A geometric extension of quantum mechanics based on an energy-time ambiguity in the Schrödinger picture
Abstract
Abstract In this letter, we show that, within the Schrödinger picture, quantum mechanics exhibits a fundamental ambiguity in the roles of energy and time, opening the possibility that neither should be regarded as ontologically primitive. Motivated by this ambiguity, we propose a geometric reformulation in which the total curvature of a surface bulk generates quantum evolution. We show that all physically detectable quantum transformations are encoded in the boundary geometry, so that the effective structure acquires a holographic character. We further consider the model from a relational perspective, examine special cases, and discuss qualitative and quantitative connections with the role of geometry in general relativity.
Fields of Study & Subjects
Algebraic and Geometric Analysis
Quantum Mechanics and Applications
Noncommutative and Quantum Gravity Theories
Publication details
- Journal / source
- Europhysics Letters (EPL)
- Publisher
- IOP Publishing
- Volume
- 154
- Issue
- 3
- Pages
- 38001–38001
- Publication date
- 7 April 2026