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Physics Reports

Symplectic capacities and the geometry of uncertainty: The irruption of symplectic topology in classical and quantum mechanics

Maurice A. de Gosson, Franz Luef

Published Aug 9, 2009• 92 citations
Publisher
DOI
10.1016/j.physrep.2009.08.001

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Derivation I: CSF Derivation of ℏ: Capacity Quantum of Foliation Updates

Yuri Alcocer

We derive Planck's constant ℏ not as a fundamental input, but as the minimal symplectic capacity required for a nontrivial, verified foliation update preserving full-rank geometry. The Heisenberg uncertainty principle emerges as a corollary of this geometric resolution limit, not as an axiom of quantum mechanics. Key Result: h≔ inf {c(CΔ) : Δ is a nontrivial verified foliation update} where is the symplectic capacity of the minimal elementary update cell, quantized by topological consistency of update phases.

•Feb 14, 2026•0 citations
We derive Planck's constant ℏ not as a fundamental input, but as the minimal symplectic capacity required for a nontrivial, verified foliation update preserving full-rank geometry. The Heisenberg uncertainty principle emerges as a corollary of this geometric resolution limit, not as an axiom of quantum mechanics. Key Result: h≔ inf {c(CΔ) : Δ is a nontrivial verified foliation update} where is the symplectic capacity of the minimal elementary update cell, quantized by topological consistency of update phases.