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arXiv:0901.2816

Background Independent Quantum Mechanics, Classical Geometric Forms and Geometric Quantum Mechanics-II

Aalok Pandya

Published Jan 19, 2009• 0 citations
arXivHTMLPDF

Abstract

The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of probability in Quantum Mechanics and its interpretations. We give yet another interpretation to the notion of Faraday lines and loops as the locus of probability flow. Also, the possibilities of visualization of spectra of area operators by means of classical geometric forms and conventional Quantum Mechanics are explored.

DOI
10.48550/arxiv.0901.2816

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We present a probabilistic-geometric formulation of quantum motion that establishes a direct geometric correspondence between statistical uncertainty and relativistic curvature. Quantum states are represented as probability distributions on a statistical manifold equipped with the Fisher–Rao metric, whose geodesic flow reproduces the dynamical evolution of quantum motion in probabilistic form. Embedding this manifold into a Lorentzian spacetime yields a unified metric structure in which stochastic fluctuations generate microscopic deformations of spacetime geometry. This framework enables the visualization and prediction of quantum motion as probabilistic geodesics, and provides a foundation for connecting information geometry, stochastic mechanics, and general relativity within a single coherent formulation.
Quantum Geometry explores the intersection of probability theory and geometric analysis, aiming to establish a framework where quantum entanglement and geometric structure are intertwined. This paper investigates the potential of leveraging quantum geometry to provide a theoretical basis for quantum computing and quantum information. We propose a novel approach by framing quantum entanglement as geometric "lines" or "shapes," employing geometric operations to describe the evolution of quantum states. This investigation introduces a new perspective on probability theory and geometry, potentially offering a more intuitive and powerful way to understand quantum systems. The paper outlines the core concepts, mechanisms, and preliminary results of this research, highlighting its significance for advancing both quantum information theory and the fundamental understanding of quantum mechanics.