We analyze Niels Bohr's proposed two-slit interference experiment with highly charged particles that argues that the consistency of elementary quantum mechanics requires that the electromagnetic field must be quantized. In the experiment a particle's path through the slits is determined by measuring the Coulomb field that it produces at large distances; under these conditions the interference pattern must be suppressed. The key is that as the particle's trajectory is bent in diffraction by the slits it must radiate and the radiation must carry away phase information. Thus the radiation field must be a quantized dynamical degree of freedom. On the other hand, if one similarly tries to determine the path of a massive particle through an inferometer by measuring the Newtonian gravitational potential the particle produces, the interference pattern would have to be finer than the Planck length and thus undiscernable. Unlike for the electromagnetic field, Bohr's argument does not imply that the gravitational field must be quantized.
Niels Bohr's doctrine of the primacy of "classical concepts" is arguably his most criticized and misunderstood view. We present a new, careful historical analysis that makes clear that Bohr's doctrine was primarily an epistemological thesis, derived from his understanding of the functional role of experiment. A hitherto largely overlooked disagreement between Bohr and Heisenberg about the movability of the "cut" between measuring apparatus and observed quantum system supports the view that, for Bohr, such a cut did not originate in dynamical (ontological) considerations, but rather in function…
It is well known that Niels Bohr insisted on the necessity of classical concepts in the account of quantum phenomena. But there is little consensus concerning his reasons, and what he exactly meant by this. In this paper, I re-examine Bohr's interpretation of quantum mechanics, and argue that the necessity of the classical can be seen as part of his response to the measurement problem. More generally, I attempt to clarify Bohr's view on the classical/quantum divide, arguing that the relation between the two theories is that of mutual dependence. An important element in this clarification consi…
The Einstein-Rupp experiments have been unduly neglected in the history of quantum mechanics. While this is to be explained by the fact that Emil Rupp was later exposed as a fraud and had fabricated the results, it is not justified, due to the importance attached to the experiments at the time. This paper discusses Rupp's fraud, the relation between Albert Einstein and Rupp, and the Einstein-Rupp experiments, and argues that these experiments were an influence on Niels Bohr's development of complementarity and Werner Heisenberg's formulation of the uncertainty relations.
The only acceptable reason why measurements are irreversible and outcomes definite is the intrinsic definiteness and irreversibility of human sensory experience. While QBists deserve credit for their spirited defense of this position, Niels Bohr urged it nearly a century ago, albeit in such elliptic ways that the core of his message has been lost or distorted beyond recognition. Then as now, the objectivity of empirical science was called into question. It was defended by Bohr along the lines of Kant's (then) revolutionary theory of science, according to which the possibility of empirical scie…
A model of the Einstein-Bohr double-slit experiment is formulated in a fully quantum theoretical setting. In this model, the state and dynamics of a movable wall that has the double slits in it, as well as the state of a particle incoming to the double slits, are described by quantum mechanics. Using this model, we analyzed complementarity between exhibiting the 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…
We have implemented a novel double-slit "which-way" experiment which raises interesting questions of interpretation. Coherent laser light is passed through a converging lens and then through a dual pinhole producing two beams crossing over at the focal point of the lens, and fully separating further downstream providing which-way information. A thin wire is then placed at a minimum of the interference pattern formed at the cross-over region. No significant reduction in the total flux or resolution of the separated beams is found, providing evidence for coexistence of perfect interference and w…
Hefei National Laboratory for Physical Science at the Microscale and Department of Modern Physics, University of Science and Technology of China（中国科学技术大学微尺度物质科学国家研究中心和现代物理系）；Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学技术大学中科院量子信息与量子物理学卓越创新中心上海分部）；New Cornerstone Science Laboratory, Shanghai Research Center for Quantum Sciences（上海量子科学研究中心新基石科学实验室）
The two-slit experiment with quantum particles provides many insights into the behaviour 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 i…
A which-way measurement in Young's double-slit will destroy the interference pattern. Bohr claimed this complementarity between wave- and particle behaviour is enforced by Heisenberg's uncertainty principle: distinguishing two positions a distance s apart transfers a random momentum q \sim \hbar/s to the particle. This claim has been subject to debate: Scully et al. asserted that in some situations interference can be destroyed with no momentum transfer, while Storey et al. asserted that Bohr's stance is always valid. We address this issue using the experimental technique of weak measurement. …
Some modified two-slit interference experiments claim to demonstrate a violation of Bohr's complementarity principle. A typical such experiment is theoretically analyzed using wave-packet dynamics. The flaw in the analysis of such experiments is pointed out and it is demonstrated that they do not violate complementarity. In addition, it is quite generally proved that if the state of a particle is such that the modulus square of the wave-function yields an interference pattern, then it necessarily loses which-path information.
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 provided a simpler answer to Einstein. We also derive the Englert-Greenberger-Yasin duality relation from this entanglement. 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 …
A modified version of Young's experiment by Shahriar Afshar indirectly reveals the presence of a fully articulated interference pattern prior to the post-selection of a particle in a "which-slit" basis. While this experiment does not constitute a violation of Bohr's Complementarity Principle as claimed by Afshar, both he and many of his critics incorrectly assume that a commonly used relationship between visibility parameter V and "which-way" parameter K has crucial relevance to his experiment. It is argued here that this relationship does not apply to this experimental situation and that it i…
It is argued that Niels Bohr ultimately arrived at positivistic and antirealist-flavored statements because of weaknesses in his initial objective of accounting for measurement in physical terms. Bohr's investigative approach faced a dilemma, the choices being (i) conceptual inconsistency or (ii) taking the classical realm as primitive. In either case, Bohr's `Complementarity' does not adequately explain or account for the emergence of a macroscopic, classical domain from a microscopic domain described by quantum mechanics. A diagnosis of the basic problem is offered, and an alternative way fo…
Shahriar S. Afshar claimed that his 2007 modified version of the double-slit experiment violates complementarity [1]. He makes two modifications to the standard double-slit experiment. First, he adds a wire grid that is placed in between the slits and the screen at locations of interference minima. The second modification is to place a converging lens just after the wire grid. The idea is that the wire grid implies the existence of interference minima(wave-like behavior), while the lens can simultaneously obtain which-way information (particle-like behavior). More recently, John G. Cramer [2] …
As per Einstein's design, particles are introduced into the double-slit experiment through a small hole in a plate which can either move up and down (and its momentum can be measured) or be stopped (and its position can be measured). Suppose one measures the position of the plate and this act verifies the statement that the interference pattern is observed in the experiment. However, if it is possible to think about the outcome that one would have obtained if one had measured plate's momentum instead of its position, then it is possible to consider, together with the aforesaid statement, anoth…
The assertion that an experiment by Afshar et al. demonstrates violation of Bohr's Principle of Complementarity is based on the faulty assumption that which-way information in a double-slit interference experiment can be retroactively determined from a future measurement.
Fringe visibility and which-way information in Young's double slit experiments with light scattered from single atoms
Massachusetts Institute of Technology（麻省理工学院）；Research Laboratory of Electronics, Massachusetts Institute of Technology（麻省理工学院电子研究实验室）；MIT-Harvard Center for Ultracold Atoms（麻省理工学院-哈佛超冷原子中心）
The complementary wave and particle character of quantum objects (or quantons) was pointed out by Niels Bohr. This wave-particle duality, in the context of the two-slit experiment, is now described not just as two extreme cases of wave and particle characteristics, but in terms of quantitative measures of these natures. These measures of wave and particle aspects are known to follow a duality relation. A very simple and intuitive derivation of a closely related duality relation is presented, which should be understandable to the introductory student.
Thought experiments based on the double-slit interferometer had a crucial role to develop ideas concerning the wave-particle duality and the Bohr's complementarity principle. Ideally, a slit with a sufficiently low mass recoils due to the passage of the photon. This motion denounces the path taken by the light and suppresses any attempt to observe an interference pattern. In real life, however, available which-way information in such a setup is significantly impaired by the typical magnitudes of photons and slits, making the verification of the effect almost impossible. Here, we extend this di…
Bohr's principle of complementarity, in the context of a two-slit interference experiment, is understood as the quantitative measures of wave and particle natures following a duality relation ${\mathcal D}^2+{\mathcal V}^2 \le 1$. Here ${\mathcal D}$ is a measure of distinguishability of the two paths, and ${\mathcal V}$ is the visibility of interference. It is shown that such a relation can be formulated for $N-$slit or $N-$path interference too, with the proviso that the wave nature is characterized by a measure of {\em coherence} (${\mathcal C}$). This new relation, ${\mathcal D}^2+{\mathca…
Niels Bohr's arguments indicating the non-applicability of quantum methodology to the study of the ultimate details of life given in his book "Atomic physics and human knowledge" conflict with the commonly held opposite view. The bases for the usual beliefs are examined and shown to have little validity. Significant differences do exist between the living organism and the type of system studied successfully in the physics laboratory. Dealing with living organisms in quantum-mechanical terms with the same degree of rigour as is normal for non-living systems would seem not to be possible without…
A new formulation of the EPR argument is presented, one which uses John Bell's mathematically precise local causality condition in place of the looser locality assumption which was used in the original EPR paper and on which Niels Bohr seems to have based his objection to the EPR argument. The new formulation of EPR bears a striking resemblance to Bell's derivation of his famous inequalities. The relation between these two arguments -- in particular, the role of EPR as part one of Bell's two-part argument for nonlocality -- is also discussed in detail.
A which-way measurement destroys the twin-slit interference pattern. Bohr argued that distinguishing between two slits a distance s apart gives the particle a random momentum transfer \wp of order h/s. This was accepted for more than 60 years, until Scully, Englert and Walther (SEW) proposed a which-way scheme that, they claimed, entailed no momentum transfer. Storey, Tan, Collett and Walls (STCW) in turn proved a theorem that, they claimed, showed that Bohr was right. This work reviews and extends a recent proposal [Wiseman, Phys. Lett. A 311, 285 (2003)] to resolve the issue using a weak-val…
The Afshar experiment is a relatively simple two-slit experiment with results that appear to show a discrepancy with the predictions of Bohr's Principle of Complementarity. We report on the results of a calculation using a simpler but equivalent set-up called the modified Afshar experiment. Numerical results are in agreement with the experimental results performed on the Afshar experiment set-up. Calculations show that the level of which-way information and visibility in the Afshar experiement is higher than originally estimated.
Taking recent experiments as examples, we discuss the conditions for sub-wavelength probing of optical field structures by single trapped atoms. We calculate the achievable resolution, highlighting its connection to the fringe visibility in an interference experiment. We show that seemingly different physical pictures, such as spatial averaging, phase modulation, and which-way information, describe the situation equally and lead to identical results. The connection to Bohr's moving slit experiment is pointed out.
The quantitative formulation of Bohr's complementarity proposed by Greenberger and Yasin is applied to some physical situations for which analytical expressions are available. This includes a variety of conventional double-slit experiments, but also particle oscillations, as in the case of the neutral-kaon system, and Mott scattering of identical nuclei. For all these cases, a unified description can be achieved including a new parameter, $ν$, which quantifies the effective number of fringes one can observe in each specific interferometric set-up.
We propose and analyze a modified ghost-interference experiment, and show that revealing the particle-nature of a particle passing through a double-slit hides the wave-nature of a spatially separated particle which it is entangled with. We derive a nonlocal duality relation, ${\mathcal D}_1^2 + {\mathcal V}_2^2 \le 1$, which connects the path distinguishability of one particle to the interference visibility of the other. It extends Bohr's principle of complementarity to a nonlocal scenario. We also propose a ghost quantum eraser in which, erasing the which-path information of one particle brin…
We investigate theoretically the dissociative ionization of a H2+ molecule using two ultrashort laser (pump-probe) pulses. The pump pulse prepares a dissociating nuclear wave packet on an ungerade surface of H2+. Next, an UV (or XUV) probe pulse ionizes this dissociating state at large (R = 20 - 100 bohr) internuclear distance. We calculate the momenta distributions of protons and photoelectrons which show a (two-slit-like) interference structure. A general, simple interference formula is obtained which depends on the electron and protons momenta, as well as on the pump-probe delay on the puls…
We report on the simultaneous determination of complementary wave and particle aspects of light in a double-slit type "welcher-weg" experiment beyond the limitations set by Bohr's Principle of Complementarity. Applying classical logic, we verify the presence of sharp interference in the single photon regime, while reliably maintaining the information about the particular pinhole through which each individual photon had passed. This experiment poses interesting questions on the validity of Complementarity in cases where measurements techniques that avoid Heisenberg's uncertainty principle and q…
A recent experiment performed by S. S. Afshar et al. has been interpreted as a violation of Bohr's complementarity principle between interference visibility and which-path information in a two-path interferometer. We have reproduced this experiment, using true single-photon pulses propagating in a two-path wavefront- splitting interferometer realized with a Fresnel's biprism, and followed by a grating with adjustable transmitting slits. The measured values of interference visibility V and which-path information, characterized by the distinguishability parameter D, are found to obey the complem…
The quest to have both which-path knowledge and interference fringes in a double-slit experiment dates back to the inception of quantum mechanics (QM) and to the famous Einstein-Bohr debates. In this paper we propose and discuss an experiment able to spy on one photon's path with another photon. We modify the quantum state inside the interferometer as opposed to the traditional physical modification of the "wave-like" or "particle-like" experimental setup. We are able to show that it is the ability to harvest or not which-path information that finally limits the visibility of the interference …
