## Tuesday, January 3, 2012

### Dharwadker and Khachatryan's prediction of the Higgs boson mass

I foresee that I will be making a series of posts about "Higgs Boson Mass predicted by the Four Color Theorem", which has to be the world champion among crackpot physics papers right now, because they may have predicted the Higgs mass correctly! The formula for the Higgs mass that they offer is very simple ... mH = 1/2 (mW+ + mW- + mZ) ... and for anyone impressed by the result, it might be tempting to appropriate the formula, but try to justify it on some other basis.

However, that's not enough for snarxiv blog. I don't want to leave this stone unturned. So I'm going to be drilling down into the "logic" of the paper, trying to unearth the quasi-deductive process whereby this formula is supposed to follow from Ashay Dharwadker's rather unusual construction. Let's start with what must be the final step in the logic - found on pages 55 and 56:

Since the Higgs particle/antiparticle will be identified (as a Cooper pair), their combined energy would then be the sum of the masses of all other bosons defined on the particle frame. We can have all types of bosons superposed on a single particle frame, and the single Cooper pair of the Higgs particle/antiparticle must be able to attribute energy/rest mass to all types of bosons on this particle frame, by the Higgs-Kibble mechanism. The particle frames of the bosons can be superposed at a point in space-time because they follow the Bose-Einstein statistics. Hence, this Cooper pair must have at least enough energy to attribute the sum of the rest masses of all types of bosons defined on the particle frame. On the other hand, the most important property of Bose condensation is that the Cooper pair of the Higgs particle/antiparticle must have minimum energy, so it can have at most the energy required to attribute the sum of the rest masses of all types of bosons defined on the particle frame. This must be the lowest energy state possible for the Higgs boson when it undergoes Bose condensation.

The "particle frame" is a type of disk structure, illustrated many times in the paper, and all the standard model particles are associated with regions of this disk.

It appears that the logic is as follows: The Higgs boson provides the mass for everything. For some reason, we will suppose that it delivers this mass in the form of a "Cooper pair" made of a Higgs particle and a Higgs antiparticle. The energy must be enough to provide the masses of all the massive bosons. But the energy of the Cooper pair will be a minimum. Therefore "masses of all the massive bosons" = "mass of Higgs particle + mass of Higgs antiparticle" and you get the formula.

The logic is illogical because Cooper pairs don't play a role in the Higgs mechanism, Bose condensation is irrelevant when we are comparing different species of boson, and probably for other reasons too. And that's not even addressing the rest of the theoretical framework, starting with Dharwadker's almost certainly wrong proof of the four-color theorem, which employs the Steiner system S(5,8,24). The symmetry group of S(5,8,24) is the exceptional group M24, a subgroup of the permutation group S24, and it appears that types of particle are associated with permutations, possibly elements of M24. But M24 has about a quarter of a billion elements, so either we're talking about certain special elements, or some very large equivalence classes...

Anyway, I don't know when I'll return to this. Mostly I just wanted to begin to understand how the paper is supposed to work. Usually the theme of this blog is about trying to find more sense than expected in a crazy idea. Here I'm instead analyzing the logic of a paper, ultimately in order to show its flaws - but also just to bring into the open how it's supposed to work. So perhaps this post will help other readers of the paper who want to understand where the prediction comes from, but who are lost among its peculiarities.

I should add that I was driven to look again at the paper by the always interesting Marni Sheppeard, who is taking it seriously.