Born Rule as a Dynamical Necessity: Phase-Density Formalism and Topological Quantization
Abstract
This paper presents a derivation of the Born rule from first principles using a phase-density formalism. We show that the probability density is necessarily the square of the wavefunction amplitude due to linearity, local conservation, and independence from absolute phase. The phase is naturally defined on a compact space S^1, leading to topological quantization and explaining the appearance of the quantum of action ħ. This approach unifies the origin of quantum probability and phase quantization from a deterministic, geometric perspective.
Fields of Study & Subjects
Quantum Mechanics and Applications
Noncommutative and Quantum Gravity Theories
Relativity and Gravitational Theory
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 10 February 2026
- Language
- EN
- Document type
- Preprint