  Inspired by recent claims for a varying fine structure constant, alpha, we
investigate the effect of ``promoting coupling constants to variables'' upon
various parameters of the standard model. We first consider a toy model:
Proca's theory of the massive photon. We then explore the electroweak theory
with one and two dilaton fields. We find that a varying alpha unavoidably
implies varying W and Z masses. This follows from gauge invariance, and is to
be contrasted with Proca' theory. For the two dilaton theory the Weinberg angle
is also variable, but Fermi's constant and the tree level fermion masses remain
constant unless the Higgs' potential becomes dynamical. We outline some
cosmological implications.
