A Geometric Substructure for Quantum Dynamics

TL;DR

This paper introduces a geometric substructure in quantum dynamics that models state evolution as movement in a complex projective space, offering a new perspective on quantum measurements and potential links to gravity.

Contribution

It proposes a novel geometric framework for quantum dynamics that incorporates a hidden substructure, extending the Heisenberg picture and connecting to gravitational effects.

Findings

Quantum state evolution modeled as movement in projective space

Measurement-induced changes in state trajectory with probabilistic paths

Potential interaction between quantum substructure and gravity

Abstract

The description of a closed quantum system is extended with the identification of an underlying substructure enabling an expanded formulation of dynamics in the Heisenberg picture. 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 the Born Interpretation of the state vector. From this previously hidden substructure a new picture of quantum dynamics and quantum measurements emerges without violating existing no-gotheorems regarding hidden variables. A natural generalisation to a Riemannian substructure is proposed, determined by the entropy of the background environment. This leads to a suggestedinteraction between the substructure of quantum dynamics and the background gravitational field.