[smaddox]

I'm curious, do you have an opinion about Stephen Wolfram's idea of graph/knot theory being the underlying principle of reality? To me, it seems much more ontologically acceptable than string theory and many-worlds interpretations of quantum mechanics. I remain unconvinced that pilot-wave-like non-local, hidden-variables interpretations are flawed; they certainly seem the most ontologically tractable. From that perspective, a graph/knot basis for the explicitly non-local hidden-variables theories seems like a reasonable solution to the ultimate basis of physics.

[danbruc]

IANAP and I don't know about Wolfram's ideas but some thoughts anyway. Graphs are incredible general, like sets, you can model almost everything with them and that looks like a bad thing to me if you want explanatory power.

The very few basic principles of relativity and quantum mechanics like the frame independence of the speed of light and unitarity put very strict constraints on possible theories, for example only particles with spin 0, 1/2, 1, 3/2 and 2 are possible. String theory on the other hand turned out to allow a ridicules large number - like 10 to the 500 - of different vacuum states and therefore you can have more or less whatever you want by fixing parameters in this way or another.

I may of course be totally wrong but that were my first thoughts, unless you can somehow derive a lot of constraints, using graphs to explain the universe seems a way to general idea to me. But again, I never read anything about Wolfram's ideas, at least nothing I can remember.

[kordless]

We're running in a simulation that appears to provide compute/causality on one hand and infinite knowledge on the other (albeit limited to short access times). The most logical conclusion is that the software we're running on is highly reliable, given things here are...highly reliable. It's a wonder we all wake up Us in the morning, which is sorta the point. What does it take to write software like that?

[dilemma]

What if it's not a simulation?

[kordless]

What if it's both?

[jules]

The universe does not seem to care all that much about what we find ontologically tractable. Besides quantum mechanics, consider relativity.

[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.