Long Range Forces and Broken Symmetries

There are reasons for believing that the gravitational constant varies with time. Such a variation would force one to modify Einstein’s theory of gravitation. It is proposed that the modification should consist in the revival of Weyl’s geometry, in which lengths are non-integrable when carried around closed loops, the lack of integrability being connected with the electromagnetic field. A new action principle is set up, much simpler than Weyl’s, but requiring a scalar field function to describe the gravitational field, in addition to the gμν. The vacuum field equations are worked out and also the equations of motion for a particle. An important feature of Weyl’s geometry is that it leads to a breaking of the C and T symmetries, with no breaking of P or of CT. The breaking does not show itself up with the simpler kinds of charged particles, but requires a more complicated kind of term in the action integral for the particle.