  Stochastic mechanics (SM), as proposed by Edward Nelson and others in the
20th century, aims to reconstruct quantum mechanics (QM) from a more
fundamental theory of classical point particles interacting with a
classical-like ether, where said interaction causes the particles to undergo a
diffusion process that conserves their average total energy. However, Timothy
Wallstrom and others have emphasized that SM runs into the problem that it
cannot recover the Schroedinger equation of QM unless an ad hoc quantization
condition is assumed. In this thesis, I reformulate SM so that the quantization
condition arises as a natural consequence of the classical point particles
interacting with the classical-like ether. This is done by combining SM with a
proposal by Louis de Broglie and David Bohm, in which an elementary particle in
its rest frame is viewed as a localized periodic phenomenon of fixed frequency,
from which it follows that the phase of the periodic phenomenon in the lab
frame satisfies a relation that's equivalent to the quantization condition. In
doing so, I argue that SM can once again be regarded as a viable approach to
reconstructing QM. In addition, I show that SM yields novel and empirically
viable models of semiclassical Newtonian gravity and electrodynamics, simply by
incorporating classical Newtonian gravitational and electrostatic interactions
between the particles. I also show how the Schroedinger-Newton equation and the
Schroedinger-Coulomb equation arise as mean-field approximations from within
these SM models of semiclassical Newtonian gravity and electrodynamics, and how
classical Newtonian gravity can be recovered from an appropriate center-of-mass
description of many interacting SM particles. Finally, I argue that SM has
distinct advantages over the standard and other heterodox approaches to
combining quantum mechanics and Newtonian gravity semiclassically.
