In the well established "General Theory of Relativity", the Einstein equations are the field equations which describe the allowed values of the gravitational field. In the Einstein equations, the gravitational field is not a single number but is instead represented by the metric gik, which is a 4x4 matrix containing 4x4=16 components. However it is required to be symmetric, meaning that

gik= gki (for every combination of i=0,1,2,3 and k=0,1,2,3)

Therefore, gik really only has 16-6=10 independent components.

Maxwell's equations are the field equations which describe the allowed values of the electromagnetic field. In Maxwell's equations, the electromagnetic field Fik is also a 4x4 matrix containing 4x4=16 components. However, it is required to be antisymmetric, meaning that

Fik= -Fki (for every combination of i=0,1,2,3 and k=0,1,2,3)

In this case, for elements along the diagonal of the matrix we have Fii= -Fii, which can only be true if they are zero. Therefore, Fik has just 16-6-4=6 independent components.

In the Einstein-Schrodinger theory, the field equations are written in terms of a matrix Nik with no symmetry properties, so that it has a full 4x4=16 independent components. Therefore, it could potentially contain both the metric and the electromagnetic field. For example we could have,

Nik=gik+Fik

By this definition and the symmetry properties of gik and Fik, it is easy to see that the symmetric part of Nik would be the metric

gik=(Nik+Nki)/2

and the antisymmetric part of Nik would be the electromagnetic field

Fik=(Nik-Nki)/2

This method of combining the metric and the electromagnetic field is meant as a simple example and does not actually work. However, there is a simliar way of doing it which does work and which is described in my papers.

Go back to lambda-renormalized einstein-schrodinger theory.