A Geometric Substructure for Quantum Dynamics

• URL: http://arxiv.org/abs/2411.08230v1
• Date: Tue, 12 Nov 2024 22:51:16 GMT
• Title: A Geometric Substructure for Quantum Dynamics
• Authors: Anthony John Bracken,
• Abstract summary: Theory of a closed quantum system is extended with the identification of an underlying substructure. A possible generalization to a Riemannian substructure is speculated upon, suggesting an unexpected interaction with the background gravitational field.
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• Abstract: The description of a closed quantum system is extended with the identification of an underlying substructure in which an expanded formulation of dynamics in the Heisenberg picture is given. Between measurements a ``state point" moves in an underlying multi-dimensional complex, projective space with constant velocity determined by the quantum state vector. Following a measurement, the point changes direction and moves with new constant velocity along one of several possible new orthogonal paths, with probabilities determined by Born's Rule. A possible generalization to a Riemannian substructure is speculated upon, suggesting an unexpected interaction with the background gravitational field.

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