  We describe the picture of physical processes suggested by Edward Nelson's
stochastic mechanics when generalized to quantum field theory regularized on a
lattice, after an introductory review of his theory applied to the hydrogen
atom. By performing numerical simulations of the relevant stochastic processes,
we observe that Nelson's theory provides a means of generating typical field
configurations for any given quantum state. In particular, an intuitive picture
is given of the field ``beable'' -- to use a phrase of John Stewart Bell --
corresponding to the Fock vacuum, and an explanation is suggested for how
particle-like features can be exhibited by excited states. We then argue that
the picture looks qualitatively similar when generalized to interacting scalar
field theory. Lastly, we compare the Nelsonian framework to various other
proposed ontologies for QFT, and remark upon their relative merits in light of
the effective field theory paradigm. Links to animations of the corresponding
beables are provided throughout.
