Does an atom interferometer test the gravitational redshift at the Compton frequency ?

TL;DR

This paper critically examines whether atom interferometers can test the gravitational redshift at the Compton frequency, concluding that under most theories they do not, and that claims to the contrary conflict with fundamental principles of physics.

Contribution

The paper refutes previous claims that atom interferometers test the gravitational redshift at the Compton frequency, showing such tests are not supported in standard theories and would require radical physics violations.

Findings

Atom interferometers test the universality of free fall, not the gravitational redshift.

In most theories, the Compton phase difference is zero, implying no redshift measurement.

Frameworks claiming redshift tests violate fundamental quantum and energy conservation principles.

Abstract

Atom interferometers allow the measurement of the acceleration of freely falling atoms with respect to an experimental platform at rest on Earth's surface. Such experiments have been used to test the universality of free fall by comparing the acceleration of the atoms to that of a classical freely falling object. In a recent paper, M\"uller, Peters and Chu [Nature {\bf 463}, 926-929 (2010)] argued that atom interferometers also provide a very accurate test of the gravitational redshift when considering the atom as a clock operating at the Compton frequency associated with the rest mass. We analyze this claim in the frame of general relativity and of different alternative theories. We show that the difference of "Compton phases" between the two paths of the interferometer is actually zero in a large class of theories, including general relativity, all metric theories of gravity, most non-metric theories and most theoretical frameworks used to interpret the violations of the equivalence principle. Therefore, in most plausible theoretical frameworks, there is no redshift effect and atom interferometers only test the universality of free fall. We also show that frameworks in which atom interferometers would test the redshift pose serious problems, such as (i) violation of the Schiff conjecture, (ii) violation of the Feynman path integral formulation of quantum mechanics and of the principle of least action for matter waves, (iii) violation of energy conservation, and more generally (iv) violation of the particle-wave duality in quantum mechanics. Standard quantum mechanics is no longer valid in such frameworks, so that a consistent interpretation of the experiment would require an alternative formulation of quantum mechanics. As such an alternative has not been proposed to date, we conclude that the interpretation of atom interferometers as testing the gravitational redshift is unsound.