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The classical and the quantum

Kryukov, Alexey (2019) The classical and the quantum. [Preprint]

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Abstract

Newtonian and Schrodinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes beyond the results provided by the Ehrenfest theorem. The Newtonian dynamics was shown to be the Schrodinger dynamics of states constrained to a submanifold of the space of states, identified with the classical phase space of the system. Quantum observables are identified with vector fields on the space of states. The commutators of observables are expressed through the curvature of the space. The resulting embedding of the Newtonian and Schrodinger dynamics into a unified geometric framework is rigid in the sense that the Schrodinger dynamics is a unique extension of the Newtonian one. Furthermore, under the embedding, the normal distribution of measurement results associated with a classical measurement implies the Born rule for the probability of transition of quantum states. In this paper, the implications of the obtained theory to the process of measurement in quantum theory are analyzed. The double-slit, EPR and Schrodinger cat type experiments are reviewed anew. It is shown that, despite reproducing the usual results of quantum theory, the framework is not simply a reformulation of the theory. New experiments to discover the predicted effects are proposed.


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Item Type: Preprint
Creators:
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Kryukov, Alexey
Additional Information: Typos in the abstract are fixed
Keywords: measurement problem, Hilbert space, Ehrenfest theorem, EPR
Subjects: Specific Sciences > Physics
Specific Sciences > Physics > Quantum Mechanics
Depositing User: Alexey Kryukov
Date Deposited: 21 Nov 2019 19:04
Last Modified: 21 Nov 2019 19:04
Item ID: 16646
Subjects: Specific Sciences > Physics
Specific Sciences > Physics > Quantum Mechanics
Date: 14 November 2019
URI: http://philsci-archive.pitt.edu/id/eprint/16646

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