  We consider a toy universe containing conventional matter and an additional
real scalar field, and discuss how the requirements of gauge and diffeomorphism
invariance essentially single out a particular set of theories which might
describe such a world at low energies. In these theories, fermion masses and
g-factors, as well as the electromagnetic coupling turn to be scalar field
dependent; fermion charges and the gravitational coupling might be assumed to
be constant. We then proceed to study the impact of a time variation of the
scalar field on measurements of atomic spectra at high redshifts. Light
propagation is not affected by a sufficiently slow change of the fine structure
constant, but changes of the latter as well as variations of fermion masses and
g-factors do affect the observed atomic spectra. Finally, we prove the
independence of these predictions on the chosen conformal frame, in a further
attempt to address differing views about the subject expressed in the
literature.
