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arXiv:1210.4248 · Quanta

Einstein's Recoiling Slit Experiment, Complementarity and Uncertainty

Tabish Qureshi, Radhika Vathsan

Published May 14, 2013• 17 citations
arXivHTMLPDF

Abstract

We analyze Einstein's recoiling slit experiment and point out that the inevitable entanglement between the particle and the recoiling slit was not part of Bohr's reply. We show that if this entanglement is taken into account, one can provide a simpler answer to Einstein. We also derive the Englert-Greenberger-Yasin duality relation from the entanglement between the particle and the recoiling slit. In addition, we show that the Englert-Greenberger-Yasin duality relation can also be thought of as a consequence of the sum uncertainty relation for certain observables of the recoiling slit. Thus, the uncertainty relations and entanglement are both an integral part of the which-way detection process. Quanta 2013; 2: 58–65.

DOI
10.12743/quanta.v2i1.11

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We analyze Einstein's recoiling slit experiment and point out that the inevitable entanglement between the particle and the recoiling slit was not part of Bohr's reply. We show that if this entanglement is taken into account, one can provide a simpler answer to Einstein. We also derive the Englert-Greenberger-Yasin duality relation from the entanglement between the particle and the recoiling slit. In addition, we show that the Englert-Greenberger-Yasin duality relation can also be thought of as a consequence of the sum uncertainty relation for certain observables of the recoiling slit. Thus, the uncertainty relations and entanglement are both an integral part of the which-way detection process. Quanta 2013; 2: 58–65.
The two-slit experiment with quantum particles provides many insights into the behavior of quantum mechanics, including Bohr’s complementarity principle. Here, we analyze Einstein’s recoiling slit version of the experiment and show how the inevitable entanglement between the particle and the recoiling slit as a which-way detector is responsible for complementarity. We derive the Englert–Greenberger–Yasin duality from this entanglement, which can also be thought of as a consequence of sum-uncertainty relations between certain complementary observables of the recoiling slit. Thus, entanglement is an integral part of the which-way detection process, and so is uncertainty, though in a completely different way from that envisaged by Bohr and Einstein.
A model of the Einstein–Bohr recoiling slit experiment is formulated in a fully quantum theoretical setting. In this model, the state and dynamics of a movable wall that has two slits in it, as well as the state of a particle incoming to the two slits, are described by quantum mechanics. Using this model, we analyzed complementarity between exhibiting an interference pattern and distinguishing the particle path. Comparing the Kennard–Robertson type and the Ozawa-type uncertainty relations, we conclude that the uncertainty relation involved in the double-slit experiment is not the Ozawa-type uncertainty relation but the Kennard-type uncertainty relation of the position and the momentum of the double-slit wall. A possible experiment to test the complementarity relation is suggested. It is also argued that various phenomena which occur at the interface of a quantum system and a classical system, including distinguishability, interference, decoherence, quantum eraser, and weak value, can be understood as aspects of entanglement. Quanta 2015; 4: 1–9.
Double-slit experiments illustrate proof for wave–particle complementarity. The essence of Einstein–Bohr's debate about wave–particle duality was whether the momentum transfer between a particle and a recoiling slit could mark the path, thus destroying the interference. We realized this recoiling double-slit gedanken experiment by resonant X-ray photoemission from molecular oxygen for geometries near equilibrium (coupled slits) and in a dissociative state far away from equilibrium (decoupled slits). Interference is observed in the former case, while the electron momentum transfer quenches the interference in the latter case.
The notion of wave–particle duality remains one of the most debated subjects in the history of quantum physics. The most famous debate on the subject occurred between Bohr and Einstein. In this work, we revisit the wave–particle duality in the Bohr–Einstein debate from the viewpoint of the recently established duality-entanglement relation. We show that the duality-entanglement relation can provide a valuable framework for quantitative analysis of the Einstein's gedanken double-slit experiment and clarify some of its fundamental aspects.
Abstract It is argued that two distinct types of complementarity are implied in Bohr's complementarity principle. While in the case of complementary variables it is the quantum mechanical uncertainty relation which is at work, the collapse hypothesis ensures this exclusiveness in the so-called wave-particle complementarity experiments. In particular it is shown that the conventional analysis of the double slit experiment which invokes the uncertainty principle to explain the absence of the simultaneous knowledge of the which-slit information and the interference pattern is incorrect and implies consequences that are quantum mechanically inconsistent.
Recent experimental realizations of the Einstein–Bohr recoiling-slit thought experiment have demonstrated a continuous tradeoff between interference visibility and recoil-induced distinguishability, often interpreted as a definitive empirical vindication of Bohr’s complementarity principle. In this work, we propose an alternative but compatible interpretation in which the effective geometry of distinguishability is induced by the experimental context itself. By introducing a context-dependent metric operator on the slit’s motional Hilbert space, we show that the standard recoil-limited visibility law emerges as a limiting case, while allowing for experimentally testable deviations when coherence bandwidth and accessibility constraints are varied. This formulation preserves complementarity while reframing its enforcement as a mechanistic, geometric process rather than an axiomatic postulate.