In a lecture held live at UCSD in April 2025 at the Astrophysics and Cosmology Seminar, Eric Weinstein presented an update to his theory of Geometric Unity.
Abstract: The Einstein Field Equations (EFE) traditionally treat the dark energy term Λ gᵤᵥ as a non-geometric addition to the curvature-based Einstein tensor Gᵤᵥ. In contrast, the framework of Geometric Unity (GU) reformulates the EFE as part of a covector field on an inhomogeneous gauge group over the Dirac spinor bundle of a 14-dimensional space of Lorentzian metrics. This setting introduces a new tensor ϑ_ω with exceptional equivariance properties, promoting dark energy to a fully geometric, gauge-theoretic quantity. This geometric approach naturally extends to a supersymmetric version of the Einstein–Dirac system and yields three Pati–Salam generations when compactification is imposed. The resulting structure aligns the Einstein–Dirac sector with both General Relativity and the Seiberg–Witten monopole equations, offering a unified and geometrically grounded view of spacetime, matter, and gauge fields.
