14 years ago
Friday, December 16, 2011
All Quiet On The Front
Pretty quiet around the physics blogosphere, isn't it? Ah, yes, everyone is locked up in the office again, furiously writing about the four color theorem as if it was their idea, even though they only heard about it for the first time yesterday. We should see another arxiv paper onslaught this week, probably triple the size of the superluminal neutrino theory burst.
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I checked out the paper. Cool stuff. The construction seems to boil down to the use of the special Steiner system S(5,8,24). Its automorphisms form the Mathieu group M_24 (an extension of PSL(2,7)~PSL(3,2)), the symmetry group of the Fano plane and Klein quartic). S(5,8,24) is a set of 24 points, with a collection of lines, such that each line contains 8 points and any set of 5 points lies on a unique line.
ReplyDeleteBlocks of S(5,8,24) correspond to Golay code words of weight 8. One can even build the 196,560 minimal vectors in the Leech lattice using the binary Golay code and S(5,8,24). The Leech lattice contains 398,034,000 vectors of norm 8 that fall into 8,292,375 crosses of 48 vectors (24 mutually orthogonal vectors and their inverses, forming vertices of 24-dimensional octahedron). Each cross has the symmetry of the binary Golay code, given by M_24.
An octonionic definition of the Leech lattice was recently given, which uses triples from octonionic 3-space, O^3. Since Steiner systems S(5,8,24) can be mapped to the 8,292,375 crosses of the Leech lattice, each of which can be taken to be the coordinate system of the lattice, the construction by Dharwadker and Khachatryan can be realized in 24-dimensional space.
So instead of considering a bundle of t-Riemann surfaces (as in done in the paper) one can consider a bundle of Leech lattice crosses or small cubicuboctahedron (immersion of tesselated Klein quartic with M_24 symmetry). The latter ways, however, allow one to make contact with the monstrous CFT that has the j-function as the partition function of a chiral worldsheet theory of 24 bosons, compactified on an even self-dual lattice - the Leech lattice. This CFT is dual to the D=3 gravitational theory discussed by Witten back in 2007 (arXiv:0706.3359).
Also, i just read the blog post the author made on Tommaso's blog and could not believe the vigorous assertions that the entire thing was bullshit. I expect nothing less from lubos since his claims that everyone else is a crackpot makes his unselective criteria less than credible to assign such a title to someone. Of course i can't comment on the validity of the article but i do find it a shame how people in the blogosphere seem to so viciously attack others. But then again it does seem to be a common trait among most adult humans that their misdirected anger and frustration with their day to day lives tends to end up being aimed at anyone that threatens their ego. It is behaviour like this which probably impedes advancement in the wider community but i assume more markedly in the paid academic community since this behaviour only encourages herd mentality. Rant over... only stating the obvious i suppose. Feel free not to approve this comment as it might only attract the wrath of the cynical, nasty, bully bloggers out there who can't see past the psychological reasons behind their behaviour and only obey petty primeval ego drives. Guess i'll get to those articles i mentioned before, i think i'll have read them all by the start of next week :)
ReplyDeletevortices1, you cannot possibly take in the current situation in one week! I have been thinking about these things since around 1982, and even I am confused. Non physics comments are usually deleted here, by the way.
ReplyDeleteWonderful, kneemo, you're onto it!
ReplyDeleteI do confess that I had started writing a paper myself on the four color formula! But I have not got to the Leech lattices yet, and I must go into the mountains next week for Newton's birthday. You must write something.
Maybe I will put a brief note on vixra in the next few days. Or maybe not.
ReplyDeleteI would ask a simple question, how many theoretical models could fit/reproduce the mass formula for the Higgs based on different assumptions than those in the four color model of SM?I mean, can SUSY/technicolor/preons/whatever produce such a linear relationship between the mass of intermediate bosons and the Higgs as a "condensate"? I like more the picture when we recant that equation in a "Koide-like" fashion:
ReplyDelete1/2= (M(W+)+M(W-)+M(Z))/M(Higgs)
Moreover, interestingly, the differences with the Koide mass formula is beyond the 1/2 (2/3) the presence of antiparticles ( charged particles) in the mass, and of course the exponent in the masses (1 versus 1/2). Any deep reason about it apart from the fact fermions are "the square root" of boson fields? Very interesting stuff!!!! I am very happy to follow you Kea and learn different uncommon stuff from here!
Juan, yes, the $W$ and $Z$ masses have been used to calculate the EW scale ever since it was invented. However, if this simple rule is the correct one, and a reasonable prediction should be taken seriously by theorists, then it comes from a larger framework that contains many interesting ideas. These ideas should help us create a new context for the formula. As it happens, we like this kind of moonshine mathematics here already, so we are unlikely to run off and study some arbitrary $E_6$ GUT model or $G_2$ thingy a la Kane.
ReplyDeletePlease, Kea. Edit my comment, I can not. I realized I didn't invert correctly the 1/2 factor...
ReplyDeleteI cannot edit comments, Juan. I can only moderate them. Don't worry, I am sure our readers can check basic algebra.
ReplyDelete