  The central idea of this work is the concept of prespace, a hypothetical
structure that is postulated to underlie the fabric of space or space-time. I
consider how such a structure could relate to space and space-time, and the
implications of the existence of this structure for quantum theory. I compare
space and space-time to other spaces used in physics, such as configuration
space, phase space, and Hilbert space. I support the 'property view' of space,
opposing both the traditional views of space and space-time, substantivalism
and relationism. I argue that configuration space has a special status in the
microscopic world similar to the status of position space in the macroscopic
world. The prespace structure is compared with a computational system, in
particular to a cellular automaton, in which space and all physical quantities
are broken into discrete units. One way open for a prespace metaphysics can be
found if physics is made fully discrete. I suggest as a heuristic principle
that the physical laws of our world are such that the computational cost of
implementing those laws on an arbitrary computational system is minimized. I
discuss the 'measurement problem' of quantum mechanics. Considering how quantum
theory could be made fully discrete leads naturally to a suggestion of how
standard linear quantum mechanics could be modified to give a solution to the
measurement problem, calling this model Critical Complexity Quantum Mechanics
(CCQM). I compare CCQM with some other proposed solutions to the measurement
problem, in particular, the spontaneous localization model of Ghirardi, Rimini,
and Weber. Finally, I argue that the measure of the complexity of quantum
mechanical states introduced in CCQM also provides a new definition of entropy
for quantum mechanics, and suggests an objective foundation for statistical
mechanics, thermodynamics, and the arrow of time.
