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arXiv:quant-ph/0703118 · Quanta

Complementarity and the Nature of Uncertainty Relations in Einstein–Bohr Recoiling Slit Experiment

Shogo Tanimura

Published Jul 15, 2015• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.12743/quanta.v4i1.35

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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.
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.
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.
Published in 2025, the recoiling-slit quantum interference experiment employs optically trapped single rubidium atoms to scatter photons. It claims to physically realize Einstein’s thought experiment of a movable physical slit and supports the principle of quantum complementarity based on experimental observations. Within the framework of the Original Light Theory, this paper strictly distinguishes the microscopic motion of individual photons and the statistical characteristics of photon ensembles. From the perspectives of acting environment, spatial scale and microscopic coupling mechanism, we demonstrate that the single rubidium atom scattering system only shares approximate mathematical appearances with the traditional double-slit system with physical wall thickness, while their physical essences are entirely different. This experiment artificially eliminates core physical conditions in real double-slit systems, including photon oscillation, slit channels and continuous momentum coupling between photons and slit walls, which constitutes typical conceptual substitution. Fundamentally, it is merely a recoil scattering experiment between single photons and isolated rubidium atoms, and cannot be equated with physical double-slit interference experiments. Once the inherent oscillation of photons and the mechanism of continuous interaction between photons and thick slit walls are incorporated, there is no basis for the equivalence of the two sets of models. Asserting model equivalence while ignoring photon oscillation and slit-wall coupling effects is nothing but self-deception. Its experimental conclusions are highly misleading. They cannot be extended to interpret real thick-wall double-slit interference and cannot serve as reliable experimental evidence for the validity of the principle of complementarity. Previous theoretical analyses built on physical slit models remain fully valid. Divergences originate from the replacement of experimental physical models rather than defects in the original physical mechanism analysis.
In December 2025, Pan Jianwei’s research team reproduced the Einstein-Bohr recoiling-slit thought experiment proposed in 1927 at the quantum limit. They observed that the interference fringe contrast changes continuously with the momentum of the slit. Mainstream physical theories currently regard this phenomenon as critical evidence for the quantum complementarity principle. Based on the Light Primitive Theory, this paper points out that all relevant theoretical models established since the century-long debate at the Solvay Conference contain two fundamental idealized simplifications: first, physical slits are abstracted as two-dimensional geometric holes with zero thickness; second, the inherent continuous spatial oscillation of photons is ignored. Photons are not point-like particles moving along fixed straight lines. Their persistent oscillation enables continuous momentum coupling between photons and the photon self-locked matter forming the slit walls throughout the whole passage through the physically thick slit channel. The inverse correlation between path detectability and interference fringe visibility observed in the experiment can be self-consistently explained by continuous photon-slit wall interaction, without abstract hypotheses such as wave-particle complementarity or quantum superposition. This paper supplements the objective physical conditions missing from traditional models and provides a brand-new interpretative framework for quantum interference phenomena at the underlying mechanism level.
The present investigation is about the quantum mechanics of multislit interference experiments. One of the cornerstones of our understanding of quantum mechanics is provided by the analysis of this type of experiments. Beginning with Bohr and Einstein, the discussion revolved mostly around single-slit diffraction and double-slit interference, probing the complementarity of path determination and the appearance of interference fringes, and contrasting the familiar with the quantum. Here, we are concerned with developing a systematic understanding and description of multislit interference experiments, i.e. setups in which a plurality of slits is illuminated. We provide a characterisation of a number of relevant observables, discussing those that are compatible and may be measured jointly, and also incompatible observables which cannot be measured jointly but instead display quantum uncertainty. \nWe begin with a discussion of a particular modification of the classic double- slit interference experiment which highlights the realisation of specific position and momentum observables which are jointly measurable. Although there are technical results regarding the coexistence of specific position and momentum observables, it may be surprising that ubiquitous experimental setups provide a preparation of such quantum states. We proceed with a discussion of the particular character of the incompatibility of certain measurements by building on an initial heuristic argument provided by Aharonov, Pendleton and Petersen. We prove, extend and discuss a formulation of un- certainty suitable for the context of multislit experiments. We conclude with a comparison of this formulation of uncertainty with an alternative uncertainty formulation developed by Uffink and Hilgevoord. Although these two uncertainty formulations are very different technically, we demonstrate that the same tradeoff is expressed independently.
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.