  Metric descriptions of gravitation, among them general relativity as today's
established theory, are founded on assumptions summarized by the Einstein
equivalence principle (EEP). Its violation would hint at unknown physics and
could be a leverage for the development of quantum gravity. Atomic clocks are
excellent systems to probe aspects of EEP connected to (proper) time and have
evolved into a working horse for tests of local position invariance (LPI). Even
though the operational definition of time requires localized and idealized
clocks, quantum systems like atoms allow for spatial superpositions that are
inherently delocalized. While quantum experiments have tested other aspects of
EEP, no competitive test of LPI has been performed or proposed allowing for an
intrinsic delocalization. We extend the concepts for tests of the universality
of clock rates (one facet of LPI) to atom interferometry generating delocalized
quantum clocks. The proposed test depends on proper time with a favorable
scaling and is, in contrast to fountain clocks, robust against initial
conditions and recoil effects. It enables optical frequencies so that the
projected sensitivity exceeds the one of state-of-the-art localized clocks.
These results extend our notion of time, detached from classical and localized
philosophies.
