An Examination of Quantum Foundations

Abstract

Quantum foundations is a field of diverse goals and methods. In this thesis, I will present three different approaches to quantum foundations, each emphasizing a different goal or perspective. The causaloid framework has the goal is to use insight from quantum foundations to study quantum gravity. Ontic models are a tool used to study realist theories of quantum mechanics from an operational quantum information perspective. Nelson's mechanics is a derivation of the Schrodinger equation using the machinery of stochastic mechanics.

As each of these approaches has different set of goals, they are suited to different purposes and have different limitations. From the causaloid, I construct the concept of causally unbiased entropy and at the same time, find an emergent idea of causality in the form of a measure of causal connectedness, termed the Q factor. In the ontic models framework, I reproduce the generalization of the concept of contextuality. For Nelson's mechanics, I examine its relationship to Bohmian mechanics - a realist formulation of quantum mechanics.

I will then examine the relationship of these different approaches to one another. From this examination I will introduce the concept of physical contextuality in order to ask whether contextuality could be more than just a mathematical artifact. I also include a discussion of the property of deficiency in ontic models and its relation to contextuality given certain constraints.