Classical Presence and Action-Phase Interaction Propensity: A Phase-Space Model of Semiclassical Quantum Spatial Density

This preprint introduces the phase-space action-phase (PSAP) model, which interprets leading semiclassical quantum spatial densities as the product of two conceptually distinct factors: a classical probability density of presence along a trajectory and an action-phase interaction-propensity kernel defined by accumulated action in phase space. The model is motivated by the standing-wave optical detection law, whose sinusoidal interaction pattern can be rewritten, via the Planck–Einstein relations, as dependence on the dimensionless action phase S/ℏS//ℏ rather than as a primitive configuration-space wave phase. The central proposal is that the same action-phase interaction structure revealed by semiclassical standing-wave light can be generalized to material particles. In classically allowed regions, this presence-times-propensity construction recovers the leading WKB spatial-density form, while phase closure of the interaction-propensity kernel around a closed orbit yields the EBK quantization condition. Soft turning points and forbidden regions are treated using the standard Airy/WKB uniform approximation and analytic continuation to complexified extended phase space. The present paper does not claim new semiclassical spectra or improved asymptotics. Its contribution is model-theoretic and interpretive: it proposes a phase-space account of semiclassical density as classical presence modulated by action-phase interaction propensity, with WKB/EBK recovery serving as the first benchmark consequence rather than as the motivating ansatz. The paper also includes an appendix developing a wrapped cumulative/complementary-cumulative distribution function (CDF/CCDF) heuristic for cyclic interaction propensity arising from monotonically accumulated action in classically allowed regions, together with a one-sided evanescent continuation in forbidden regions.