The correspondence principle, the wave-corpuscle duality, the complementarity principle and the slit experiment

Karl Raimund Popper

Thuan Vo Van, Vinh Vu Duc, Hưng Nguyễn Thành +1 more

Abstract We perform spectral analysis based on a suitable theoretical correlation between V-wave visibility and D-particle distinguishability following the complemen-tarity principle to verify wave-particle duality in the asymmetrical double-slit experiments. The selective interference spectra obtained in the experiments ensure the single-photon approximation in the Fraunhofer far-field condition. The results show that the theoretical interpretation following wave-particle complementarity may not be consistent with the experimental data, especially at the first main minima of the optical diffraction distributions. A dilemma would arise when one tries to revise the theoretical explanations for preserving the complementarity principle.

Évandro Agazzi

Kazufumi Sakai

The principle of complementarity is the foundation of quantum mechanics; its correctness has been verified by several studies. At present, the Englert-Greenberger duality relation is used for quantitative evaluations. We fabricated a new double slit experimental apparatus capable of simultaneously measuring the visibility and path-distinguishability, and measured the wave and particle properties. We thus obtained results in disagreement with the principle of complementarity.

Peter Bokulich

M. C. Boscá, C María

Updating the wave-particle duality Maria C. Bosca e-mail: bosca@ugr.es Departamento de Fisica Atomica, Molecular y Nuclear Universidad de Granada E-18071. Granada Spain The wave-particle-duality, the fundamental component of the new quantum formalism in Bohr’s opinion, must be reformulated by incorporating the results of some experiments accomplished in the last decades of twentieth century. The Bohr´s complementarity principle stated the mutual exclusiveness and joint full completeness of the two (classical) descriptions of quantum systems; after Einstein-Podolsky-Rosen’paper, the wave-particle duality, or wave-particle complementarity, could be expressed by stating that it is impossible to build up an experimental arrangement in which we observe at the same time both corpuscular and wave aspects. In a two-slit experiment, they would correspond, respectively, to the which-way knowledge and the observation of interference pattern. Bohr showed this mutual exclusivity in numerous examples , and linked it to the unavoidable disturbance inherent in any measurement event. In quantum mechanical formalism, the complementarity principle has a clear mathematical expression: two observables are complementary if precise knowledge of one of them implies that all possible outcomes of the other are equally probable; their extension to classical concepts (as wave and particle) is not concerned. In 1991 Scully et al published a variant of the two-slit experiment that incorporates two micromasers cavities and a laser beam to provide which-path information without net momentum transferred during the interaction ; the impossibility of know which slit an atom went through and still observe the interference fringes is preserved by the establishing of quantum correlations between the measuring apparatus and the system being observed. They claimed that complementarity, of which wave-particle duality would be to them a manifestation, is more fundamental than the uncertainty principle . In 1996 B-G. Englert, following an approach originally due to Wooters and Zurek , derived , without making use of Heisenberg’s uncertainty relation, an inequality that quantifies the mutual compatibility relation between fringe visibility and which-way information. The inequality, that they denominated as “interferometric duality”, has the expression D^2 + V^2 ≤ 1, where D stands for the distinguishability of the ways and V for the fringe visibility; both of them are mathematical expressions that can be measured to check experimentally the inequality . Today, it is clear that intermediate particle-wave behaviours exist and, in addition to that, there are single experiments in which both classical wave-like and particle-like behaviours are showed total and simultaneously on an individual system. For instance, in the Bose’s double-prism experiment , tunnelling and perfect anticoincidence were observed in single photon states. Consequently, the meaning of the wave-particle duality must incorporate the simultaneous use of the two classical descriptions in the interpretation of experiments, loosing their original mutual exclusivity , which is incorporated as an extreme case in the new interferometric duality, a continuous quantum concept . The wave-particle duality, therefore, must be formulated as an interpretative addition to quantum mechanics, to which is possible to renounce if any pretension of visualize quantum phenomena in terms of classical concepts and intuitions is abandoned.