One of the main principles on which the Global Positioning System (GPS) technology is based is the strict proportionality between the rates of clocks in relative motion. In recent work it has been demonstrated that relativity theory can be modified to incorporate this principle without violating Einstein’s postulate of the constancy of light in free space, also assumed in GPS. In the present work attention is centered on Einstein’s relativistic treatment of electromagnetic interactions. For example, it is pointed out that forces are assumed to be invariant in the revised theory, whereas Einstein concluded that transverse components of the Lorentz electromagnetic force have different values in the rest frame of accelerated electrons than in that of the stationary frame from which they are observed. It is shown that the necessary modifications of relativity theory can be achieved by eliminating an undeclared assumption in Einstein’s original derivation of the Lorentz transformation (LT) and replacing it with the GPS axiom of the strict proportionality of clock rates in different rest frames. An assumption about the form of the inverse transformation of the electromagnetic field components also has to be changed. The example of two electrons being repelled as they move alongside each other in the laboratory is used as an application of the revised theory.