What question did this study set out to answer?

To establish the existence of a new fundamental force originating from Lorentzian-Euclidean indistinguishability at the Planck scale.

May 22, 2026Open Access

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

Key Points

To establish the existence of a new fundamental force originating from Lorentzian-Euclidean indistinguishability at the Planck scale.
Applied the Discrete Fourier Transform on the G2 Fano lattice and continuous Fourier Transform in quantum field theory.
Examined the implications of the Generalised Uncertainty Principle and black hole formation limits on metric signature resolution.
Derived the force law and coupling constant for the new force through geometric and topological considerations.
The Thangavelu force is repulsive, universal, and decreases as r−4.
Coupling constant GT is derived to be 4Gℓ2P with zero free parameters.
The new force manifests significant implications for our understanding of fundamental interactions.

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.

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