  Paying attention to conformal invariance as the invariance under local
transformations of units of measure, we take a conformal invariant quantum
field as a quantum matter theory in which one has the freedom to choose the
values of units of mass, length and time arbitrarily at each point. To be able
to have this view, it is necessary that the background on which the quantum
field is based be conformal invariant as well. Consequently, defining the
unambiguous expectation value of the energy-momentum tensor of such a quantum
field through the Wald renormalizing prescription necessitates breaking down
the conformal symmetry of the background. Then, noticing the field equations
suitable for describing the back-reaction effect, we show that the existence of
trace anomaly, known for indicating the brokenness of conformal symmetry in
quantum field theory, can also indicate the above gravitational conformal
symmetry brokenness
