On factorization of Einstein's formalism into a pair of quaternion field equations

Abstract

It is proposed that a full exploitation of the principle of general relativity in the costruction of the metrical field equations implies that the fundamental variables should be quaternion fields rather than the metric tensor field of the conventional formulation. Thus, the tensor property of Einstein's formalism is replaced here by a formalism that transforms as a quaternion—a vector field in co-ordinate space and a second-rank spinor field of the type η ⊗ η* in spinor space. The geometrical field variables of the Riemann space are derived in quaternion form. The principle of least action (with the Palatini technique) is then used to derive a pair of time-reversed quaternion field equations, from the (quaternionic form of ) Einstein's Lagrangian. It is then shown how the conventional tensor form of the Einstein formalism is recovered from a particular combination of the derived time-reversed quaternion equations.