The Born Rule from Configurational Stability: A Timeless Derivation

The Born rule, assigning probabilities via |ψ|², is traditionally introduced as an independent axiom of quantum mechanics. Despite its empirical success, its foundational origin remains unresolved. In this paper we derive the Born rule as a necessary consequence of configurational stability in a timeless, pre-metric configuration space. Physical states are described by field configurations Φ, weighted by a stability functional SΦ. Quantum states ψ arise as representational coordinates encoding relative stability rather than as ontological wave objects. We show that requiring: projective invariance, factorizability for independent subsystems, and classical additivity under phase degradation, uniquely selects the quadratic probability map |ψ|², without assuming Hilbert space structure, Gleason-type theorems, or temporal dynamics. Measurement is identified as a topological transition at a stability threshold Σ*, where the Hessian spectrum becomes marginally stable. This leads to a distinctive, non-analytic “kink” in decoherence behavior. Unlike stochastic collapse models, the framework predicts pure dephasing without energy injection, avoiding existing experimental heating constraints. The theory yields explicit, falsifiable experimental signatures, including structure-dependent decoherence effects in mesoscopic systems, accessible to current matter-wave interferometry and levitated nanosphere experiments. The framework is fully timeless at the fundamental level; laboratory time emerges only as an epistemic ordering parameter. This work is self-contained and does not rely on gravitational, cosmological, or dark-matter assumptions. Keywords quantum foundations; Born rule; measurement problem; decoherence; timeless physics; configuration space; stability theory; quantum-classical boundary