START in a five-dimensional conformal domain

TL;DR

This paper reviews the geometry of a five-dimensional conformal space related to the conformal group O(4,2), exploring its topology, metric, and potential applications to START theory and higher-dimensional physics.

Contribution

It provides a detailed geometric and topological analysis of the five-dimensional conformal space, connecting it to compactification, Lie-sphere geometry, and previous theories like Rumer's 5-optics.

Findings

Derived the metric of the 5D conformal space using a half-space representation

Described the topology and compactification of the space

Outlined potential applications to START theory and higher-dimensional models

Abstract

In this paper we give a brief review of the pseudo-Riemannian geometry of the five-dimensional homogeneous space for the conformal group O(4,2). Its topology is described and its relation to the conformally compactified Minkowski space is described. Its metric is calculated using a generalized half-space representation. Compactification via Lie-sphere geometry is outlined. Possible applications to Jaime Keller's START theory may follow by using its predecessor - the 5-optics of Yu. B. Rumer. The point of view of Rumer is given extensively in the last section of the paper. Keywords. Kaluza,Klein, Rumer, conformal symmetry, hyperbolic space, START, fifth dimension, action coordinate, 5-optics