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arXiv:2404.03057 · Physica Scripta

Matter waves and clocks do not observe uniform gravitational fields

Peter Asenbaum, Chris Overstreet, Mark A. Kasevich

Published Mar 14, 2024• 7 citations
arXivHTMLPDF

Abstract

Abstract In a uniform gravitational field, classical test objects fall universally. Any reference object or observer will fall in the same universal manner. Therefore, a uniform gravitational field cannot create dynamics between observers and classical test objects. The influence of a uniform gravitational field on matter waves and clocks, however, is described inconsistently throughout research and education. To illustrate, we discuss the behavior of a matter-wave interferometer and a clock redshift experiment in a uniform gravitational field. As a consistent formulation of the equivalence principle implies, a uniform gravitational field has no observable influence on these systems and is physically equivalent to the absence of gravity.

DOI
10.1088/1402-4896/ad340c

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Abstract In our paper, ‘Matter waves and clocks do not observe uniform gravitational fields’ (Asenbaum et al 2024 Phys. Scr. 99 046103), we analyze how measurements with matter waves and clocks depend on non-gravitational forces and on a UGF. The comment on our paper rests primarily on a misreading of the paper’s central physical setup. We do not consider the simplification that the redshift apparatus is fixed. Rather, our description remains general and keeps the non-gravitational forces independent of the UGF, which covers all configurations: the redshift setup being fixed, in free fall, or arbitrary upward or downward acceleration. This allows us to establish that the redshift measurement follows the non-gravitational forces rather than the UGF.

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Abstract In a uniform gravitational field, classical test objects fall universally. Any reference object or observer will fall in the same universal manner. Therefore, a uniform gravitational field cannot create dynamics between observers and classical test objects. The influence of a uniform gravitational field on matter waves and clocks, however, is described inconsistently throughout research and education. To illustrate, we discuss the behavior of a matter-wave interferometer and a clock redshift experiment in a uniform gravitational field. As a consistent formulation of the equivalence principle implies, a uniform gravitational field has no observable influence on these systems and is physically equivalent to the absence of gravity.
Abstract In our paper, ‘Matter waves and clocks do not observe uniform gravitational fields’ (Asenbaum et al 2024 Phys. Scr. 99 046103), we analyze how measurements with matter waves and clocks depend on non-gravitational forces and on a UGF. The comment on our paper rests primarily on a misreading of the paper’s central physical setup. We do not consider the simplification that the redshift apparatus is fixed. Rather, our description remains general and keeps the non-gravitational forces independent of the UGF, which covers all configurations: the redshift setup being fixed, in free fall, or arbitrary upward or downward acceleration. This allows us to establish that the redshift measurement follows the non-gravitational forces rather than the UGF.
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, Müller, 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.
From the principle of equivalence, Einstein predicted that clocks slow down in a gravitational field. Since the general theory of relativity is based on the principle of equivalence, it is essential to test this prediction accurately. Muller, Peters and Chu claim that a reinterpretation of decade old experiments with atom interferometers leads to a sensitive test of this gravitational redshift effect at the Compton frequency. Wolf et al dispute this claim and adduce arguments against it. In this article, we distill these arguments to a single fundamental objection: an atom is NOT a clock ticking at the Compton frequency. We conclude that atom interferometry experiments conducted to date do not yield such sensitive tests of the gravitational redshift. Finally, we suggest a new interferometric experiment to measure the gravitational redshift, which realises a quantum version of the classical clock "paradox".
The computation of the phase shift in a symmetric atom interferometer in the presence of a gravitational field is reviewed. The difference of action-phase integrals between the two paths of the interferometer is zero for any Lagrangian which is at most quadratic in position and velocity. We emphasize that in a large class of theories of gravity the atom interferometer permits a test of the weak version of the equivalence principle (or universality of free fall) by comparing the acceleration of atoms with that of ordinary bodies, but is insensitive to that aspect of the equivalence principle known as the gravitational redshift or universality of clock rates.
The calculation of the phase shift of a matter-wave interferometer looks different for different coordinate choices or the addition of a uniform gravitational field, but the final result of the observable phase shift does not depend on the coordinate choices or the uniform gravitational field. We find that the phase shift observed in ``Observation of the quantum equivalence principle for matter-waves'' is a magnetic recoil phase shift, similar to the recoil phase shift in light-pulse interferometers. Recoil phase shifts are inversely proportional to the inertial mass and do not depend on the gravitational mass. Our analysis highlights the difference between magnetic and gravitational acceleration in quantum mechanics.
Atomic interference experiments can probe the gravitational redshift via the internal energy splitting of atoms and thus give direct access to test the universality of the coupling between matter-energy and gravity at different spacetime points. By including possible violations of the equivalence principle in a fully quantized treatment of all atomic degrees of freedom, we characterize how the sensitivity to gravitational redshift violations arises in atomic clocks and atom interferometers, as well as their underlying limitations. Specifically, we show that: (i) Contributions beyond linear order to trapping potentials lead to such a sensitivity of trapped atomic clocks. (ii) Bragg-type interferometers, even with a superposition of internal states, with state-independent, linear interaction potentials are at first insensitive to gravitational redshift tests. However, modified configurations, for example by relaunching the atoms, can mimic such tests under certain conditions and may constitute a competitive alternative. (iii) Guided atom interferometers are comparable to atomic clocks. (iv) Internal transitions lead to state-dependent interaction potentials through which light-pulse atom interferometers can become sensitive to gravitational redshift violations.