On the quantization of electrical charge from general relativity

Abstract

In a series of articles in It Nuovo Cimento, during the past 10 years, I have developed a generalization of the formal structure of the theory of general relativity. Starting from the fact that the underlying symmetry of this theory is defined in terms of covariance of the laws of nature with respect to only continuous trans]ormations in space-time, it was shown that Einstein's original tensor-field equation factorize into a pair of conjugated quaternion-field equations (~). This result followed from the feature of the symmetry group of general relativity--the (~ Einstein group ))--that its irreducible representations obey the algebra of a quaternion-number system, and their basis functions arc twocomponent spinor-field variables in a Riemannian space-time. The solutions of the generalized metrieM-field equations, q~(x), are, geometrically four-vectors, but each of the components of the vector is a quaternion--thus , this is a 16-component variable. The factorized quaternion-ficld equations are then 16 independent-field relations at each space-time point. It was then shown, by iterating these equations with their conjugated solutions, that these 16 relations could be expressed as a sum of a symmetric-tensor form (10 relations) and an antisymmetric-tensor form (6 relations), and that because of the respective reflection properties of these sets of equations, the former I0 relations can be uniquely associated with Einstein's original tensor equations, and the latter 6 relations can be uniquely associated with the Maxwell formalism for electromagnetism (~). This generalized quaternion structure of general relativity was then applied to problems in the astronomical domain (a) and to problems in the domain of elementaryparticle physics--which is the domain of interest of the present note. What has been proven so far in this domain of physics from the generalized version of general relativity is that a) o'm can establish an unambiguous formal relation between the inertial mass of an elementary particle and the field properties of space-time--thereby explicitly dclnonstrating the validity of the Mach principle, as well as proving with this relationship that gravitational forces can only be attractive (4), b) matter and antimatter are distinguishable aspects participating in elementary interactions (5), c) in the asymptotic