Wolfram Physics Project

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2021-05-21 17:00:07

This bulletin is a writeup of work done in collaboration with Xerxes Arsiwalla and Stephen Wolfram, as publicly presented and discussed in livestreams here, here and here. This bulletin is intended to be a high-level survey of the effort so far; a more formal article, intended to give rigorous formulations and proofs of the various ideas discussed here, is currently in preparation for submission to an appropriate journal.

The field of “metamathematics”—a term first popularized by David Hilbert in the context of Hilbert’s program to clarify the foundations of mathematics in the early 20th century—may ultimately be regarded as the study of “pre-mathematics”. In other words, while mathematics studies what the properties of particular mathematical structures (such as groups, rings, fields, topological spaces, etc.) may be, metamathematics studies what the properties of mathematics itself, when regarded as a mathematical structure in its own right, are. Metamathematics is thus “pre”-mathematics in the sense that it is the structure from which the structure of mathematics itself develops (much like “pre-geometry” in theoretical cosmology is regarded as the structure from which the structure of the universe itself develops).

In much the same way, the Wolfram Physics Project may be thought of as being the study of “pre-physics”. The Wolfram model is not a model for fundamental physics in and of itself, but rather an infinite family of models (or, if you prefer, a “formalism”), within which concepts and theories of fundamental physics can be systematically investigated and validated. However, one of the most remarkable things that we have discovered over the year or so that we’ve been working on this project is that a shockingly high proportion of the known laws of physics (most notably, both general relativity and quantum mechanics) appear to be highly “generic” features of the formalism, i.e. they are exhibited by a wide class of models, as opposed to being features that are somehow peculiar to our specific universe, as one might otherwise expect. This leads us to the tantalizing possibility that, just as metamathematics aims to explain why mathematics has the structure that it does, the Wolfram model may serve to explain why physics has the structure that it does.

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