The Fermi Non-paradox: Statistical Experiments, Observational Indistinguishability, and SETI Null Results

Abstract

Statistical Experiments, Observational Indistinguishability, and SETI Null Results reframes the Fermi question not as a cosmic verdict, but as a problem of statistical inference under limited observational power. The central claim is simple but decisive: a SETI null result constrains only those technosignature models that a declared experiment would probably have detected. A finite survey does not test “civilizations in general”; it tests a bounded combination of source class, propagation, instrument, pipeline, threshold, false-alarm control, and decision rule. In this framework, the real evidential quantity is not the abstract abundance of life, but P(Dₑ | H) — the probability that experiment e would produce a validated detection under a specified hypothesis H. The paper develops SETI as a typed statistical experiment on a stratified source-model space Θ = ⨆ᶻ {z} × Θ_z, where different technosignature classes — radio beacons, optical pulses, waste heat, atmospheric pollutants, probes, artifacts, and settlement traces — are not forced into a single artificial coordinate system. Propagation, measurement, feature extraction, and decision are represented as Markov-kernel compositions, producing an experiment-specific law Pᵉ_θ for each source model θ. This allows the authors to define exact observational equivalence θ ∼ₑ θ′ ⇔ Pᵉ_θ = Pᵉ_θ′ and an experiment-induced pseudometric dₑ(θ, θ′) = d(Pᵉ_θ, Pᵉ_θ′). The result is a disciplined language for saying which models are separable, which are approximately indistinguishable, and which are invisible to a given survey by construction. Population inference is formulated through a marked point-process model. Detection power βₑ(θ) is integrated against a population intensity Λ_ψ, giving the expected detection count λₑ(ψ) = ∫_Θ βₑ(θ)Λ_ψ(dθ). The familiar Poisson null likelihood becomes P(Nₑ = 0 | ψ, e) = exp[−∫_Θ βₑ(θ)Λ_ψ(dθ)]. This makes the interpretation of null results precise: a null suppresses models with large expected detection counts, but it has little force against models whose emissions are rare, weak, short-lived, narrowly directed, strategically minimized, causally disconnected, or outside the experiment’s observational alphabet. A distinctive part of the framework is the treatment of strategic observational indistinguishability. Technological sources are allowed, in principle, to choose strategies that alter their observability. The observer–source problem is expressed through minimax quantities such as V₋(h) = supₑ infₛ d(Pᵉ_{θ,s}, Pᵉ₀) and V₊(h) = infₛ supₑ d(Pᵉ_{θ,s}, Pᵉ₀). This does not claim that extraterrestrial intelligence is hiding; rather, it separates three different mechanisms of non-observation: passive weak detectability, strategic statistical matching, and causal disconnection. The broader research message is methodological. Geometric “cosmic haystack” measures remain useful only as chart-dependent summaries over declared bounded domains; they cannot replace calibrated power surfaces, false-alarm behavior, exposure integrals, and dependence-aware survey combination. The paper therefore proposes an operational standard for SETI null claims: declare the experiment, measure βₑ(θ) through end-to-end injection and recovery, calibrate αₑ, model survey dependence, distinguish signal SETI from persistent artifact and settlement branches, and report exactly which model class the null constrains. Its final question is not “Where is everyone?” in the abstract, but: which explicit populations would our experiments probably have detected, which remain observationally indistinguishable, and what new experiment best separates the surviving models?