What does this research mean for the field?

The physical indistinguishability of Lorentzian and Euclidean metrics at the Planck scale generates a fifth fundamental force, the Thangavelu force, which is repulsive, universal, and falls off as r^-4. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

What question did this study set out to answer?

This work investigates the emergence of a fifth fundamental force, termed the Thangavelu force, derived from metric indistinguishability at the Planck scale.

June 8, 2026Open Access

Paper CXXXII: The Thangavelu Force: A Fifth Fundamental Force from LorentzianEuclidean Metric Indistinguishability at the Planck Scale

Key Points

This work investigates the emergence of a fifth fundamental force, termed the Thangavelu force, derived from metric indistinguishability at the Planck scale.
Utilized the discrete Fourier transform on the G2 Fano lattice and the continuous Fourier transform in quantum field theory to establish physical identities.
Applied arguments around the Generalized Uncertainty Principle (GUP) and black hole formation to analyze the metric signatures.
Derived the force law, coupling constant, and potential observational signatures of the Thangavelu force.
Identified the Thangavelu force as a universal, repulsive force decaying as r−4 with a derived coupling constant GT = 4Gℓ2P.
Demonstrated the physicality of Wick rotation at the Planck scale, indicating deep connections between geometry and force.
Established that the Thangavelu force emerges from the Brown-York extrinsic curvature tensor at the Lorentzian-Euclidean interface.

Abstract

Paper CXXXI established that the Discrete Fourier Transform on the G2 Fano lattice (spacing ℓP ) and the continuous Fourier Transform of quantum eld the- ory are physically identical: modes with k > π/ℓP are inaccessible by the Generalised Uncertainty Principle (GUP). We apply the identical argument to the metric signa- ture itself. Distinguishing the Lorentzian metric ηµν = diag(−1, +1, +1, +1) from the Euclidean metric δµν = diag(+1, +1, +1, +1) requires resolving a time interval ∆t < ℓP /c the Planck time which is physically impossible by the GUP and black hole formation argument. Therefore the Wick rotation t →−iτ is not a math- ematical trick at the Planck scale; it is a physical identity. The G2 Fano brane nu- cleates from a 5D Anti-de Sitter (AdS) parent whose hyperbolic geometry mediates the transition between the Lorentzian brane boundary and the Euclidean bulk inte- rior. The stress at this LorentzianEuclidean interface is the BrownYork extrinsic curvature tensor T BY µν , which generates a new physical force distinct from gravity, elec- tromagnetism, and the nuclear forces. We derive its force law, coupling constant, and observational signatures. The force is repulsive, universal, falls o as r−4, and has cou- pling GT = |χ(K)| · G · ℓ2 P = 4Gℓ2 P , where χ(K) = −4 is the Euler characteristic of the Klein quartic and 4 = C2(G2, adj) the same Casimir that appeared in Papers CXXXI and CXVI. Zero free parameters. We name this force the Thangavelu force in honour of Thangavelu (d. 1 December 1999), uncle of the author. Contents Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.

Paper CXXXII: The Thangavelu Force: A Fifth Fundamental Force from LorentzianEuclidean Metric Indistinguishability at the Planck Scale

Key Points

Abstract

Cite This Study

Also Consider

Also Consider