[smaddox]

Wolfram shows quite convincingly that the key properties of special and general relativity can be captured in a graph model. As for quantum mechanics, most of the ontological complications are a consequence of attempting to abolish nonlocality. If, instead, you model the nonlocality explicitly, as in pilot-wave theories, all of the ontological complications evaporate.

Prior to reading his proposal, I likely would have agreed with you that ontology is lost; I'm less sure now. After reading his ideas, I see a glimmer of hope for discovering a small, simple set of primitives and rules for modeling the universe. A graph/knot-based theory would be composed of far more simple primitives than differential equation based theories; the more abstract differential equation models would arise through statistical mechanics.

[jules]

Pilot wave formulations of QM and graph based or otherwise discrete theories of space are two very different things. The reasons to like the latter are similar to the reasons to dislike the former. At a large scale physics looks continuous, but like matter turned out to be made of atoms, perhaps space is similar. Extrapolating our everyday experience of continuous physics to the fundamental laws may be a mistake. However, that's precisely what pilot wave theories are doing: trying to fit the fundamental laws into our everyday experience and intuition. At the end of the day it doesn't matter which mathematical formalism we use to express the laws, so we may as well use the simplest and most elegant one rather than picking based on our ontological commitments based on our everyday experience. The simplest model also tends to be the one on which further progress is built, like QFT.

By the way, I think in some sense space is already discrete in QM. E.g. for a particle in a box you have a discrete set of states.