The Distribution That Goes Negative: Wigner's Phase-Space Function, Priced
Year: 2026
Type: preprint
Abstract: In 1932 Eugene Wigner rewrote the quantum state as a function W(x,p) on classical phase space that returns the exact position and momentum marginals, and founded the quantum-correction programme for thermodynamic equilibrium. I credit that paper at full strength: the phase-space formulation of quantum mechanics is exact, its marginals are theorems — re-verified on my own bench to grid grade — and Moyal later recognised the function as the generating object of the full phase-space formalism. Nothing in this paper falsifies the construction or its marginals. What I evaluate is the statistical interpretation used on the object. The function takes negative values — it fails the defining property of a probability density — and no step in 1932 derives why an object failing that property may carry the statistical interpretation the paper puts on it; Wigner himself conceded the function cannot be really interpreted as the simultaneous probability for coordinates and momenta, and asked that this must not hinder its use as an auxiliary function. The negativity is accepted as the cost of the marginals, and the acceptance is the postulate. My bench evaluates that acceptance on declared inputs only. The Gaussian ground state contributes nothing: negative mass 0.000000, total variation 1.000000. The first excited state carries W(0,0) = −0.318310 and a negative mass of 0.213061 exactly (2e^(−1/2) − 1; 0.213062 on the declared grid), with total variation 1.426123. Even cat states carry negative mass 0.021753 at separation 2, 0.223787 at separation 4 and 0.300094 at separation 6 — growing with the interference the state carries. Counted plainly: 1 accepted quasi-probability against 0 derivations in 1932. Grade for this census entry, printed at full size: **REASON FOUND / STILL TURNING** — PREMISE-ONLY, explicitly not a kill and not a falsification. The program headline stands unmoved: **vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.**
Author: Aldred, William Alexander
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225423277