What if the Schwarzschild Sign Change is Physical? (Particle) Physics from a Fully Complexified (3+1) Spacetime

The sign change of coordinates at the Schwarzschild horizon is usually treated as a coordinate artefact. This paper treats it as a physical process and follows the consequences. The resulting spacetime is (3+1)C: three complex spatial coordinates zk = xk + i wk (expanded real parts, compact imaginary parts on S3) and one complex time τ = t + iσ (macroscopic real part, compact Euclidean Hawking circle). The Kähler structure and a single geometric parameter — the Berger deformation ε = 1.01027, fixed by the electron mass — determine all particle physics. From this geometry follow, without additional free parameters: the gauge group SU(3)×SU(2)×U(1), the complete charge, colour, and chirality structure of the Standard Model, three fermion generations (topological; fourth excluded), matter/antimatter distinction, all fermion and boson masses, the electroweak mixing parameters, the CKM matrix at tree level, the proton mass, and the uncertainty relation, the Born rule, and the Schrödinger equation as geometric consequences. In total, ∼ 34 quantitative observables are reproduced with a maximum deviation of 6 % for geometric quantities and1.3 % for masses. Three independent determinations of ε (from me, mH , and MP ) agree to 370 ppm. The framework makes falsifiable predictions: a mass-ratio-independent remnant spin a∗(q) ≈ 0.69 for binary black-hole mergers (testable with LIGO O4/O5), r = 0 exactly (testable with CMB-S4), and a neutrino luminosity gap in core-collapse supernovae (retro-consistent with SN 1987A to 3 %). All derivations carry explicit status labels; all known weaknesses and refuted approaches are documented. Additionally, the framework suggests a geometric suppression of the strong-CP phase, because SU(3) arises as Kähler holonomy rather than as an independent gauge sector; if the loop-induced mass-matrix phase also vanishes, no QCD axion is required

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-04-24
DOI
https://doi.org/10.5281/zenodo.19786628
Primary Topic
Relativity and Gravitational Theory
Type
article
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article

What if the Schwarzschild Sign Change is Physical? (Particle) Physics from a Fully Complexified (3+1) Spacetime

Guido Widman
Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
article

What if the Schwarzschild Sign Change is Physical? (Particle) Physics from a Fully Complexified (3+1) Spacetime

Guido Widman
article en

Abstract

The sign change of coordinates at the Schwarzschild horizon is usually treated as a coordinate artefact. This paper treats it as a physical process and follows the consequences. The resulting spacetime is (3+1)C: three complex spatial coordinates zk = xk + i wk (expanded real parts, compact imaginary parts on S3) and one complex time τ = t + iσ (macroscopic real part, compact Euclidean Hawking circle). The Kähler structure and a single geometric parameter — the Berger deformation ε = 1.01027, fixed by the electron mass — determine all particle physics. From this geometry follow, without additional free parameters: the gauge group SU(3)×SU(2)×U(1), the complete charge, colour, and chirality structure of the Standard Model, three fermion generations (topological; fourth excluded), matter/antimatter distinction, all fermion and boson masses, the electroweak mixing parameters, the CKM matrix at tree level, the proton mass, and the uncertainty relation, the Born rule, and the Schrödinger equation as geometric consequences. In total, ∼ 34 quantitative observables are reproduced with a maximum deviation of 6 % for geometric quantities and1.3 % for masses. Three independent determinations of ε (from me, mH , and MP ) agree to 370 ppm. The framework makes falsifiable predictions: a mass-ratio-independent remnant spin a∗(q) ≈ 0.69 for binary black-hole mergers (testable with LIGO O4/O5), r = 0 exactly (testable with CMB-S4), and a neutrino luminosity gap in core-collapse supernovae (retro-consistent with SN 1987A to 3 %). All derivations carry explicit status labels; all known weaknesses and refuted approaches are documented. Additionally, the framework suggests a geometric suppression of the strong-CP phase, because SU(3) arises as Kähler holonomy rather than as an independent gauge sector; if the loop-induced mass-matrix phase also vanishes, no QCD axion is required

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 5%
Relativity and Gravitational Theory
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What if the Schwarzschild Sign Change is Physical? (Particle) Physics from a Fully Complexified (3+1) Spacetime — Guido Widman · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS