A unified theory of matter. II. Derivation of the fundamental physical law

Abstract

The equation for the fundamental field quantity ϱ is obtained. It is Div$\rho ^\mu (\Omega _1 ) = \operatorname{h} \int {[\rho _\mu (\Omega _1 ),\rho ^\mu (\Omega _2 )]_ - \operatorname{d} \Omega _2 }$,where h is an arbitrary function oft andr, and [,]₋ is the commutator. The derivation requires the following hypotheses:(1) All of physical reality is completely described by the field ϱ.(2) Relativistic covariance of the equations governing ϱ.(3) Principle of continguous action.(4) Conservation of total amount of ϱ. The equation appears to be unique. It is suggested that the physical world corresponds to ϱ being a2×2 matrix. A close correspondence between the basic equation and Maxwell's equation is displayed. The electromagnetic vector potential A^μ is identified with ε ρ^μ dΩ. Conservation laws on various measures of ϱ are obtained. The symmetry groups of the basic equation are derived. A preliminary attempt to connect the field ϱ to the metric is made via Einstein's gravitational equation G_μυ =_KT_μυ.