  In this Letter, we discuss the general problem of exciting radiationless
field distributions in open cavities, with the goal of clarifying recent
findings on this topic. We point out that the radiationless scattering states,
like anapoles, considered in several recent studies, are not eigenmodes of an
open cavity; therefore, their external excitation is neither surprising nor
challenging (similar to the excitation of nonzero internal fields in a
transparent, or cloaked, object). Even more, the radiationless anapole field
distribution cannot be sustained without the actual presence of external
incident fields. Conversely, we prove that the Lorentz reciprocity theorem
prevents the external excitation of radiationless optical eigenmodes, as in the
case of embedded eigenstates and bound states in the continuum in open
cavities. Our discussion clarifies the analogies and differences between
invisible bodies, nonradiating sources, anapole scatterers and emitters, and
embedded eigenstates, especially in relation to their external excitation.
