arXiv:0709.0936v9 [physics.gen-ph] 6 Sep 2008 On the Anomalous Gyromagnetic Ratio G. G. Nyambuya ∗ North-West University -Potchefstroom Campus, School of Physics - Unit for Space Research, P. Bag X6001, Potchefstroom, Republic of South Africa. G. G. Nyambuya (Dated: October 9, 2018) Submitted: 25 February 2008. Accepted : 28 May 2008 Published : July 2008, Foundations of Physics, Vol. 38, Issue 7, pages 665-677. I propose three new curved spacetime versions of the Dirac Equation. These equations have been developed mainly to try and account in a natural way for the observed anomalous gyromagnetic ratio of Fermions. The derived equations suggest that particles including the Electron which is thought to be a point particle do have a finite spatial size which is the reason for the observed anomalous gyromagnetic ratio. A serendipitous result of the theory, is that, two of the equation exhibits an asymmetry in their positive and negative energy solutions the first suggestion of which is clear that a solution to the problem as to why the Electron and Muon – despite their acute similarities - exhibit an asymmetry in their mass is possible. The Mourn is often thought as an Electron in a higher energy state. Another of the consequences of three equations emanating from the asymmetric serendipity of the energy solutions of two of these equations, is that, an explanation as to why Leptons exhibit a three stage mass hierarchy is possible. Keywords: Curved Space, Dirac Equation, Gyromagnetic Ratio, Fundamental Parti- cle. PACS numbers (2006): 03.65.Pm, 11.30.j, 04.62.b, 04.62.+v, 98.80.Jk, 04.40.b, “The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.” – Paul Adrien Maurice Dirac (1902-1984) I. INTRODUCTION The Dirac Equation is a relativistic quantum mechanical wave equation invented by Paul Dirac in 1928 (Dirac 1928a, 1928b) originally designed to overcome the criticism of the Klein- Gordon Equation. The Klein-Gordon equation gave negative probabilities and this is considered to be physically meaning- less. Despite this fact, this equation accounts well for Bosons, that is spin zero particles. This criticism leveled against the Klein-Gordon equation, motivated Dirac to successfully seek an equation devoid of negative probabilities. ∗ Electronic address: gadzirai@gmail.com, fskggn@puk.ac.za The Dirac Equation is consistent with Quantum Mechanics (QM) and fully consistent with the Special Theory of Relativ- ity (STR). This equation accounts in a natural way for the na- ture of particle spin as a relativistic phenomenon and amongst its prophetic achievements was its successful prediction of the existence of anti-particles. In its bare form, the Dirac Equa- tion provided us with an impressive and accurate description of the Electron hence it being referred in most of the literature as the “Dirac Equation for the Electron”. It also accounts well for quarks and other spin half particles although in some of the cases, there is need for slight modifications while in others is fails - for example, one needs the Procca Equation to describe the neutron which is a spin-1/2 particle as the Electron. The first taste of glory of the Dirac Equation was it being able to account for the gyromagnetic ratio of the electron, that is g = 2, which can not be accounted for using non-relativistic