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Mapana Journal of Sciences

Classical Limit in the Double-Slit Experiment for Quantum Particles

K. S. Mallesh, B. A. Kagali

Published Mar 19, 2024• 0 citations
Publisher

Abstract

It is well known that the double-slit experiment, under proper conditions, reveals the wave nature of both light and quantum particles like electrons. The wave nature of quantum particles is demonstrated by assuming plane or spherical de Broglie waves to be associated with quantum particles. In this article we deduce the wave nature of material particles starting with proper quantum mechanical amplitudes for propagation as arrived at in the path integral formulation. The classical particle limit of the interference pattern follows right away along the same lines as the corpuscular limit follows from wave optics.

DOI
10.12723/mjs.67.5

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It is well known that the double-slit experiment, under proper conditions, reveals the wave nature of both light and quantum particles like electrons. The wave nature of quantum particles is demonstrated by assuming plane or spherical de Broglie waves to be associated with quantum particles. In this article we deduce the wave nature of material particles starting with proper quantum mechanical amplitudes for propagation as arrived at in the path integral formulation. The classical particle limit of the interference pattern follows right away along the same lines as the corpuscular limit follows from wave optics.
Interference and diffraction phenomena are the basic properties shown by waves. De-Broglie concept of matter waves brought in the extended version of wave properties of material particles. Wave properties of quantum particles are important to understand various phenomena in physics. Matter waves are a core part of quantum theory. Now wave-particle duality is exploited for many applications such as imaging microscopic particles using electron microscopes etc. Here we deduce the interference and diffraction of quantum particles on the basis of the propagation amplitude according to the path integral formulation of quantum mechanics. The intensity distribution due to interference and diffraction of quantum particles are compared with those obtained from the formal methods. The results agree with the traditional approach assuming a deBroglie wave associated with particles.
The classical interpretation of Young’s double slit experiment is that, before and after passing through the diaphragm of the double slit, the light behaves as waves. Feynman called the double slit experiment “the only mystery [of quantum mechanics]. We have shown for the first time in the classical wave experiments: (1) Particle patterns (non-interference patterns) indicating the particle nature of light are near the diaphragm, and Interference patterns are near the screen; (2) Particle patterns evolve to Transition patterns (non-interference patterns) and finally, evolve to Interference patterns. We proposed Postulates of lens for utilizing lens in wave experiments. In this article, we experimentally suggest that Particle patterns, Transition patterns and Interference patterns simultaneously emerging on the screen in the double slit experiments show that the light beams are photons. The photon chamber shows that the photons distribute as waves in the wave experiments. We suggest that these phenomena and the physical mechanism of them are new mystery.
The double slit interference experiment has been famously described by Richard Feynman as containing the "only mystery of quantum mechanics". The history of quantum mechanics is intimately linked with the discovery of the dual nature of matter and radiation. While the double slit experiment for light is easily undertsood in terms of its wave nature, the very same experiment for particles like the electron is somewhat more difficult to comprehend. By the 1920s it was firmly established that electrons have a wave nature. However, for a very long time, most discussions pertaining to interference experiments for particles were merely gedanken experiments. It took almost six decades after the establishment of its wave nature to carry out a 'double slit interference' experiment for electrons. This set the stage for interference experiments with larger particles. In the last decade there has been spectacular progress in matter-wave interefernce experiments. Today, molecules with over a hundred atoms can be made to interfere. In the following we discuss some of these exciting developments which probe new regimes of Nature, bringing us closer to the heart of quantum mechanics and its hidden mysteries.
Electron double-slit experiments, the essence of quantum mechanical “wave/particle duality”, have been extensively and continuously studied because their unrealistic interpretations have attracted many researchers. Here, we discuss recent sophisticated V-shaped double-slit experiments to elucidate electron-path information, i.e., which slit electrons pass through, which path they pursue, and where they arrive and interfere on the image plane. In a transmission electron microscope, an optically zero-propagation distance condition was realized, where the double-slit position was imaged just on the detector plane. Interference fringes composed of dot images were controlled by using two electron biprisms. Using a V-shaped double slit, we confirmed that it is possible to observe interference fringes only when the path information of individual electrons is not available. Furthermore, we studied how the interference fringes would shift their detected positions when electron wave phases were modulated before illumination to the double slit. Phase shifts were generated by tilting electron beams. We confirmed that each single electron as a wave changed its phase even when it traveled alone inside the microscope.
We report observations of Cross-Double-Slit Experiment and Which-Path-Cross-Double-Slit experiment. Cross-Double-Slit apparatus contains two double-slit, where first double-slit is perpendicular to second double-slit. The first double-slit and the second double-slit generate not only their own interference pattern perpendicular to each other, but also generate “Cross-interference-patterns”. When we do which-way experiment with one of two double-slit, say first double-slit, then its interference pattern disappeared, i.e., photons behave as particles; but the second double-slit’s interference pattern and the cross-interference-pattern still exist; which implies an significant phenomenon that in the same experiment, photons behave as both wave and particle, which is first time caught on film. Thus we suggest to re-study wave-particle duality, which is the basic mystery of quantum mechanics. We postulate that the particle nature of photons is intrinsic; while the wave-like of photons is manifest-behavior.
Young’s double slit experiments revived the wave theory of light. The standard interpretation is that the light behaves as waves before and after passing through the double slit, and the superposition of waves produces the interference pattern. Feynman called the double slit experiment the only mystery in quantum mechanics. In this article, we experimentally show the novel universal phenomena: (1) the light is particles, but waves: within macro-distance from a diaphragm, the light rays produce non-interference patterns; while near the screen, the photons produce orthogonal interference patterns; (2) the non-interference patterns evolve to the orthogonal interference patterns gradually in the same experiment; (3) the evolution of the patterns cannot be interpreted by either classic optics or the quantum optics; (4) the non-interference patterns and the orthogonal interference patterns can show on the screen simultaneously; (5) The convex lens stops the further evolution. The experiments: (1) challenge the classical optics and quantum optics; (2) violate both Bohr’s complementarity principle and wave particle duality; (3) provide profound phenomena for developing optics and for studying the nature of light; (4) suggest that a complete theory should be able to consistently interpret all phenomena, including the non-interference pattern, the interference pattern, and the evolution from the non-interference to the interference pattern in the same wave experiment.