Quantifying The Fermi Paradox Via Passive SETI: A General Framework

In this paper we consider the extent to which a lack of observations from SETI may be used to quantify the Fermi paradox.

Building on previous research, we construct a geometrical model to compute the probability of at least one detection of an extraterrestrial electromagnetic (EM) signal of galactic origin, as a function of the number N of communicative civilizations.

We show how this is derivable from the probability of detecting a single signal; the latter is ≈0.6δ/R, where δ is the distance between the initial and final EM signals and R is the radius of the Milky Way, for δ/R≪1.

We show how to combine this analysis with the Drake equation N=𝒩δ/c, where c is the speed of light; this implies, applying a simplified toy model as an example, that the probability of detecting at least one signal is >99% for δ/c≳102.8 years, given that 𝒩=1. Lastly, we list this toy model’s significant limitations, and suggest ways to ameliorate them in more realistic future models.

Matthew Civiletti

Comments: 7 pages, 5 figures
Subjects: Instrumentation and Methods for Astrophysics (astro-ph.IM)
Cite as: arXiv:2505.00062 [astro-ph.IM] (or arXiv:2505.00062v1 [astro-ph.IM] for this version)
https://doi.org/10.48550/arXiv.2505.00062
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Submission history
From: Matthew Civiletti
[v1] Wed, 30 Apr 2025 15:40:18 UTC (1,473 KB)
https://arxiv.org/abs/2505.00062
Astrobiology, SETI,