Grounding the Kaluza-Klein Fifth Dimension in Observed Physical Reality, Using Dirac's Quantum Theory of the Electron to Ensure Five-Dimensional General Covariance

Abstract

We require all components of the Kaluza-Klein metric tensor to be generally-covariant across all five dimensions by deconstructing the metric tensor into Dirac-type square root operators. This decouples the fifth dimension from the Kaluza-Klein scalar, makes this dimension timelike not spacelike, makes the metric tensor inverse non-singular, covariantly reveals the quantum fields of the photon, makes Kaluza-Klein fully compatible with Dirac theory, and roots this fifth dimension in the physical reality of the chiral, pseudo-scalar and pseudo-vector particles abundantly observed in particle physics based on Dirac’s gamma-5 operator, thereby “fixing” all of the most perplexing problem in Kaluza-Klein theory. Albeit with additional new dynamics expected, all the benefits of Kaluza-Klein theory are retained, insofar as providing a geometrodynamic foundation for Maxwell’s equations, the Lorentz Force motion and the Maxwell-Stress energy tensor, and insofar as supporting the viewpoint that the fifth dimension is, at bottom, the matter dimension. We find that the Kaluza-Klein scalar must be a massless, luminous field quantum to solve long-standing problems arising from a non-zero scalar field gradient, and we suggest multiple pathways for continued development.