Motional Decoherence of the internal state of an atom by vacuum and thermal fluctuations of a quantum field: Necessity of a fully relativistic treatment

We consider a massive object, such as a neutral atom or an Unruh-DeWitt detector, moving at constant speed in a quantum field and investigate how motion affects the quantum coherence of its internal degrees of freedom, manifesting as quantum dispersion in the absence of a quantum field, and decoherence in its presence. Our investigation aims to serve two purposes: One is to obtain the correct results for these effects, which are essential for the design of quantum information processing schemes where the quantum coherence of an atom's internal degrees of freedom is of major concern. The other is to expose the fallacies in commonplace approaches, which start with a non-relativistic calculation and then add on relativistic ``corrections". We first show a fully relativistic calculation of the internal dynamics based on covariance principles, and then one which ignores these principles, often justified by the atom's slow motion. By a direct comparison of results from these two approaches, we identify {significant discrepancies} in a non-relativistic treatment, even at low atomic speeds. The proper procedure, and a much safer one in terms of accuracy, is recommended here: first derive the dynamics and the necessary regularizations within a fully covariant relativistic framework. Only after the exact, internally consistent equations of motion are established should low-velocity limits be extracted from them. Only in this way can all the relativistic effects which matter: time dilation, aberration, non-inertial mass shifts, be systematically preserved, and accurate results obtained.