2021/07/18 by Ariel Caticha, Caticha, Ariel · 2 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2107.08502
openalex publication_date 2021/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The mathematical formalism of Quantum Mechanics is derived or "reconstructed" from more basic considerations of probability theory and information geometry. The starting point is the recognition that probabilities are central to QM: the formalism of QM is derived as a particular kind of flow on a finite dimensional statistical manifold -- a simplex. The cotangent bundle associated to the simplex has a natural symplectic structure and it inherits its own natural metric structure from the information geometry of the underlying simplex. We seek flows that preserve (in the sense of vanishing Lie derivatives) both the symplectic structure (a Hamilton flow) and the metric structure (a Killing flow). The result is a formalism in which the Fubini-Study metric, the linearity of the Schrödinger equation, the emergence of a complex numbers, Hilbert spaces, and the Born rule, are derived rather than postulated.