  It has often been the case in history that the laws of physics have been used
as the framework for understanding and implementing information processing. The
tacit assumption is that the laws of physics are fundamental and that the
notion of information is derived from these laws. Here we take the opposite
view: the laws of physics are an application of the rules for processing
information. In this dissertation we apply the Entropic Dynamics (ED) framework
to construct a quantum dynamics for scalar fields in space-time. We begin by
considering a toy model consisting of many interacting particles, resulting in
the familiar Schrodinger equation for non-relativistic particles. Using a
similar methodology, we construct a theory of quantum scalar fields in flat
space-time that is relativistic, but not manifestly so. Here we also discuss a
novel way in which the ED of quantum scalar fields appears to evade the
so-called Wallstrom objection. To go further towards constructing a manifestly
covariant quantum ED of fields on a curved space-time, both fixed and
dynamical, we borrow from the "many-time" approaches of P. Weiss, P. Dirac, K.
Kuchar, and C. Teitelboim. For a fixed background the result is a manifestly
covariant ED of scalar fields that is in the spirit of the covariant quantum
theories proposed by S. Tomonaga and J. Schwinger. However, the formalism is
sufficiently flexible so as to allow for the possibility of modeling the back
reaction of the quantum matter fields on a fully dynamical classical
background. The simplest realization of this classical-quantum interaction
shares some formal similarity to semi-classical gravity models, and the
semi-classical Einstein equations, in particular. We consider such a theory and
discuss its plausibility as a candidate for a quantum gravity theory.
