Grand Unification: Why Eight Decades of Unification Failed
The GUT program (SU(5), SO(10), etc.) failed because it rests on manifold ontology. The Boundary Unification Principle (V.R245) replaces gauge-group embedding with algebra projection — no larger gauge group, no extra dimensions, no new particles. Baryogenesis threshold at 10¹² GeV (V.P133) sits naturally without GUT-scale unification.
Overview
The Grand Unified Theory program — SU(5), SO(10), E₆, and their supersymmetric extensions — has been pursued for nearly fifty years without observational success: proton decay predictions are excluded, coupling unification in non-SUSY GUTs misses, and no SUSY-GUT superpartners have been found. Book V ch66-67 (“Why Eight Decades of Unification Failed”) diagnoses the root failure: the GUT program rests on manifold ontology, assuming that the Standard Model gauge groups embed into a larger Lie group within a continuous 4-manifold. V.R245 (Boundary Unification Principle, ch57) replaces this with algebra projection from the boundary algebra A_spec(L) onto sectoral components. No larger gauge group is needed, no extra dimensions, no new particles; V.P133 places the baryogenesis threshold naturally at ~10¹² GeV without requiring GUT-scale physics.
Detail
Unification pursued through Lie-group embedding (SU(3) × SU(2) × U(1) ↪ SU(5) or SO(10)) predicts (i) specific sin²θ_W values, (ii) proton decay with rates determined by the GUT scale, and (iii) additional bosons. Non-SUSY GUTs fail (i) by ~20σ once loop-level corrections are included; proton decay searches at Super-Kamiokande exclude minimal SU(5); and SUSY-GUT extensions fail once LHC null-results on superpartners are folded in. Book V ch66 and ch67 (books/V-CategoricalMacrocosm/latex/sections/part07/ch66-why-unification-failed.tex and ch67-why-unification-failed.tex) argue that these failures share a common root: the program treats gauge unification as an embedding within a manifold, but the Standard Model sectors are not parts of a larger group — they are projections of a single boundary algebra. V.R245 (Boundary Unification Principle, books/V-CategoricalMacrocosm/latex/sections/part06/ch57-boundary-unification.tex line 417) records: sectors are algebra projections of A_spec(L), not Lie-group embeddings; there is no larger gauge group to seek. V.P133 places the baryogenesis threshold at ~10¹² GeV from sector-coupling structure without needing GUT-scale new physics. This is consistent with current observations: the absence of proton decay, of superpartners, of new bosons all agree with “no larger gauge group exists”.
Result Statement
V.R245 + V.P133: Boundary Unification Principle — sectors are algebra projections, not Lie-group embeddings. Baryogenesis threshold at ~10¹² GeV without GUT-scale unification. The GUT program failed because its ontology was manifold-based; τ replaces it with boundary-algebraic unification.