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1 March 1994 Fuzziness in quantum mechanics
Alex Granik
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Proceedings Volume 10277, Adaptive Computing: Mathematics, Electronics, and Optics: A Critical Review; 102770D (1994) https://doi.org/10.1117/12.171191
Event: SPIE's International Symposium on Optical Engineering and Photonics in Aerospace Sensing, 1994, Orlando, FL, United States
Abstract
The fussy "roots" of quantum mechanics are traced directly to the Hamilton-Jacobi equation of classical mechanics. It is shown that the Shroedinger equation can be derived from the Hamilton-Jacobi equation. A deep underlying unity of both equations lies in the fact that a unique trajectory of a classical particle is "selected" out of many-continuum paths according to the Principle of least action. We can say that a classical particle has a membership in every path of the above set, which collapses to the winning single trajectory of a real motion.

At the same time it can also be said that a quantum mechanical "particle" has different degrees of membership in a set of many-continuum paths where all of them contribute to the dynamics of the quantum mechanical particle.

This allows one to provide an interpretation of the wave function as a parameter describing deterministic entity endowed by a fuzzy character. As a logical consequence of such an interpretation the complimentarity principle and the wave-particle duality concept can be abandoned in favor of a fuzzy deterministic microobject. This idea leads to a possibility of a quantum mechanical computer based on the fuzzy logic.
© (1994) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
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Alex Granik "Fuzziness in quantum mechanics", Proc. SPIE 10277, Adaptive Computing: Mathematics, Electronics, and Optics: A Critical Review, 102770D (1 March 1994); https://doi.org/10.1117/12.171191
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