Reexamining the roles of gravitational and inertial masses in gravimetry with atom interferometers

We reassess the true roles of the gravitational charge (mass) and the inertial mass in quantum phases acquired in matter-wave interferometry in a gravitational field. The insights gained allow us to address the question of whether gravimetry with atom interferometers is equivalent to a high precision measurement of the relative gravitational time dilation of two clocks separated in space. In particular we show that the gravitational phase is inversely related to the Compton frequency, invalidating the suggested equivalence to a Compton clock. Clarity of arguments is achieved by comparison to a charged matter-wave interferometer. Though quantum states have a similarity to oscillator clocks through the Planck–Einstein–de Broglie relations, it is shown clearly that the claim of greatly enhanced precision over real atomic clock comparison cannot be maintained.

► Debate whether atom interferometry is equivalent to high precision comparison of two Compton clocks is resolved, with answer in negative.
► The true roles of the gravitational and inertial masses in matter-wave interferometry is highlighted and explained.
► Showed that interferometer phase shift in the gravitational field is inversely proportional to the Compton frequency, rather than proportional to it.
► Comparison with a charged particle interferometer removes the ambiguity present in all previous discussions.