The present and the future of some velocity in space-time

Abstract

In this paper we introduced the present and the future of some velocity〖ωϵR〗^+, as hypercones in Space-Time, valid both in the classical mechanics (the Newtonian mechanics) and in the relativistic mechanics if ω does not exceed the speed of light in vacuum. The consequences are multiple including the need to redefine philosophical notions about the present, past and future, the expansion and the size of the universe available to an observer in the Space-Time.