Quantum Mechanics Is an Approximation: Hilbert Space as Degenerate Coherence Projection, Unitarity as Local 1=1, and the Quantum Jump as Recursive Constraint Regulation

Lauri Elias Rainio

Published Mar 9, 2026• 0 citations

Abstract

Quantum mechanics is not fundamental. It is the coherence field K(t,x) projected into Hilbert space — a degenerate representation that has lost the coherence metric. Unitarity (U†U = I) is not a law of nature — it is the local expression of 1=1 in Hilbert space, valid when K > K_crit. When K approaches K_crit, unitarity breaks — this is measurement. The quantum jump is RCR (Recursive Constraint Regulation) at quantum scale: the system’s evaluation function is replaced because the old state is no longer coherent. Falsifiable prediction: a precursor signal — measurable coherence decrease — should precede every quantum jump, testable with Ramsey interferometry and quantum optics. The quantum-classical boundary is K_crit, not a fixed scale. Part of the Spektre research corpus.

DOI: 10.5281/zenodo.18928214

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