lend them inherently non-local characteristics, and it is only when we forcibly ‘collapse’ the wave function by making a measurement that we are taken aback by what appears to be contradictory or counter-intuitive behaviour.
Gennaro Auletta University of Cassino gennaro.auletta@gmail.com Classically, the main ontological attempts at understanding quantum mechanics focus on the corpuscular behavior of these systems and especially on detection events, since these are the most classical phenomena that we have in such a context (indeed, they also require the presence of a classical apparatus). The main trend has been to consider wave-like aspects as deprived of ontological substrate and as reflecting rather the mathematical abstract formalism of the theory. The few attempts that have been done in order to assign some form of ontological reference to wave-like aspects have tried to interpreted this in terms of classical waves and have been disproved across the last 30 years (see Auletta & Tarozzi, 2004b; Auletta & Torcal, 2011). It is perhaps time to try a different approach, by renouncing any attempt at a classical ontology and by taking seriously into account the non-local aspects of the theory (which are mostly associated with wave-like phenomena). When we consider things in this perspective, we shall discover that all non-local phenomena in quantum mechanics, although different, have something in common: they all rely on non-local interdependencies among possible events or measurement outcomes (see Auletta, 2011). This is true for all interference phenomena for isolated systems, this is true for entangled systems, this is true for the Aharonov-Bohm effect, and so on. What is sad is that we do not have until now a name for denoting this mysterious reality. It is indeed mysterious, since we cannot directly measure it. There is in fact no way to have a direct experimental evidence of it. In most cases we can only reconstruct the interference profile after many experimental runs, a circumstance that has led many scientists to discard any ontological attribution to wave-like phenomena. However, a proposed
Abstract Quantum delayed-choice experiments are designed to probe the robustness of the complementarity principle. In this proceeding, we revisit the main ideas reported recently in Ref. [Commun. Phys. 5, 82 (2022)] concerning a setup (quantum-controlled reality experiment) that has the same final visibility as the quantum version of Wheeler’s delayed-choice arrangement. Besides the same final statistics, upon an operational criterion of physical realism, the authors claimed a different state of affairs for the wave-and-particle behavior in delayed-choice experiments. To this end, we put forward an analysis by employing the relative entropy of coherence to study how the local wave and particle coherences when the system is traveling inside the interferometer change accordingly to the final observed visibility.
A simple conceptual experiment which seems to violate the general principles of quantum mechanics is reported. The reasoning leading to this contradiction contains a trick which makes the paradox possible. By discussing the failure of the argument the author wishes to draw attention to a fundamental feature of the wave function which is frequently overlooked. Finally, in light of this discussion, a kind of delayed-choice experiment is described, and an analysis of the related issue of complementarity is made.
The principle of complementarity is one of the cornerstones of quantum theory. The aim of this study was to advance our understanding of complementarity by analyzing the role of delayed choice and quantum erasers in two-slit experiments, and by proposing experiments for verifying the analysis. The analysis is based on models consisting of measurable spaces and probability measures involved in the experiments. The main findings are as follows: (a) The complementarity principle manifests itself in such a way that wave and particle behaviors cannot be simultaneously observed almost surely with respect to any single, fixed measure. (b) Described by different measures, complementary properties can coexist in the same experimental setup. (c) Which-way information will not preclude or erase interference fringes. (d) Delayed choice and quantum erasers are irrelevant to testing complementarity. (e) It is possible for us to know through which slit each quantum object passed almost surely with respect to the measure corresponding to the slit while the interference pattern is intact. Based on the experiments analyzed, realizable experiments are proposed for verifying the above results.
In this chapter, we shall collect and generalize the results of the previous three chapters. We shall come back to the issue of quantum correlations in terms of information. We shall consider now the second aspect of quantum information [see Section 11.3], that is, information selection leading to a local growth of entropy (as it is the case during ameasurement). This will be the basis for examining again the whole process of measurement and finally assign an ontological status to fundamental entities of quantum theory like states, observables, and properties.