The photon box thought experiment can be considered a forerunner of the EPR-experiment: by performing suitable measurements on the box it is possible to ``prepare'' the photon, long after it has escaped, in either of two complementary states. Consistency requires that the corresponding box measurements be complementary as well. At first sight it seems, however, that these measurements can be jointly performed with arbitrary precision: they pertain to different systems (the center of mass of the box and an internal clock, respectively). But this is deceptive. As we show by explicit calculation, although the relevant quantities are simultaneously measurable, they develop non-vanishing commutators when calculated back to the time of escape of the photon. This justifies Bohr's qualitative arguments in a precise way; and it illustrates how the details of the dynamics conspire to guarantee the requirements of complementarity. In addition, our calculations exhibit a ``fine structure'' in the distribution of the uncertainties over the complementary quantities: depending on when the box measurement is performed, the resulting quantum description of the photon differs. This brings us close to the argumentation of the later EPR thought experiment.
Critique of Quantum Optical Experimental Refutations of Bohr's Principle of Complementarity, of the Wootters-Zurek Principle of Complementarity, and of the Particle-Wave Duality Relation
Federal University of Santa Maria（圣玛丽亚联邦大学）；State University of Campinas（坎皮纳斯州立大学）；Centre for Theoretical Physics, Jamia Millia Islamia（贾米亚米利亚伊斯兰大学理论物理中心）
In quantum physics, the notion of contextuality has a variety of interpretations which are typically associated with the names of their inventors, say Bohr, Bell, Kochen and Specker, and recently Dzhafarov. In fact, Bohr was the first who pointed to contextuality of quantum measurements as a part of formulation of his principle of complementarity. (Instead of "contextuality", he considered dependence on "experimental conditions.") Unfortunately, the contextuality counterpart of the complementarity principle was overshadowed by the issue of incompatibility of observables. And the interest for c…
The Copenhagen interpretation of quantum mechanics, which first took shape in Bohr's landmark 1928 paper on complementarity, remains an enigma. Although many physicists are skeptical about the necessity of Bohr's philosophical conclusions, his pragmatic message about the importance of the whole experimental arrangement is widely accepted. It is, however, generally also agreed that the Copenhagen interpretation has no direct consequences for the mathematical structure of quantum mechanics. Here I show that the application of Bohr's main concepts of complementarity to the subsystems of a closed …
Illustration of quantum complementarity using single photons interfering on a grating
最近由S. S. Afshar等人的理论被解释为违反了玻尔的互补原理，即干涉可见度和双光路干涉仪中的哪一路信息之间的互补原理。我们复制了这个实验，使用真正的单光子脉冲在一个双路波前分裂干涉仪中传播，该干涉仪是用菲涅耳双棱镜实现的，然后是一个具有可调透射狭缝的光栅。发现用可分辨性参数D表征的干涉可见度V和哪条路径信息的测量值服从互补关系V^2+D^2=<1。这一结果表明，实验可以完美地解释的量子力学的哥本哈根解释。
Bohr's complementarity principle has been challenged by quantum delayed-choice experiments wherein quantum systems are claimed to behave neither as wave nor as a particle, but in an intermediary way. However, this conclusion has been supported by retro-inference and with no direct link with the system quantum state. Here, we consider a framework that employs an operational criterion of physical reality to diagnosis the system ontology directly from the quantum state at each instant of time. We show that, in disparity with previous proposals, our setup ensures a formal link between the output v…
According to Bohr's principle of complementarity, a quanton can behave either as a wave or a particle, depending on the choice of the experimental setup. Some recent two-path interference experiments have devised methods where one can have a quantum superposition of the two choices, thus indicating that a quanton may be in a superposition of wave and particle nature. These experiments have been of interest from the point of view of Wheeler's delayed-choice experiment. However, it has also been claimed that this experiment can violate complementarity. Here we theoretically analyze a multipath i…
We compare different approaches to quantum ontology. In particular, we discuss an interpretation of quantum mechanics that we call objective quantum field theory (OQFT), which involves retrocausal fields. Here, objective implies the existence of fields independent of an observer, but not that the results of conjugate measurements are predetermined: the theory is contextual. The ideas and analyses of Einstein and Bohr through to more recent approaches to objective realism are discussed. We briefly describe measurement induced projections, the guided wave interpretation, many-universes, consiste…
By filtering out the philosophic component we can be said that the EPR-paper was directed against the straightforward interpretation of the Heisenberg's uncertainty principle or more generally the Bohr's complementarity principle. The latter expresses contextuality of quantum measurements: dependence of measurement's output on the complete experimental arrangement. However, Bell restructured the EPR-argument against complementarity to justify nonlocal theories with hidden variables of the Bohmian mechanics' type. Then this Bell's kind of nonlocality - {\it subquantum nonlocality} - was lifted …
We present a reformulation of Bohr's analysis of Einstein's thought experiment with the photon box, which hopefully settles some unclear issues. The box is weighed by two position measurements, the first immediately before the emission of the photon and the second after a quarter period of oscillation of the box, or alternatively after a half period. These times are precisely defined with respect to the moving clock installed in the box, but vary statistically when measured with a stationary clock outside the box, due to gravitational time dilation in accordance with Bohr's original idea. More…
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.
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）
