Four Fundamental Forces from a Single Equation (FFFE)

This article presents Four Fundamental Forces from a Single Equation (FFFE), a historic and explicit realization of the Universal Physical Equation (UPE)—a single variational framework unifying the four fundamental interactions of nature: gravity, electromagnetism, the weak force, and the strong force. Built upon the foundations established in Universal Physical Theory and Equation (UPTE), this work extends the same master equation from the theoretical unification of relativity, quantum mechanics, and thermodynamics to the direct recovery of all four forces that govern the physical universe. The UPE is formulated as one master action whose variation yields the equations of motion for all interacting fields, gravitational and gauge alike, under a single geometrical and thermodynamic principle. Within this framework, dissipative and non-equilibrium phenomena—such as viscosity, heat flow, and entropy production—are not external corrections but arise naturally within the same master functional through a Schwinger–Keldysh/GENERIC degenerate structure, enforcing the Second Law of thermodynamics on every admissible evolution. The causal Israel–Stewart formulation is recovered as an on-shell representation of this dissipative block, providing a self-consistent bridge between field theory and relativistic hydrodynamics. To ensure physical validity, the theory enforces four binary guardrails: causality, linear stability, non-negative entropy production, and non-negative sound attenuation. Under these constraints, the system admits no unphysical solutions. Using empirical anchors (T∗,μB∗)=(0.16,0.30) GeV(T^*, \mu_B^*) = (0.16, 0.30)\,\mathrm{GeV}(T∗,μB∗)=(0.16,0.30)GeV, the framework predicts several quantitative cross-sector relations—termed locks—that connect gravitational, thermodynamic, and quantum gauge phenomena. Key outcomes include:• a Tri-Equality that ties the thermodynamic cumulant ratio r42=χ4/χ2r_{42} = \chi_4/\chi_2r42=χ4/χ2 to transport derivatives of the shear and bulk viscosities (η/s,ζ/s)(\eta/s, \zeta/s)(η/s,ζ/s), confirmed along the lock line r42=0r_{42}=0r42=0;• a Bulk-cap bound ζ/s≤λ2x2\zeta/s \le \lambda_2 x^2ζ/s≤λ2x2 with λ2=1.516×10−3\lambda_2 = 1.516\times10^{-3}λ2=1.516×10−3 that is saturated at the baseline (T∗,μB∗)=(0.16,0.30) GeV(T^*, \mu_B^*) = (0.16, 0.30)\,\mathrm{GeV}(T∗,μB∗)=(0.16,0.30)GeV, providing a falsifiable constraint for QCD and dense-matter models;• and a Kerr–viscosity sign-lock, predicting that in any rotating frame the longitudinal viscosity exceeds the transverse one (η∥>η⊥)(\eta_{\parallel} > \eta_{\perp})(η∥>η⊥), ensuring that dissipation remains positive-definite under frame rotation. Together these results establish that the same universal equation—the UPE—governs gravity, the gauge forces, and the laws of thermodynamics. The derivation is fully constructive, requires no new postulates, and provides a falsifiable, data-connected framework for the long-sought unification of the four forces. The implications extend from subnuclear matter and QCD transport to relativistic fluids, neutron stars, and black-hole thermodynamics, suggesting a single coherent description of all physical interactions. Reproducibility and Supplementary Material:All detailed derivations, step-by-step validations, and numerical datasets used in this study are provided in the companion record:Baek, M.J. (2025). FFFE Supporting Document: Derivations and Reproducibility Notes. Zenodo.DOI: https://doi.org/10.5281/zenodo.17297092 License: CC BY-NC 4.0 — free to share and adapt with attribution, for non-commercial use only.Version: 1.0 (UPE/FFFE unified release) The FFFE study completes the logical chain initiated by UPTE, advancing from theoretical unification to full physical unification. It stands as a milestone in the search for a single governing equation of the universe.