Experimental
tests of general relativity performed so far involve systems that can be
effectively described by classical physics. On the other hand, observed gravity
effects on quantum systems do not go beyond the Newtonian limit of the theory.
In light of the conceptual differences between general relativity and quantum
mechanics, as well as those of finding a unified theoretical framework for the
two theories, it is of particular interest to look for feasible experiments
that can only be explained if both theories apply.
We
propose testing general relativistic time dilation with a single “clock” in a
superposition of two paths in space-time, along which time flows at different
rates. We show that the interference visibility in such an experiment will
decrease to the extent to which the path information becomes available from
reading out the time from the “clock”. This effect would provide the first test
of the genuine general relativistic notion of time in quantum mechanics. We
consider implementation of the “clock” in evolving internal degrees of freedom
of a massive particle and, alternatively, in the external degree of a photon
and analyze the feasibility of the experiment.