The Displacement Principle: A Radial-Displacement Paradigm for the Unification of Quantum Mechanics and Relativity

We present a framework in which accumulated radial displacement, rather than velocity, is treated as the fundamental geometric quantity governing physical processes. By carefully defining the radial displacement operator and its domain, we show that this perspective is mathematically consistent and equivalent to standard formulations via a canonical transformation. A scale-invariant coherence potential Φ(r) = Φ0/r and an informational depth ψ = ln(r/r0) naturally emerge, leading to a modulation function λ(ψ) = 1/(1 + ψ) that governs the transition from quantum to classical behaviour. Within this framework, long-standing puzzles such as the cosmological constant discrepancy, the hierarchy of fundamental scales and aspects of the quantum measurement problem are addressed through simple geometric scaling arguments. We outline three experiments that could distinguish displacementbased predictions from velocity-based ones: (i) a comparison of radial and circular clock transport using optical lattice clocks, (ii) detection of a coherence transition at r0 ∼ 1 mm using trapped ions or macroscopic interferometers, and (iii) high-precision measurements of gravitational lensing in eccentric orbits. Together, these developments suggest that radial displacement offers a novel and experimentally testable organising principle that complements conventional physics.