  Using the relativistic concept of time dilation we show that a superposition
of gravitational potentials can lead to nonunitary time evolution. For
sufficiently weak gravitational potentials one can still define, for all
intents and purposes, a global coordinate system. A probe particle in a
superposition of weak gravitational fields will, however, experience dephasing
due to the different time dilations. The corresponding instability timescale is
accessible to experiments, and can be used as a degree of macroscopicity.
Finally, we suggest an experiment with smoothly tunable amplification in a
microwave interferometer that allows a quantitative study of the quantum to
classical boundary.
