Predictions and observations in theories with varying couplings

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 out 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.