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Welcher Weg? A trajectory representation of a quantum Young's diffraction experiment

Floyd, E R

Published May 14, 2006• 7 citations
OpenAlex

Abstract

The double slit problem is idealized by simplifying each slit by a point source. A composite reduced action for the two correlated point sources is developed. Contours of the reduced action and trajectories are developed in the region near the two point sources. The trajectory through any point in configuration space also passes simultaneously through both point sources.

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The double slit problem is idealized by simplifying each slit by a point source. A composite reduced action for the two correlated point sources is developed. Contours of the reduced action and trajectories are developed in the region near the two point sources. The trajectory through any point in configuration space also passes simultaneously through both point sources.
Young’s double slit experiments, which represent the mystery of quantum mechanics (Feynman), have been described by optics, electromagnetic wave theory, quantum wave theory and Bohm’s trajectory theory. The double slit has the varieties of the applications. To test the description theories, we perform the comprehensive double slit experiments, which show that (1) before passing through the double slit/cross-double slit and before landing on the screen, the laser light behaves as particles, not as waves; (2) the experiments challenge the computer simulation of the trajectory theory at near field, however support the trajectory theory at far field. Those novel phenomena provide the comprehensive information for further theoretical development and applications.
Young’s double slit experiments, which represent the mystery of quantum mechanics (Feynman), have been described by optics, electromagnetic wave theory, quantum wave theory and Bohm’s trajectory theory. The double slit has the varieties of the applications. To test the description theories, we perform the comprehensive double slit experiments, which show that (1) before passing through the double slit/cross-double slit and before landing on the screen, the laser light behaves as particles, not as waves; (2) the experiments challenge the computer simulation of the trajectory theory at near field, however support the trajectory theory at far field. Those novel phenomena provide the comprehensive information for further theoretical development and applications.
The Young’s single- and double-slit experiments are explained using six-component quantum and one-component quasi-classical photon wave functions in the coordinate representation, which are modeled by different mechanisms of photon diffraction on slits or simultaneous emission of two photons by (two) independent sources. This explanation is compared with the well-known statement about the interference of a particle with itself when passing through both slits simultaneously in the Young’s experiment on the basis of the postulated Feynman amplitudes. It is argued that these amplitudes cannot be wave functions, in the literal sense, describing some states of quantum particles. In all cases, under the assumption of the linear polarization of photons, a pronounced interference pattern has been obtained, which suggests that the coordinate wave function of a photon can explain the phenomena of the one- and two-photon interference. This conclusion, in turn, makes it possible to associate the coordinate wave function of a photon (two photons, in the entangled state) measured in some recent experiments with the quasi-classical wave function of a photon (two photons), although it does not take into account its (their) polarization properties.
The interference pattern produced by a quantum particle in Young's double-slit setup is attributed to the particle's wave function having gone through both slits. In the path integral formulation, this interference involves a superposition of paths, going through either slit, linking the source to the detection point. We show how these paths superpositions can in principle be observed by implementing a series of minimally perturbing weak measurements between the slits and the detection plane. We further propose a simplified protocol in order to observe these ``weak trajectories'' with single photons.
Young's double slit experiments representing the mystery of quantum mechanics have been described by wave theories and Bohm's trajectory theory. By placing shields/blockers near the detector /screen, the comprehensive double slit/cross-doble slit experiments show that the fringes are created independently and partially, which violates the wave description. In this article we show that by placing the shields contacting the slide of the double slit, the comprehensive experiments show: (1) the existence of trajectories/photons immediately next to the double slit; and (2) the trajectories cross, which violate the prediction of the computer simulation of Bohm's trajectory theory. The comprehensive double slit/cross-double slit experiments violate both wave theory and trajectory theory. The comprehensive double slit/cross-double slit experiments provide the comprehensive phenomena/data for developing theoretical model to study the mystery of double slit, complementarity principle, wave-particle duality, wave theory and trajectory theories.