Interference of Clocks: A Quantum Twin Paradox

The phase of matter waves depends on proper time and is therefore susceptible to special-relativistic (kinematic) and gravitational (redshift) time dilation. Hence, it is conceivable that atom interferometers measure general-relativistic time-dilation effects. In contrast to this intuition, we show: (i.) Closed light-pulse interferometers without clock transitions during the pulse sequence are not sensitive to gravitational time dilation in a linear potential. (ii.) They can constitute a quantum version of the special-relativistic twin paradox. (iii.) Our proposed experimental geometry for a quantum-clock interferometer isolates this effect.