Sakharov (1967): The Conditions Without the Number

Sakharov stated three necessary conditions for baryogenesis. Baryon-number violation. C and CP violation. Departure from thermal equilibrium. The census record states the count plain: the 1967 paper contains no mechanism that computes the asymmetry. I priced that count. In a labelled product toy, the three conditions are three "0" statements. All 15,625 triples on a three-factor grid pass them. Only 400 triples, 2.560%, land within ±0.5 dex of the observed η_B ≈ 6 × 10⁻¹⁰. The census statement on the Standard Model prices as arithmetic: it satisfies all three conditions in principle and fails the magnitude by ~8 orders, an implied scale of 6 × 10⁻¹⁸ against the observed 6 × 10⁻¹⁰. Deficit: 3 necessary conditions, 0 quantitative mechanisms, 0 equations outputting η_B. Verdict: a reason was found, and the question remains open (not solved). This paper does not address the vacuum catastrophe. That problem remains unsolved: no derivation in this program has produced the observed vacuum energy.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-01
DOI
https://doi.org/10.5281/zenodo.23889582
Primary Topic
Particle physics theoretical and experimental studies
Type
preprint
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Sakharov (1967): The Conditions Without the Number

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
preprint

Sakharov (1967): The Conditions Without the Number

William Alexander Aldred
preprint en

Abstract

Sakharov stated three necessary conditions for baryogenesis. Baryon-number violation. C and CP violation. Departure from thermal equilibrium. The census record states the count plain: the 1967 paper contains no mechanism that computes the asymmetry. I priced that count. In a labelled product toy, the three conditions are three "0" statements. All 15,625 triples on a three-factor grid pass them. Only 400 triples, 2.560%, land within ±0.5 dex of the observed η_B ≈ 6 × 10⁻¹⁰. The census statement on the Standard Model prices as arithmetic: it satisfies all three conditions in principle and fails the magnitude by ~8 orders, an implied scale of 6 × 10⁻¹⁸ against the observed 6 × 10⁻¹⁰. Deficit: 3 necessary conditions, 0 quantitative mechanisms, 0 equations outputting η_B. Verdict: a reason was found, and the question remains open (not solved). This paper does not address the vacuum catastrophe. That problem remains unsolved: no derivation in this program has produced the observed vacuum energy.

Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
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