PostNewtonian Hamiltonian description of an atom in a weak gravitational field
Abstract
We extend the systematic calculation of an approximately relativistic Hamiltonian for center of mass and internal dynamics of an electromagnetically bound twoparticle system by Sonnleitner and Barnett [Phys. Rev. A 98, 042106 (2018), 10.1103/PhysRevA.98.042106] to the case including a weak postNewtonian gravitational background field, described by the EddingtonRobertson parametrized postNewtonian metric. Starting from a proper relativistic description of the situation, this approach allows us 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.
 Publication:

Physical Review A
 Pub Date:
 November 2019
 DOI:
 10.1103/PhysRevA.100.052116
 arXiv:
 arXiv:1908.06929
 Bibcode:
 2019PhRvA.100e2116S
 Keywords:

 Quantum Physics;
 General Relativity and Quantum Cosmology;
 Physics  Atomic Physics;
 81V17;
 81V45
 EPrint:
 27+4+3 pages (main text, appendix, and references), to be published in Physical Review A. Differences to v1: added references, extended conclusions, corrected typos