Fantappie's group as an extension of special relativity on Cantorian space-time

TL;DR

This paper explores extending special relativity using Fantappie's group within Cantorian space-time, suggesting cosmological models like Big Bang and stationary state can coexist, and examines implications for galactic dynamics.

Contribution

It introduces a novel extension of special relativity based on Fantappie's group in Cantorian space-time, linking it to cosmological and galactic phenomena.

Findings

Big Bang and stationary state models become compatible.

Projective fractal geometry influences galactic dynamics.

Extension of relativity offers new cosmological insights.

Abstract

In this paper we will analyze the Fantappie group and its properties in connection with Cantorian space-time. Our attention will be focused on the possibility of extending special relativity. The cosmological consequences of such extension appear relevant, since thanks to the Fantappie group, the model of the Big Bang and that of stationary state become compatible. In particular, if we abandon the idea of the existence of only one time gauge, since we do not see the whole Universe but only a projection, the two models become compatible. In the end we will see the effects of the projective fractal geometry also on the galactic and extra-galactic dynamics.