A Novel Equivalence Relation in Relativity

Abstract

This paper proves a proposition which says that existence in a spacetime which meets four commonly satisfied principles is an equivalence relation by absolute dimensionality, and briefly discusses three of its implications: (1) the equivalence relation opens the serious possibility for things to exist in a physical sense without existing in spacetime, (2) it establishes a novel classical geometric correspondence between proper time intervals and Euclidean distances in a spacetime one dimension higher, and (3) it may serve as a theoretical tool for checking the internal consistency of higher- dimensional models of reality.