Enfolding N-dimensional Euclidean spaces with N-dimensional spheres as a framework to define the structure of time foam

Abstract

This paper discusses the enfolding of the N-dimensional Euclidean space through N-dimensional spheres. The objective is to construct a framework that can be associated with space in the company of time. To arrive at this purpose, it is suggested that the properties of the Euclidean norms and modules of the vectors, which can be considered with origin in some space point and ending into a spherical surface, might be associated with a time-like representation that can enfold any space point. In this manner, an existing particle can be associated with a time-like sphere, and any object, lying in an arbitrary space point, can be associated with one or of several component time-like spheres. Even the Universe can be connected to one time-like sphere. Therefore, in the 3-dimensional Euclidean space where particles and objects exist one can talk about the structure of a time foam.