Five-dimensional relativity without parallel transport, outside sources or added symmetries

A formalism is developed in which General Relativity is derived without parallel transport. Matter and electromagnetic fields are brought in by adding a fifth dimension. The author uses Lie derivatives instead of covariant derivatives so as to get rid of the idea of parallel transport and torsion. To bring in matter and electromagnetic fields the author follows the ideas of Kaluza and Klein and applies the Einstein equations of a pure gravitational field to a five dimensional space-time. Then, by allowing the metric to vary in the fifth dimension, and using the ideas of Nelson's Stochastic Mechanics, the author is able to come up with a quantization of matter and the electromagnetic field. Although the basic laws of physics seem to be contained in this theory, some of its predictions don't appear to agree with experiment