A Unified Geometric Theory of Trembling Spacetime Relativity

Theoretical physics remains divided between incompatible frameworks for gravity, quantum fields, and the fundamental forces. This work introduces a unifying geometric theory—Trembling Spacetime Relativity Theory (TSRT)—in which spacetime undergoes fine-scale, deterministic fluctuations constrained by causality. These metric tremblings replace probabilistic postulates and field assumptions with a curvature-dependent causal structure that governs interaction, distinguishability, and information flow.

In this framework, Lorentzian geometry and proper time emerge from causal invariance rather than being imposed. Planck’s constant arises as a minimal resolution scale needed to preserve temporal order. The Schrödinger and Dirac equations are recovered as emergent statistical descriptions of trembling-induced motion. The Heisenberg uncertainty relation is refined into a dual-bound form, with both minimal action and maximal curvature coherence limits.

All four known fundamental forces emerge as the only causally admissible gauge structures consistent with trembling constraints. Quantum indeterminacy, wave–particle duality, and Hilbert space dynamics are shown to arise from deterministic geometric structure. Black hole entropy and the holographic principle are similarly derived from curvature-limited distinguishability, without invoking unitarity or thermodynamic postulates. TSRT provides a causally grounded, geometrically complete foundation that unifies relativistic and quantum phenomena.