Discriminating Danielson-Satishchandran-Wald from Fahn-Pesci Decoherence at a Polariton Analogue Horizon: a magnitude test, a κ-fingerprint protocol, and the first-principles prediction

Abstract

Two concrete theoretical frameworks predict the low-frequency dephasing environmentnear a horizon: the Danielson–Satishchandran–Wald (DSW) / Gralla–Wei class, in whichsoft quanta crossing the horizon impose a decoherence rate of order the surface gravity κ,and the Fahn–Pesci quantum-geometry correction, which suppresses that rate by ∼ 104. Wepropose their discrimination on the polariton analogue horizon of Falque et al., whose fieldtheory, metric, and surface-gravity control are demonstrated — two smooth configurationsat κ = 0.07, 0.08 ps−1 and one steep at 0.11 ps−1, the latter at a different detuning. Theobservable is the soft spectral weight W(x) in a fixed instrumental band. The discriminationitself is a magnitude test: the two hypotheses are separated by ≈ 10σ on the demonstratedthree-configuration set even at a 50% noise floor — 6σ in any single configuration, 13σ onthe proposed five-configuration design. Because the horizon length structurally coincideswith the healing length, a bare detection is not yet an identification; we therefore compute the conventional (DSW-class) prediction from first principles on the explicit metric— through a validated reduction, four analytic anchors, and a gated two-route production— and extract its experimental fingerprints: a horizon-localized profile with exterior decaylength ξpD(2 − D)/2 = 1.214 µm, κ-invariant to 10−5 and scaling as 1/∆; an amplitudelaw S ∝ κ1.37; and a mild near-horizon rise. A differential-κ protocol, using the demonstrated in-situ tunability of the surface gravity at fixed material, verifies these fingerprints:the decay length is measurable to ±4% per configuration at a 20% noise floor, and the computed shape is identified against a generic pinned crossover with 100% probability at anynoise floor up to 50%, robustly under exclusion of the sub-ξ grid points. The scope is statedprecisely: the analogue tests the kinematics of the DSW mechanism and the structuralform of the Fahn–Pesci claim — whether real cutoff-scale structure gates the soft sector —not horizon-area quantization itself. This is a proposal with derivations, computations andchecks, not a measurement.