On the Interactions of Birkhoff's Gravitational Field with the Electromagnetic and Pair Fields

The flat space-time theory of gravitation proposed by G. D. Birkhoff is discussed from the standpoint of a field theory and, in particular, the interaction of Birkhoff's field with other fields is developed. This interaction is shown to take place through the interaction Lagrangian function $h_{\mu \nu }{\theta }_{\mu \nu }$, and when applied to the electromagnetic and pair fields, it leads to a modification of the Maxwell and Dirac equations. These modified equations determine a change in the index of refraction and a shift of the energy levels of the atom, which account for the bending of light and the red shift in gravitational phenomena. Furthermore, they predict a gravitational correction to the magnetic moment associated with the spin and orbital motion of the electron.