  Free electron beams and their quantum coupling with photons is attracting a
rising interest due to the basic questions it addresses and the cutting-edge
technology these particles are involved in, such as microscopy, spectroscopy,
and quantum computation. This work investigates theoretically the concept of
electron-photon coupling in the spatial domain. Their interaction is discussed
as a thought experiment of spontaneous photon emission from a dual-path
free-electron (free-e) beam. We discuss a retro-causal paradox that may emerge
from naively extending perceptions of single-path e-photon coupling to
transversely separated paths, and its resolution through the physics of
two-particle interference. The precise spatial control of electrons and photons
within e-microscopes enables manipulation of their respective states, thus,
such instruments can harness position-encoded free-e qubits for novel quantum
sensing and the transfer of quantum information.
