The Speed of Light and the Event Horizon as Simulability Limits: An Experiment-Theoretic Derivation of Relativity, Time Dilation, and Hawking Radiation

Abstract

We offer an experiment-theoretic reinterpretation of Maxwell's equations and spacetime geometry using Le Cam's statistical decision theory. Physical theories are framed not as geometric axioms but as families of statistical experiments subject to operational simulability constraints. Within this framework, we demonstrate that: (1) the speed of light $c$ is the unique constant preserving simulability for physically realizable electromagnetic experiments (within the Gaussian measurement model); (2) Special Relativity corresponds to the class of two-way simulable experiments under restricted causal kernels; (3) General Relativistic time dilation represents a one-way simulability breakdown; and (4) black hole horizons induce experiment collapse: the channel mapping local near-horizon microstates to asymptotic observations contracts statistical distance exponentially (with explicit rate $\exp(-\kappa u/c)$). We establish the Horizon Contraction Theorem and characterize Hawking radiation as the minimax-optimal envelope of the collapsed experiment. These results are epistemic characterizations of known physics, not derivations from first principles; they concern operational equivalence under physical resource constraints. They do not posit new empirical anomalies. Key bounds are non-asymptotic with explicit rates; limiting ``collapse'' statements are obtained by taking explicit limits of these bounds rather than assuming asymptotic contiguity of an experiment sequence. The horizon thermality discussion assumes a stationary semiclassical background and local regularity (Hadamard) conditions; extremal horizons, strong backreaction, and quantum-gravity corrections are outside scope. Idealization error can be formalized via $\varepsilon$-deficiency; causal interventions (do-operator) are treated separately via intervention deficiency, so observational simulability is not promoted to interventional equivalence. We draw no inference from empirical adequacy or simulability to scientific realism (nor to ``structural continuity'' across theory change), and any universality claim is conditional on the stated modelling idealizations and the chosen class of physically admissible simulators.