  Can a relativistic quantum field theory be consistently described as a theory
of localizable particles? There are many known issues with such a description,
indicating an answer in the negative. In this paper, we examine these
obstructions by tracing how they (partially) subside in passing to an
approximation of ordinary quantum mechanics in the non-relativistic regime. We
undertake a recovery of the characteristic features of non-relativistic quantum
mechanics beyond simply the Schr\"odinger equation. We find that once this is
achieved, there are persisting issues in the localizability of particle states.
A major focus is on the lingering discrepancy between two different
localization schemes in quantum field theory. The non-relativistic
approximation of the quantum field theory is achieved by introducing an
ultraviolet cutoff set by the Compton scale. The other main undertaking of this
paper is to quantify the fate of ground state entanglement and the Unruh effect
in the non-relativistic regime. Observing that the Unruh temperature vanishes
in the naive limit as the speed of light is taken to infinity motivates the
question: is the Unruh effect relativistic? It happens that this is closely
related to the former issues, as ground state entanglement causes obstructions
to localizability through the Reeh-Schlieder theorem.
