We study the coupling of abelian gauge theories to four-dimensional simplic
ial quantum gravity. The gauge fields live on dual links. This is the corre
ct formulation if we want to compare the effect of gauge fields on geometry
with similar effects studied so far for scalar fields. It shows that gauge
fields couple equally weakly to geometry as scalar fields, and it offers a
n understanding of the relation between measure factors and abelian gauge f
ields observed so-far.