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arXiv:1112.4522

A Very Common Fallacy in Quantum Mechanics: Superposition, Delayed Choice, Quantum Erasers, Retrocausality, and All That

David Ellerman

Published Dec 16, 2011• 5 citations
arXivHTMLPDF

Abstract

There is a very common fallacy, here called the separation fallacy, that is involved in the interpretation of quantum experiments involving a certain type of separation such as the: double-slit experiments, which-way interferometer experiments, polarization analyzer experiments, Stern-Gerlach experiments, and quantum eraser experiments. It is the separation fallacy that leads not only to flawed textbook accounts of these experiments but to flawed inferences about retrocausality in the context of "delayed choice" versions of separation experiments.

DOI
10.48550/arxiv.1112.4522

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There is a very common fallacy, here called the separation fallacy, that is involved in the interpretation of quantum experiments involving a certain type of separation such as the: double-slit experiments, which-way interferometer experiments, polarization analyzer experiments, Stern-Gerlach experiments, and quantum eraser experiments. It is the separation fallacy that leads not only to flawed textbook accounts of these experiments but to flawed inferences about retrocausality in the context of "delayed choice" versions of separation experiments.
Delayed choice and quantum eraser experiments have attracted much interest recently, both theoretically and experimentally. In particular, they have prompted suggestions that quantum mechanics involves acausal effects. Using a recently developed approach which takes apparatus into account, we present a detailed analysis of various double-slit experiments to show that this is never the case. Instead, quantum experiments can be described in terms of a novel concept of time called stages. These can cut across the conventional linear time parameter as experienced in the laboratory and appear to violate causality.
As “Stern-Gerlach first” becomes increasingly popular in the undergraduate quantum mechanics curriculum, we show how one can extend the treatment found in conventional textbooks to cover some exciting new quantum phenomena. Namely, we illustrate how one can describe a delayed choice variant of the quantum eraser which is realized within the Stern-Gerlach framework. Covering this material allows the instructor to reinforce notions of changes in basis functions, quantum superpositions, quantum measurements, and the complementarity principle as expressed in whether we know “which-way” information or not. It also allows the instructor to dispel common misconceptions of when a measurement occurs and when a system is in a superposition of states.
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.
The quantum eraser variant of the double-slit experiment, and its 'delayed choice' sub-variant, are considered from the perspective of weak value and weak measurement theory (which is briefly reintroduced here). The interference fringes that appear when measuring certain spin states, which can then be 'erased' when measuring other spin states, are shown to be anomalous weak values that depend on particular post-selection choices. By framing the choice of spin measurement as a weak value of a certain weak measurement, it is then made clear what physical claims can and cannot be made about what occurs in the quantum eraser experiment. Specifically, claims about the choice of spin-state `retrocausally' influencing the choice of slit(s) for the particles to travel through are discredited, and a simple framework is presented for understanding how the fringes arise and why they can be 'erased'.