2026/01/29 by Jonathon Sendall · 1 voice · 1 citation
Physics and Astronomy · #physics.hist-ph #quant-ph
Quantum mechanics provides extraordinarily accurate probabilistic predictions, yet the framework remains silent on what distinguishes quantum systems from definite measurement outcomes. This paper develops a measurement-theoretic framework for projective gating. The central object is the β-bound, an inequality that controls how much probability assignments can drift when gating and measurement fail to commute. For a density operator ρ, projector F, and effect E, with gate-passage probability s = \rm Tr(ρF) and commutator norm ε = ‖[F, E]‖, the symmetric partial-gating drift satisfies |ΔpF(E)| ≤ 2 √((1 - s)/s) ⋅ ε. The constant 2 is sharp. We introduce two diagnostic quantities: the coherence witness W(ρ, F) = ‖F ρ(I - F)‖1, measuring cross-boundary coherence, and the record fidelity gap ΔT(ρF, R), measuring expectation-value change under symmetrisation. Three experimental vignettes demonstrate falsifiability: Hong--Ou--Mandel interferometry, atomic energy-basis dephasing, and decoherence-induced classicality. The framework is operational and interpretation-neutral, compatible with Everettian, Bohmian, QBist, and collapse approaches. It provides quantitative structure that any interpretation must accommodate, along with a template for experimental tests.