Quantum mechanics is an extremely successful and accurate physical theory,
yet since its inception, it has been afflicted with numerous conceptual
difficulties. The primary subject of this thesis is the theory of entropic
quantum dynamics (EQD), which seeks to avoid these conceptual problems by
interpreting quantum theory from an informational perspective.
We begin by reviewing probability theory as a means of rationally quantifying
uncertainties. We then discuss how probabilities can be updated with the method
of maximum entropy (ME). We then review some motivating difficulties in quantum
mechanics before discussing Caticha's work in deriving quantum theory from the
approach of entropic dynamics.
After entropic dynamics is introduced, we develop the concepts of symmetries
and transformations from an informational perspective. The primary result is
the formulation of a symmetry condition that any transformation must satisfy in
order to qualify as a symmetry in EQD. We then proceed to apply this condition
to the extended Galilean transformation. This transformation is of interest as
it exhibits features of both special and general relativity. The transformation
yields a gravitational potential that arises from an equivalence of
information.
We conclude the thesis with a discussion of the measurement problem in
quantum mechanics. We discuss the difficulties that arise in the standard
quantum mechanical approach to measurement before developing our theory of
entropic measurement. In entropic dynamics, position is the only observable. We
show how a theory built on this one observable can account for the multitude of
measurements present in quantum theory. Furthermore, we show that the Born rule
need not be postulated, but can be derived in EQD. Finally, we show how the
wave function can be updated by the ME method as the phase is constructed
purely in terms of probabilities.Comment: Doctoral Thesi