  In models of emergent gravity the metric arises as the expectation value of
some collective field. Usually, many different collective fields with
appropriate tensor properties are candidates for a metric. Which collective
field describes the "physical geometry"? We resolve this "metric ambiguity" by
an investigation of the most general form of the quantum effective action for
several metrics. In the long-distance limit the physical metric is universal
and accounts for a massless graviton. Other degrees of freedom contained in the
various metric candidates describe very massive scalars and symmetric second
rank tensors. They only play a role at microscopic distances, typically around
the Planck length. The universality of geometry at long distances extends to
the vierbein and the connection. On the other hand, for distances and time
intervals of Planck size geometry looses its universal meaning. Time is born
with the big bang.
