The Unmeasured Ground: Why Quantum Mechanics Cannot Explain What It Measures

Matt Prager

Published Apr 27, 2026• 0 citations

Abstract

Quantum physics has a measurement problem, and it’s not the one the field usually means: it’s that physics has built a precise theory of measurement outcomes without a theory of what measurement structurally is. The Galley-Kent exchange makes this gap unusually visible. Galley, Masanes, and Müller argued that quantum measurement postulates follow necessarily from structural postulates plus the possibility of state estimation. Kent refuted this, constructing alternative measurement postulates consistent with those assumptions. We argue that both positions operate one level above the question that would resolve their debate: what is the minimum structure that makes any measurement coherent in the first place? We show that this floor — two faces, one non-directed comparator, and the invariant sameness that makes their difference determinate — forces complex Hilbert space as the unique minimal field consistent with its constraints, and forces the Born rule as the unique probability assignment that closes both faces simultaneously. Galley et al. are correct that measurement postulates are necessary, but the proof does not live inside quantum mechanics. Kent's alternatives are formally consistent but do not instantiate coherent measurement: they either abandon ratio structure or treat measurement as directed rather than comparative. The proof of necessity lives below quantum mechanics, not inside it.

DOI: 10.5281/zenodo.19818300

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