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Physics in the space of quantum states

Kryukov, Alexey (2000) Physics in the space of quantum states. [Preprint]

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Abstract

It has been recently shown that Newtonian dynamics is the Schrodinger dynamics of the system whose state is constrained to a submanifold in the space of states of the system. Thus defined, the submanifold can be identified with the classical phase space of the system. The classical space is then also embedded into the space of states in a physically meaningful way. The resulting unified geometric framework establishes a new connection between classical and quantum physics. The framework is rigid in the sense that the Schrodinger dynamics is a unique extension of the Newtonian one from the classical phase space submanifold to the space of states. Quantum observables in the framework are identified with vector fields on the space of states. The commutators of canonical conjugate observables are expressed through the curvature of the sphere of normalized states. The velocity and acceleration of a particle in Newtonian dynamics are components of the velocity of state under the corresponding Schrodinger evolution. The metric properties of the embedding of the classical space into the space of states result in a relationship between the normal distribution of the position of a particle and the Born rule for the probability of transition of quantum states.
In this paper the implications of the obtained mathematical results to the process of measurement in quantum physics are investigated.
It is argued that interaction with the environment constrains the state of a macroscopic body to the classical space. The notion of collapse of a quantum state is 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:
CreatorsEmailORCID
Kryukov, Alexeykryukov@uwm.edu
Additional Information: Based on the mathematics part, published in J. Math. Phys., 61, 082101
Keywords: measurement problem; wave function collapse; entangled states; Hilbert space; projective Hilbert space; Fubini-Study metric; differential geometry; functional analysis
Subjects: Specific Sciences > Physics
Specific Sciences > Physics > Quantum Mechanics
Depositing User: Alexey Kryukov
Date Deposited: 08 Aug 2020 02:22
Last Modified: 08 Aug 2020 02:22
Item ID: 17704
Subjects: Specific Sciences > Physics
Specific Sciences > Physics > Quantum Mechanics
Date: 6 August 2000
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/17704

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