The Maximal Distance of Detectable Isotropic Signals – Solving Fermis Paradox with Grimaldi’s Model

Abstract

Abstract In 1950, the Italian physicist Enrico Fermi expressed his astonishment with the sentence "Where is Everybody?" that humanity does not receive signals from extraterrestrial civilizations. A solution to this contradiction for isotropic signals, known as Fermi's paradox, is provided by a model by Claudio Grimaldi. In the present work, with the help of a physical model for signal power, the finite range of isotropic signals assumed in Grimaldi's model is specifically calculated. For this purpose, the FAST telescope in Guizhou and a hypothetical satellite network spanning the Earth are regarded as exemplary receiving instruments. In addition, corresponding signal powers are determined for three potentially habitable planets discovered by the Kepler mission and for stars close to the Sun. It turns out that even the FAST telescope cannot receive corresponding signals, but this is theoretically possible with a satellite network, similar to the GPS network. Accordingly, Grimaldi's assumption turns out to be correct, but the maximum range is considerably smaller than Grimaldi assumed.