Tau Unified Field Theory (TUF): A Gradient-Based Framework for Unifying the Four Fundamental Forces

We propose the Tau Unified Field Theory (TUF), a novelframework that unifies gravity, electromagnetism, the strong nuclearforce, and the weak nuclear force through a single scalar field denotedas τ (tau). In this model:• The strong force manifests as a steady source of τ emitted byhadrons (e.g., protons);• The weak force is encoded in the finite interaction range andirreversible nature of τ;• Electromagnetism is governed by the fine-structure constantα ≈1/137.036;• Gravity emerges as the spatial gradient response of the τ field:⃗Fg =−G∇τThrough numerical simulation of a hydrogen-like system, we achieveexact force balance at the Bohr radius (r = 1), where the electromagnetic attraction equals the τ-induced gravitational attraction. Theratio ⃗FEM/⃗Fg = 1.000, corresponding to an effective coupling ratioEM/Strongeff = α = 0.007297, matching natural observation. Thiswork demonstrates that gravity can emerge as a gradient-driven phenomenon, and four-force unification is achievable at atomic scales.Keywords: unified field theory, emergent gravity, tau field, fine-structureconstant, information gradient, numerical simulation