Post-Newtonian Hamiltonian description of an atom in a weak gravitational field

Abstract

We extend the systematic calculation of an approximately relativistic Hamiltonian for centre of mass and internal dynamics of an electromagnetically bound two-particle system by Sonnleitner and Barnett [1] to the case including a weak post-Newtonian gravitational background field, described by the Eddington-Robertson parametrised post-Newtonian metric. Starting from a proper relativistic description of the situation, this approach allows to systematically derive the coupling of the model system to gravity, instead of 'guessing' it by means of classical notions of relativistic effects.We embed this technical result into a critical discussion concerning the problem of implementing and interpreting general couplings to the gravitational field and the connected problem of how to properly address the question concerning the validity of the Equivalence Principle in Quantum Mechanics. 1 arXiv:1908.06929v2 [quant-ph]

Palatini f(R) gravity in the solar system: Post-Newtonian equations of motion and complete PPN parameters

“…This is in contrast with a result from Ref. [39]: the reason for the difference comes from nonasymptotically flat effects which should not be considered in PPN, unless a proper explanation on the validity of the method is included. 8 To determine the equations of motion of massive, finite-volume bodies, further details are necessary.…”

“…As expected, whenã 2 andã 3 go to zero, the 1PN metric of GR is recovered. Also, we note that our result for the metric is not in conflict with previous analysis on the PN limit of f (R) Palatini theories using the scalar-tensor equivalence [32,39,40], when the latter are particularized to an analytic f (R) function. On the other hand, the relevant particular case here studied allow us to present all the terms in explicit form and to proceed rigorously with the PPN formalism.…”

“…The latter restriction is essential for finding a picture closer to the standard Will-Nordtvedt PPN formalism [27,28]. Considering the previous analyses of Palatini f (R) gravity in the solar system context [32,34,39,40], our work does not use the equivalence between f (R) and scalartensor theories and, more importantly, we test directly the equations of motion, which is a necessary step since Palatini f (R) gravity leads to new terms in the metric that are not part of the 10 potentials from the standard Will-Nordtvedt PPN formalism.…”

“…For the matter part, we use expressions (32) and (39) and compute u 0 and ρ * up to the second order, namely…”

Light propagation and atom interferometry in gravity and dilaton fields

“…Quantum clock interferometry [19-21, 23, 84-87] is based on a superposition of two different internal states. Even though their eigenenergies are associated with different masses [88][89][90][91] through the relativistic mass-energy relation, the factor Ω/𝜔 𝐶 1 acts perturbatively. Such interferometers are often operated with magic Bragg diffraction [45], which implies Δ𝑘 = 0.…”