  High-energy backward ($u$-channel) reactions can involve very large momentum
transfers to the target baryons, shifting them by many units of rapidity. These
reactions are difficult to understand in conventional models in which baryon
number is carried by the valence quarks. Backward Compton scattering is an
especially attractive experimental target, because of its simple final state.
There is currently limited data on this process, and that data is at low
center-of-mass energies. In this paper, we examine the prospects for studying
backward Compton scattering at the future Electron-Ion Collider (EIC). We model
the cross-section and kinematics using the limited data on backward Compton
scattering and backward meson production, and then simulate Compton scattering
at EIC energies, in a simple model of the ePIC detector. Generally, the proton
is scattered toward mid-rapidity, while the produced photon is in the
far-forward region, visible in a Zero Degree Calorimeter (ZDC). We show that
the background from backward $\pi^0$ production can be rejected using a
high-resolution, well-segmented ZDC.
