  The theory of Gravitomagnetism and spinor quantum mechanics describing the
interaction between the Dirac spinor field, the electromagnetic field, and a
weak gravitational field is extended by including the Lagrangian density of the
free electromagnetic field. It is shown that the newly added term in the
Lagrangian density is necessary to restore a symmetric energy-momentum tensor
in the interaction term of the Lagrangian density within the theory. We prove
that when the electromagnetic energy term is missing, the tensor in the
interaction Lagrangian density does not represent the energy-momentum tensor of
the Dirac field minimally coupled to the electromagnetic field on flat
space-time. Moreover, it follows that the Lagrangian density remains unchanged
regardless of whether the theory is developed from the principle of general
covariance or is defined as a flat space-time theory with the gravitational
field treated as a regular tensor field, in analogy to the electromagnetic
field. This contradicts previous findings.
