The Nature of the Fifth Dimension in Classical Relativity
Abstract
Hyperdimensional unified field theories date back to 1921, when Kaluza reported that the Einstein equations of general relativity written in five dimensions (5D) would yield both the standard fourdimensional Einstein equations as well as the Maxwell equations, thus unifying general relativity and electrodynamics. Subsequent research focused on the field equations, with little attention paid to the equations of motion. While unified field theories have since evolved to address quantum forces with many extra compactified dimensions, the original classical 5D theory of Kaluza makes some compelling predictions about a macroscopic fifth dimension. These include identification of electric charge with the space/time manifestation of motion in the fifth dimension, emergence of the gravitational constant as a cosmic chargetomass ratio, and the prediction of hyperluminal 5D proper velocities. This paper provides the mathematical derivation of these and other results with a focus on the equations of motion, a critical consideration of the underpinnings and assumptions of the 5D theory, and a discussion of the historical context of the development of the 5D Kaluza theory and how its serious consideration could have been neglected for so long.
 Publication:

Space, Propulsion & Energy Sciences International Forum: SPESIF2009
 Pub Date:
 March 2009
 DOI:
 10.1063/1.3115502
 Bibcode:
 2009AIPC.1103..243W
 Keywords:

 03.50.De;
 98.80.k;
 95.30.Sf;
 Classical electromagnetism Maxwell equations;
 Cosmology;
 Relativity and gravitation