What is a theory of everything?

In other words, when someone hands you a theory, how do you know it’s a TOE?

I’m in the awkward position of having a channel called Theories of Everything where I explicate different theories, yet I have never defined this term.

This isn’t as straightforward a question as you may think… To answer it rigorously, we’d need to explore what a “theory” is, what a “thing” is, and what “every” of that “thing” means. Indeed, it means exploring what “unification” even means.

Each of these bolded terms (what’s a theory / thing / every / unification) will be explored in more detail in upcoming Substack posts here, so feel free to subscribe.

Defining unification, for instance, isn’t as undemanding as one thinks, as although it’s commonly said that electromagnetism and the weak force have been “unified” into the electroweak interaction, you can rightfully claim this is not a unification because there’s mixing. John Donoghue said this to me here. There’s still no single interaction with a single coupling in the electroweak case.

So what? Can’t you just extend “unification of X and Y” to just mean “X and Y are brought into a coherent framework”? Sure, but then you have to define what “coherent framework” means, which is equally demanding! Indeed, EM+GR are already coherent with one another (you can write Maxwell coupled to dynamical spacetime), but few would say that standard EM has been “unified” standard GR. A cocktail’s not a marriage… though one may unhappily lead to the other.

There are various lists of contenders to a TOE (I even have a cheeky Top 10 list) but today I’m writing an exposition on what I have not seen before. Namely, a classification of the different kinds of TOEs.

In this article, I won’t be specifying exactly what quantum field theory is, nor the standard model, nor general relativity, nor interpretations of quantum mechanics, nor what a law is, nor what “existence” is, nor what “reality” is. I’ll assume you have a rough understanding, but if you don’t you can click the hyperlinks. If you don’t understand, just nod like everyone else.

Wikipedia Has Six Inconsistent Definitions

If you read the Wikipedia article on “Theory of Everything” closely, you’ll