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N-path quantum interference and hypergraphs

F.J. Duarte

Published Apr 21, 2025• 0 citations
Publisher

Abstract

It is elucidated that N-slit, or N-path, quantum interference utilizes the intrinsic nonlocality of the photon to illuminate simultaneously from the source the entire N-slit array thus allowing the characterization of the interference via the Dirac-Feynman interferometric principle. This simultaneous illumination of N-paths also applies to the Feynman path integral formulation of quantum mechanics. This quantum mechanism of simultaneous and whole illumination of N-slits, or N-paths, is quite different to the sequential illumination of N-paths via the hypergraph methodology where the N is achieved via the classical diagrammatical binary sequence 1, 2, 4, 8, 16, 32, … .

DOI
10.1364/opticaopen.28378301.v3

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It is elucidated that N-slit, or N-path, quantum interference utilizes the intrinsic nonlocality of the photon to illuminate simultaneously from the source the entire N-slit array thus allowing the characterization of the interference via the Dirac-Feynman interferometric principle. This simultaneous illumination of N-paths also applies to the Feynman path integral formulation of quantum mechanics. This quantum mechanism of simultaneous and whole illumination of N-slits, or N-paths, is quite different to the sequential illumination of N-paths via the hypergraph methodology where the N is achieved via the classical diagrammatical binary sequence 1, 2, 4, 8, 16, 32, … .
It is elucidated that N-slit, or N-path, quantum interference utilizes the intrinsic nonlocality of the photon to illuminate simultaneously from the source the entire N-slit array thus allowing the characterization of the interference via the Dirac-Feynman interferometric principle. This simultaneous illumination of N-paths also applies to the Feynman path integral formulation of quantum mechanics. This quantum mechanism of simultaneous and whole illumination of N-slits, or N-paths, is quite different to the sequential illumination of N-paths via the hypergraph methodology where the N is achieved via the classical diagrammatical binary sequence 1, 2, 4, 8, 16, 32, … .
It is elucidated that N-slit, or N-path, quantum interference utilizes the intrinsic nonlocality of the photon to illuminate simultaneously from the source the entire N-slit array thus allowing the characterization of the interference via the Dirac-Feynman interferometric principle. This simultaneous illumination of N-paths also applies to the Feynman path integral formulation of quantum mechanics. This quantum mechanism of simultaneous and whole illumination of N-slits, or N-paths, is quite different to the sequential illumination of N-paths via the hypergraph methodology where the N is achieved via the classical diagrammatical binary sequence 1, 2, 4, 8, 16, 32,…2^r.
It is elucidated that N-slit, or N-path, quantum interference utilizes the intrinsic nonlocality of the photon to illuminate simultaneously from the source the entire N-slit array thus allowing the characterization of the interference via the Dirac-Feynman interferometric principle. This simultaneous illumination of N-paths also applies to the Feynman path integral formulation of quantum mechanics. This quantum mechanism of simultaneous and whole illumination of N-slits, or N-paths, is quite different to the sequential illumination of N-paths via the hypergraph methodology where the N is achieved via the classical diagrammatical binary sequence 1, 2, 4, 8, 16, 32, … .
Quantum interference, which is a physical phenomenon, and probability amplitudes à la Dirac are miraculously like synonyms. Indeed, the way probability amplitudes are written down on paper is very much as a single photon, or an ensemble of indistinguishable photons, propagates from one plane to the next. And then, if at one of the planes an N -slit array alternative is offered then the probability amplitude notation à la Dirac cleverly describes the N -path alternative via a mathematical summation. Here we should emphasize that since the photon is a nonlocal quantum entity, all the microscopic slits in the N -slit array, or transmission diffraction grating, are illuminated simultaneously.