Weak equivalence principle and nonrelativistic limit of general dispersion relations

We study the weak equivalence principle in the context of modified dispersion relations, a prevalent approach to quantum gravity phenomenology. We find that generic modified dispersion relations violate the weak equivalence principle. The acceleration in general depends on the mass of the test body,...

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Bibliographic Details
Published inarXiv.org
Main Authors Hohmann, Manuel, Pfeifer, Christian, Wagner, Fabian
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 29.04.2024
Subjects
Acceleration
Equivalence principle
Parameterization
Phenomenology
Quantum gravity
Relativistic particles
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Summary:We study the weak equivalence principle in the context of modified dispersion relations, a prevalent approach to quantum gravity phenomenology. We find that generic modified dispersion relations violate the weak equivalence principle. The acceleration in general depends on the mass of the test body, unless the Hamiltonian is either two-homogeneous in the test particles' 4-momenta or the corresponding Lagrangian differs from the homogeneous case by a total derivative only. The key ingredient of this calculation is a \(3+1\) decomposition of the parametrization invariant relativistic test particle action derived from the dispersion relation. Additionally, we apply a perturbative expansion in the test particle's spatial velocity and the inverse speed of light. To quantify our result, we provide a general formula for the E\"otvós factor of modified dispersion relations. As a specific example, we study the \(\kappa\)-Poincaré dispersion relation. Comparing the ensuing non-vanishing E\"otvós factor to recent data from the MICROSCOPE experiment, we obtain a bound of \(\kappa^{-1}\geq10^{15}{\rm GeV}/c^2.\).
ISSN:2331-8422