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A proposed resolution of the delayed-choice paradox

Michael B. Heaney

Published Sep 22, 2014• 1 citation
OpenAlex

Abstract

Abstract. This paper proposes a resolution of the delayed-choice paradox of the Conven-tional Theory of quantum mechanics, where a particle seems to know what will happen in the future, and changes its present behavior accordingly. A comparison of the Conventional Theory with an Advanced Theory and a Symmetrical Theory of the same delayed-choice experiment suggests that the apparent paradox is caused by an incorrect assumption about the interaction of a wavefunction with a beam-splitter. Once this assumption is corrected, there is no delayed-choice paradox in any of the three theories. 1.

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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.

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Ever since the proposal of delayed choice quantum erasure and subsequent realization in the experiment by Kim et al., the interpretation and implications of delayed-choice experiments have remained a subject of intense foundational debate. This paper resolves the apparent paradox attached to the experiment using standard quantum mechanics. Using an extended Mach-Zehnder interferometer which captures every operational feature of the original experiment, we show that choosing between which-path and erasure detectors is simply a choice of measurement bases, which does not rewrite a photon's past. Furthermore, by mapping the experiment to a two-way Stern-Gerlach framework, we prove that quantum erasure is an expected result of measuring entangled states, not a physical anomaly. Ultimately, through a pedagogical game, we illustrate that the illusion of retrocausality arises from asking illegitimate questions, and that a forward-in-time description is entirely sufficient to explain the logic.

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Alternative analysis of the delayed-choice quantum eraser with two entangled particles

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According to Quantum Mechanics, the particles can exhibit either particle properties or wave properties depending on the experimental set up (wave-particle dualism). A special behavior occurs for a system of two entangled particles 1 and 2 that propagate along two different directions in the space. In such a case, the entangled particle 2 should exhibit either the particle behavior or the wave behavior depending on the kind of measurement that is performed on particle 1 whatever is the actual distance between the two particles. The apparently surprising fact is that the "choice" of what kind of measurement is performed on particle 1 can be also made when particle 2 has been already detected (delayed-choice quantum eraser).These theoretical predictions have been confirmed by the experiments and seem to suggest that a future measurement can affect a past event. Recently, both the concepts of "delayed choice" and of "quantum erasure" have been criticized by Ellerman and by Kastner. In this paper we propose an alternative analysis of the delayed-choice quantum eraser with two entangled particles and we show that it does not imply an inversion of the natural cause-effect temporal order of the physical events.

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Bram Gaasbeek

The delayed choice experiments are a collection of experiments where the counterintuitive laws of quantum mechanics are manifested in a very striking way. Although the delayed choice experiments can be very accurately described with the standard framework of quantum optics, a more didactical and intuitive explanation seems not to have been given so far. In this note, we fill that gap.

arXiv:1007.3977•Jul 22, 2010•8 citations
Abstract. This paper proposes a resolution of the delayed-choice paradox of the Conven-tional Theory of quantum mechanics, where a particle seems to know what will happen in the future, and changes its present behavior accordingly. A comparison of the Conventional Theory with an Advanced Theory and a Symmetrical Theory of the same delayed-choice experiment suggests that the apparent paradox is caused by an incorrect assumption about the interaction of a wavefunction with a beam-splitter. Once this assumption is corrected, there is no delayed-choice paradox in any of the three theories. 1.
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.
John Wheeler devised a gedanken experiment in which a piece of apparatus can be altered just before the arrival of particle, and this “delayed choice ” can, seemingly, alter the quantum state of the particle at a much earlier time, long before the choice is made. A slightly different gedanken experiment, which exhibits the same conceptual difficulty, is analyzed using the techniques of consistent history quantum theory. The idea that the future influences the past disappears when proper account is taken of the diversity of possible quantum descriptions of the world, and their mutual compatibility or incompatibility. John Wheeler proposed a delayed-choice experiment in which the second beam splitter of a Mach-Zehnder interferometer is or is not removed at the very last instant before a photon reaches it and passes out of the interferometer [1]. A modified version which exhibits essentially the same paradox is shown in Fig. 1. A photon enters the interferometer through channel a, and two detectors in the c and d arms are either (a) left in position, or (b) removed just before the photon reaches (one of) them, so that it is free to proceed on to the second
Hidden-variable models aim to reproduce the results of quantum theory and to satisfy our classical intuition. Their refutation is usually based on deriving predictions that are different from those of quantum mechanics. Here instead we study the mutual compatibility of apparently reasonable classical assumptions. We analyze a version of the delayed-choice experiment which ostensibly combines determinism, independence of hidden variables on the conducted experiments, and wave-particle objectivity (the assertion that quantum systems are, at any moment, either particles or waves, but not both). These three ideas are incompatible with any theory, not only with quantum mechanics.
Ever since the proposal of delayed choice quantum erasure and subsequent realization in the experiment by Kim et al., the interpretation and implications of delayed-choice experiments have remained a subject of intense foundational debate. This paper resolves the apparent paradox attached to the experiment using standard quantum mechanics. Using an extended Mach-Zehnder interferometer which captures every operational feature of the original experiment, we show that choosing between which-path and erasure detectors is simply a choice of measurement bases, which does not rewrite a photon's past. Furthermore, by mapping the experiment to a two-way Stern-Gerlach framework, we prove that quantum erasure is an expected result of measuring entangled states, not a physical anomaly. Ultimately, through a pedagogical game, we illustrate that the illusion of retrocausality arises from asking illegitimate questions, and that a forward-in-time description is entirely sufficient to explain the logic.
According to Quantum Mechanics, the particles can exhibit either particle properties or wave properties depending on the experimental set up (wave-particle dualism). A special behavior occurs for a system of two entangled particles 1 and 2 that propagate along two different directions in the space. In such a case, the entangled particle 2 should exhibit either the particle behavior or the wave behavior depending on the kind of measurement that is performed on particle 1 whatever is the actual distance between the two particles. The apparently surprising fact is that the "choice" of what kind of measurement is performed on particle 1 can be also made when particle 2 has been already detected (delayed-choice quantum eraser).These theoretical predictions have been confirmed by the experiments and seem to suggest that a future measurement can affect a past event. Recently, both the concepts of "delayed choice" and of "quantum erasure" have been criticized by Ellerman and by Kastner. In this paper we propose an alternative analysis of the delayed-choice quantum eraser with two entangled particles and we show that it does not imply an inversion of the natural cause-effect temporal order of the physical events.