
TL;DR
This paper presents a geometric approach to quantum indeterminacy using convex geometry and symplectic topology, deriving uncertainty principles as fundamental phase space constraints.
Contribution
It introduces a novel geometric framework that explains quantum uncertainty without relying on statistical measures, emphasizing symplectic invariants and convex bodies.
Findings
Standard uncertainty inequalities emerge from geometric relations
Robertson-Schrodinger inequalities are natural consequences of the framework
Quantum indeterminacy is shown as a structural property of phase space
Abstract
We introduce a geometric formulation of quantum indeterminacy from which the standard uncertainty inequalities emerge as necessary consequences. Our approach is based on convex geometry in phase space and on methods from symplectic topology, and does not rely on statistical descriptors such as variances or covariances. Instead, we associate to empirical position and momentum data with convex bodies whose mutual relations encode the fundamental constraints of quantum mechanics. The central tools are h-polar duality and symplectic capacities, which provide intrinsic, coordinate-free bounds on admissible phase-space configurations. Within this framework, the Robertson-Schrodinger inequalities arise naturally as manifestations of deeper geometric and topological principles. This perspective suggests that quantum indeterminacy is not primarily a statistical phenomenon, but rather a…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
