Boundary Interface Theory: Membrane Pressure from Relative Motion and the Dynamical Origin of Local Light Speed Invariance

This paper presents a key advance in the Boundary Interface Theory (BIT)—a unified framework based on the idea that spacetime behaves as an elastic, mechanical boundary membrane with intrinsic stiffness. In this work, we complete the unification of static gravitational effects and dynamic kinematic effects within a single membrane-mechanical paradigm. We provide a consistent, dynamical explanation for: Gravitational time dilation and length contraction The local invariance of the speed of light The origin of relativistic kinematics By introducing dynamic membrane pressure from relative motion, we show that both gravity and inertial effects arise from the same underlying membrane deformation. This closes a major logical gap in the BIT framework and establishes a self-contained, experimentally testable foundation for macroscopic and cosmological physics. Notably, this work unifies the classical and relativistic domains but does not yet address quantum mechanics, quantum fields, or quantum gravity. The full, ultimate unification of BIT with quantum physics remains the final, conclusive step of the entire framework. This article is therefore a critical, necessary milestone—but not yet the ultimate, final piece of the complete unified theory.