The Chosen Tensor, Priced: Einstein's 1915 Field Equation, Its Matched Coupling, and the 43 Arcseconds It Returns

Census pricing (row CC-100) of the field-equation step of Einstein's 'Die Feldgleichungen der Gravitation,' Sitzungsber. Preuss. Akad. Wiss. (1915) 844-847, against a fixed bench (what is postulated, what is derived, what the postulates return numerically, what they cannot reach). The step is two-layered: the Einstein tensor is CHOSEN under stated demands (covariance, second order, divergence-free) with no uniqueness theorem in existence until Lovelock (1971) -- Einstein's own 1913 Entwurf tensor is the live counterfactual, returning half the deflection and no Mercury anomaly -- and the coupling is MATCHED, not derived: kappa = 8 pi G / c^4 imports the measured G of the theory being replaced. Computed in the notebook (4 checks, exit 0) from named inputs: kappa = 2.076647e-43 SI with kappa c^4 / 2 = 4 pi G verified identically; Mercury's anomalous perihelion advance 0.103520 arcsec/orbit x 415.20 orbits/century = 42.98 arcsec/century against the measured input 42.98; solar-limb deflection 1.7512 arcsec against the round input 1.75, exactly twice the discarded accounting's 0.8756 arcsec; Sun's Schwarzschild radius 2953.3 m as scale check. Remainders at full size: G stands underived at this address; the uniqueness promotion belongs to Lovelock 1971, credited there, not to the 1915 paper; the 1917 cosmological term is CC-08's separate insertion; numeric exhibits run on modern named constants, fenced on the face. EXTENSION. Vacuum catastrophe NOT SOLVED; quantum gravity NOT SOLVED.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-04
DOI
https://doi.org/10.5281/zenodo.23937766
Primary Topic
Relativity and Gravitational Theory
Type
preprint
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preprint

The Chosen Tensor, Priced: Einstein's 1915 Field Equation, Its Matched Coupling, and the 43 Arcseconds It Returns

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
preprint

The Chosen Tensor, Priced: Einstein's 1915 Field Equation, Its Matched Coupling, and the 43 Arcseconds It Returns

William Alexander Aldred
preprint en

Abstract

Census pricing (row CC-100) of the field-equation step of Einstein's 'Die Feldgleichungen der Gravitation,' Sitzungsber. Preuss. Akad. Wiss. (1915) 844-847, against a fixed bench (what is postulated, what is derived, what the postulates return numerically, what they cannot reach). The step is two-layered: the Einstein tensor is CHOSEN under stated demands (covariance, second order, divergence-free) with no uniqueness theorem in existence until Lovelock (1971) -- Einstein's own 1913 Entwurf tensor is the live counterfactual, returning half the deflection and no Mercury anomaly -- and the coupling is MATCHED, not derived: kappa = 8 pi G / c^4 imports the measured G of the theory being replaced. Computed in the notebook (4 checks, exit 0) from named inputs: kappa = 2.076647e-43 SI with kappa c^4 / 2 = 4 pi G verified identically; Mercury's anomalous perihelion advance 0.103520 arcsec/orbit x 415.20 orbits/century = 42.98 arcsec/century against the measured input 42.98; solar-limb deflection 1.7512 arcsec against the round input 1.75, exactly twice the discarded accounting's 0.8756 arcsec; Sun's Schwarzschild radius 2953.3 m as scale check. Remainders at full size: G stands underived at this address; the uniqueness promotion belongs to Lovelock 1971, credited there, not to the 1915 paper; the 1917 cosmological term is CC-08's separate insertion; numeric exhibits run on modern named constants, fenced on the face. EXTENSION. Vacuum catastrophe NOT SOLVED; quantum gravity NOT SOLVED.

Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
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The Chosen Tensor, Priced: Einstein's 1915 Field Equation, Its Matched Coupling, and the 43 Arcseconds It Returns — William Alexander Aldred · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS