A Unique Unification Law – The Primordial Vibration of Matter

This preprint proposes a mechanical unification of physics based on a single primordial vibration of matter, modeled as an elastic membrane oscillating at very high frequency from an initial singularity. The fundamental equation is □g ρ = κ ρ sin (ω t + k · x + α ρ), where ρ is the mass/energy field, and the metric g_μν follows Einstein’s equation. Physics is reduced to three fundamental units (M, T, L). All phenomena (cosmological expansion, gravitation, relativity, quantum effects, spin, masses) emerge mechanically without arbitrary constants or fundamental randomness. Time and space arise from the vibration itself. Persistent singularities (classical black holes) are avoided by the natural feedback of the membrane. Open to discussion and constructive criticism.