The Linear Ansatz, Priced: What Dirac Assumed, What the Assumption Returns, and the g = 2 It Pays Out

Census pricing (row CC-96) of the linear ansatz of Dirac's 'The Quantum Theory of the Electron,' Proc. R. Soc. A 117, 610-624 (1928), against a fixed bench (what is postulated, what is derived, what the postulates return numerically, what they cannot reach). The ansatz -- the relativistic energy written linear in momentum with matrix coefficients, E = c alpha.p + beta m c^2, constrained only by demanding its square return E^2 = p^2 c^2 + m^2 c^4 -- is postulated, not derived; the Klein-Gordon equation satisfies the same dispersion without it. Verified in the notebook (22 checks, exit 0) from the ansatz plus named CODATA constants (inputs, never spent as derived): the standard representation satisfies every anticommutation relation exactly; H^2 = (p^2 c^2 + m^2 c^4) I at three stated momenta; rest energy 510998.95 eV; spin as a component count, S_z = +/- hbar/2 each twice, returning as a theorem the two-valuedness Uhlenbeck and Goudsmit postulated in 1925 (CC-97, closure by replacement, credited to the 1928 text); and g = 2 at tree level, mu_B = e hbar/(2 m_e) = 9.2740100784e-24 J/T against the measured input |mu_e| = 9.2847647043e-24 J/T (ratio 1.00115965). Remainders at full size: the negative-energy branch stands uninterpreted inside the 1928 equation (its discharges belong to the 1930 hole theory, CC-44, and to field theory); the measured moment's 0.1160% excess over the tree return is the anomalous moment, QED's property, not claimed. EXTENSION. Vacuum catastrophe NOT SOLVED; quantum gravity NOT SOLVED.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-04
DOI
https://doi.org/10.5281/zenodo.23937753
Primary Topic
Quantum and Classical Electrodynamics
Type
preprint
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The Linear Ansatz, Priced: What Dirac Assumed, What the Assumption Returns, and the g = 2 It Pays Out

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Quantum and Classical Electrodynamics
preprint

The Linear Ansatz, Priced: What Dirac Assumed, What the Assumption Returns, and the g = 2 It Pays Out

William Alexander Aldred
preprint en

Abstract

Census pricing (row CC-96) of the linear ansatz of Dirac's 'The Quantum Theory of the Electron,' Proc. R. Soc. A 117, 610-624 (1928), against a fixed bench (what is postulated, what is derived, what the postulates return numerically, what they cannot reach). The ansatz -- the relativistic energy written linear in momentum with matrix coefficients, E = c alpha.p + beta m c^2, constrained only by demanding its square return E^2 = p^2 c^2 + m^2 c^4 -- is postulated, not derived; the Klein-Gordon equation satisfies the same dispersion without it. Verified in the notebook (22 checks, exit 0) from the ansatz plus named CODATA constants (inputs, never spent as derived): the standard representation satisfies every anticommutation relation exactly; H^2 = (p^2 c^2 + m^2 c^4) I at three stated momenta; rest energy 510998.95 eV; spin as a component count, S_z = +/- hbar/2 each twice, returning as a theorem the two-valuedness Uhlenbeck and Goudsmit postulated in 1925 (CC-97, closure by replacement, credited to the 1928 text); and g = 2 at tree level, mu_B = e hbar/(2 m_e) = 9.2740100784e-24 J/T against the measured input |mu_e| = 9.2847647043e-24 J/T (ratio 1.00115965). Remainders at full size: the negative-energy branch stands uninterpreted inside the 1928 equation (its discharges belong to the 1930 hole theory, CC-44, and to field theory); the measured moment's 0.1160% excess over the tree return is the anomalous moment, QED's property, not claimed. EXTENSION. Vacuum catastrophe NOT SOLVED; quantum gravity NOT SOLVED.

Zenodo (CERN European Organization for Nuclear Research)
Quantum and Classical Electrodynamics
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The Linear Ansatz, Priced: What Dirac Assumed, What the Assumption Returns, and the g = 2 It Pays Out — William Alexander Aldred · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS