Nostr Web Client

nostr:nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqgyewnrnvhqg0dlqmn5mfp0wjcvpkgxycjat9527w8cmf0c6cxwqs9njev0 wrote: "But how do we proceed from there - how do we decide which of these constructions is the best/most interesting/most promising for physics?"

Nobody has a fucking clue, which is why particle physics has been completely stuck since 1980, except for the experimental revelation that neutrinos have mass.

Well, "completely stuck" is a bit of an exaggeration. People are trying lots of things, none of them have worked, but we are still perhaps learning things in this frustrating process. Different approaches succeed to different extents, and the full answer to your question would outline all of what's been done - too long for a post here!

I am trying to follow a particular approach now, which may be wrong but deserves to be tried. Namely, to take the octonions, exceptional Jordan algebra, and so on seriously. This means, for example, taking seriously the fact that a Euclidean Jordan algebra serves as both an algebra of observables and a kind of "spacetime", with a lightcone structure. The consequences of this fact are well-understood for 𝔥₂(ℂ): we get the connection between qubits, spinors, the Riemann sphere, and Minkowski spacetime, some of which is nicely explained in Penrose and Rindler's books.

Maybe we should think about how all this works for 𝔥₃(𝕆).

The fact that the Standard Model gauge group arises from the interplay of 𝔥₃(𝕆) and 𝔥₂(ℂ) feels incredibly suggestive to me.

But I hadn't known where to go with it.

John Carlos Baez 3mo ago

nostr:nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqgyewnrnvhqg0dlqmn5mfp0wjcvpkgxycjat9527w8cmf0c6cxwqs9njev0 wrote: "Also, now I'm curious what these new avenues are!"

In physics we use the Higgs mechanism to explain spontaneous symmetry breaking. Most notably, the electroweak group SU(2) × U(1) breaks down to the subgroup observed at low energies, U(1), via the Higgs field. Here's how: the Higgs field takes values in ℂ², and SU(2) × U(1) acts on ℂ² in a certain way, and the subgroup fixing a nonzero vector in ℂ² is the relevant U(1).

I should look at how a similar mechanism can break the automorphism group of the exceptional Jordan algebra down to the Standard Model gauge group.

Also, I know a lot about how the fermions (i.e., matter) form a representation of SU(5) and how the Standard Model gauge group is the subgroup S(U(3) × U(2)) - see below. I should transfer this knowledge to think about how the fermions show up in the exceptional Jordan algebra approach.

Reply to this note

Discussion