  It has long been debated whether gravity should be quantized or not.
Recently, the authors in [Sci. Rep. 6, 22777 (2016); Proc. Natl. Acad. Sci.
U.S.A. 106, 3035 (2009)] discussed the inconsistency between causality and
complementarity in a Gedankenexperiment involving the quantum superposition of
massive/ charged bodies, and Belenchia et al. [Phys. Rev. D 98, 126009 (2018);
Int. J. Mod. Phys. D 28, 1943001 (2019)] resolved the inconsistency by
requiring the quantum radiation and vacuum fluctuations of
gravitational/electromagnetic field. Stimulated by their works, we reanalyze
the consistency between the two physical properties, causality and
complementarity, according to the quantum field theory. In this analysis, we
consider a Gedankenexperiment inspired by [Sci. Rep. 6, 22777 (2016); Proc.
Natl. Acad. Sci. U.S.A. 106, 3035 (2009); Phys. Rev. D 98, 126009 (2018); Int.
J. Mod. Phys. D 28, 1943001 (2019)], in which two charged particles coupled
with a photon field are in a superposition of two trajectories. First, we
observe that causality is satisfied by the retarded propagation of the photon
field. Next, by introducing an inequality between visibility and which-path
information, we show that the quantum radiation and vacuum fluctuations of the
photon field ensure complementarity. We further find that the Robertson
inequality associated with the photon field leads to the consistency between
causality and complementarity in our Gedankenexperiment. Finally, we mention
that a similar feature appears in the quantum field of gravity.
