In Search Of A Variant Kaluza Theory

Kaluza’s 1921 theory of gravity and electromagnetism using a fifth wrapped-up spatial dimension is at the root of many modern attempts to develop new physical theories. Lacking non-null electromagnetic fields however the theory is incomplete. Variants of the theory are explored to find ways to introduce non-null solutions by making the fifth dimension more physical, using alternative, weaker cylinder conditions. The Lorentz force law is investigated starting with a non-Maxwellian definition of charge, this is assumed to be related to Maxwellian charge by ansatz. Order of magnitude methods are used. Kaluza theory remains inadequate to support electromagnetism in full, non-null solutions are not readily shown to be admitted. An argument is made in favour of torsion resolving this issue. Postulates are derived from the argument for a variant theory. The charge ansatz is shown to follow from the postulates. It is concluded that Kaluza’s 5D space and torsion need to go together in a Kaluza-Cartan theory. Tentatively, generalized Bel super-energy is hypothesized to be a conserved quantity.