Friday, July 31, 2015

Today's crackpot synthesis

1. If one assumes that QCD embeds in a GUT group, then one can show that the proton mass mp is proportional to a power of the top mass, mt2/27.

Today I realized that Brannen's reformulation of the Koide relation can be described as follows: the Brannen mass scale of e,mu,tau is mp/3, and the Brannen phase is 3 * 2/27.

2. If the quark families (b,s,d and u,c,t) are treated as Koide triples, their phases are also (arguably) multiples of 2/27.

There is also a "waterfall" of Koide triples, descending from the top, which alternate between the families. One of these triples - s,c,b - has a Brannen mass of mp, and a Brannen phase of 2/3.

3. In Rivero's sBootstrap, the leptons are superpartners of mesons made of the five light quark flavors, and the quarks themselves are superpartners of diquarks made of those five flavors.

I proposed to interpret this as similar to a Seiberg duality. The primordial theory is like six-flavor QCD with one heavy quark and five massless quarks, and N=1 supersymmetry. The other is the standard model, with the light quark masses, the leptons, and the electroweak sector all emerging from the duality.

The leptons would then be the mesinos of the primordial theory, and the phenomenological quarks would be a mixture of the primordial quarks and the diquarkinos.

4. This suggests a way of thinking about the numerology in 1 & 2.

The primordial fact would be that mp ∝ mt2/27 is already true in the QCD-like theory on one side of the duality. The appearance of mp and 2/27 in standard model numerology is then to be attributed to the duality. 1 comes from the "lepton-mesino duality", and everything in 2 from the "quark-diquarkino self-duality".

Monday, March 30, 2015

hep-dada #2

Another transparently fake paper, posted to vixra. Maybe they are coming from David Simmons-Duffin, the inventor of snarxiv, or even from Andrew Bulhak, who wrote the original Postmodernism Generator. Anyway, it gets old fast.

Sunday, March 22, 2015

hep-dada

This blog was originally inspired by the parodies of arxiv abstracts produced by snarxiv. snarxiv in turn reminded me of the Postmodernism Server, which generated whole essays written in bland postmodernese. Now the wheel has turned further and someone has posted to vixra a whole "paper", expanding on a snarxiv-like abstract.

Coincidentally, the Italian net.artist Roberta Betti recently took to tweeting out the text of imaginary papers in mathematics, complete with the typographic mangling produced e.g. by viewing Google's cached copy of such a document. Behold "Canonically Stochastic Fibonacci Spaces Over Matrices", "Existence In Real Logic", and "On the Integrability of Universally Parabolic Lines". Could Betti (aka Stalagmathron) be behind the new vixra paper by "Baruch Seiberg and Claude Witten"? Has someone written a script which generates full-length snarxiv papers? Will vixra now be spammed with cheap machine dada? Time will tell.

edit: @Stalagmathron has disappeared, but some of Betti's earlier work lives on at archive.org

Friday, September 19, 2014

Vik's relation

Over two years ago, a series of posts on tHWZ relations was launched here, starting with the observation that

<ϕ> ~ √2 mt, mt ~ √2 mH

which I was prompted to record, when Andrew Oh-Willeke remarked that

<ϕ> ~ 2 mH

(Where <ϕ>, also often written as v, is the Higgs field "vacuum expectation value".)

Recently a paper appeared on arxiv, noting that first relation, in the form

4 mH2 = 2 mt2 = v2

and Andrew commented that

"I think it is more likely that the observed relationship is really an approximation of the relationships

sum((Fi(^2)=v^2/2 and sum((Bj)^2)=v^2/2 for all fundamental fermion rest masses Fi and fundamental boson rest masses Bj"

which is an aspect of the LC&P sum rule, of which he also says that it is

"quite a bit more profound than the fact that the heaviest fermion by itself accounts for about half of the Higgs vev squared, or that the Higgs mass square accounts for about a quarter of the Higgs vev squared."

I agree that the LC&P sum rule looks to be the fundamental thing here. But there is an interesting final twist which he didn't note.

To recapitulate:

1. The sum of the squares of all the fundamental particle masses, is approximately the square of the Higgs VEV.

2. The contributions to this total from bosons and fermions are approximately equal. (Given the love of supersymmetry in the particle physics community, it really is remarkable that this isn't visibly being talked about.)

3. The top quark is responsible for the great majority of the fermion contribution, and thus about half of the total.

4. The Higgs boson is responsible for about half the bosonic contribution, and thus about a quarter of the total.

So where does the rest of the bosonic contribution come from? It comes from the W and Z bosons. So we have a fifth fact:

5. The W and Z bosons are responsible for the other half of the bosonic contribution, and thus for the remaining quarter of the total.

If we write this up as an equation, we get

mH2 ~ mW2 + mZ2 ~ 1/2 mt2

The first part of this equation appeared as a blog comment by S. Vik, who is apparently a retired physicist from Wilfrid Laurier University in Canada. At the time I gave it a low probability of being meaningful, but I did record it. It would be ironic if it is yet another genuine clue to what lies beneath the standard model.

Friday, September 12, 2014

vixra watch

Many times on this blog I have cited papers from vixra, the alternative to arxiv. Today I just want to note two surprising new additions to the vixra user base, Simon Plouffe and Jacob Barnett. They both have biographies at Wikipedia: Plouffe is, I guess, a computational number theorist, and Barnett is a teenage theoretical physicist who has been in the media since he was 12 (he's 16 now).

Friday, June 27, 2014

Goldfain on LC&P

I record here the existence of two papers by Ervin Goldfain 1 2 claiming to derive the LC&P sum rule.

His concept seems to be that the effective dimension of space-time varies with energy scale, that the masses of SM particles define special scales, and that the LC&P formula follows from a "closure relation" that must connect these different scales.

Incidentally, he is not just talking about spaces with an integer number of dimensions, as in Kaluza-Klein theories or string theories, where e.g. the number of dimensions may increase from 4 to 10 or 11, at energies above the compactification scale. Instead he talks of there being 4+ε dimensions, reminiscent of dimensional regularization... but the modified concept of dimensionality that he really emphasizes is that of fractals.

Informally, one might say that Goldfain's concept is that space is crinkled or creased in a fractal way, so that e.g. the volume of space inside a cube doesn't simply vary as the third power of the side of the cube. Instead, the exponent describing the change in volume is non-integer, and also varies with the size of the cube (length of its side). If we take a cube and shrink it, we might find that as the side shrinks to one millimeter, volume is proportional to size^3.1, but by the time we have shrunk to one micrometer, volume is proportional to size^3.3. Apparently in the world of fractals, such behavior is called multifractal.

The references to millimeter and micrometer above are purely illustrative. Goldfain seems to believe that the first significant deviations from integer dimensionality (4 space-time dimensions) only begin to occur above the electroweak energy scale, which would correspond to distances less than 10^-18 meters.

Goldfain is an independent investigator who publishes at vixra and in various web "journals", but the concept of multifractal space-time isn't just some whimsy of his, it has seen some mathematical development. The real problem I am having with his work so far, is that I don't understand where the "closure relation" comes from - and that's the crucial step towards obtaining the LC&P formula. 

See for example equation 5 in paper "1". The "r"s are the different scales, and the "D" is a fractal dimension. The LC&P formula is a sum of squares, and so if scales were associated with masses, and if D was equal to 2, then we might be able to obtain it from equation 5. 

Goldfain has written other papers trying to obtain SM mass ratios from fractal dimensional flow. A skeptical reading might say that all we have here is a conceptual framework in which multiple length scales can assume a special significance, and since masses can be mapped to length scales in physics, this multiscale conceptual framework can be a playground for a physics numerologist trying to explain particle masses. 

I am skeptical, but dimensional flow is not a bad thing to think about. I will make a follow-up post if I have anything more concrete to add.

Thursday, May 8, 2014

BICEP2 numerology

It's been a while since I've posted. It's been a while since I talked cosmology. And meanwhile BICEP2 came out with what may be the big measurement of the decade, along with LHC's 2012 determination of the Higgs boson mass.

Specifically, BICEP2 has estimated the cosmological "r" parameter, which quantifies the relative magnitude of tensor perturbations and scalar perturbations of the cosmic microwave background, as 0.2. I'll confess that I'm still working out the basic meaning of this quantity. It seems to be a ratio of energies-squared - the square of the energy in the tensor perturbations, divided by the square of the energy in the scalar perturbations. And the physical meaning of squaring the energy may be, that it corresponds to the "work done" by that type of perturbation. So perhaps it would mean that the fluctuations of the inflaton field (which supposedly caused the scalar perturbations) did five times as much work on the CMB photons, as was done by the fluctuations of the gravitational field (which supposedly caused the tensor perturbations). But you should probably ask someone better informed, before believing me about this.

Now there are all sorts of complicated models out there - Higgs inflation... axion monodromy inflation from string theory... - in which people are trying to get an "r" near 0.2. Meanwhile, what are physics numerologists saying? So far, I have spotted two examples of BICEP2 numerology.

First was a vixra paper by Tony Smith, in which Tony estimates "r" as 7/28 = 0.25. 7 and 28 are the dimensions of different algebras which he associates with the tensor and scalar perturbations, respectively, in the context of an octonionic theory of inflation. Of course I don't understand Tony's logic, but an important part is probably the proposition, a few pages along, that "Cl(64) is the smallest Real Clifford algebra for which we can reflexively identify each component Cl(8) with a vector in the Cl(8) vector space". So it all has something to do with space-time qubits and Bott periodicity and self-embeddings.

Then there was a characteristically laconic post by Marni Sheppeard, in which the idea is that "r" is about 1/5, and that this would be a ratio of... dimensions of certain Hilbert spaces, I think, that are relevant for her theory of mass generation in quantum gravity. In her paradigm, space-time is something like a big concatenation of morphisms between these vector spaces. For more, see her papers at vixra.

My "contribution" to BICEP2 numerology is not going to be based on advanced math - though it does build on the observation that 0.2 = 1/5. My thought is just that this is also the ratio of baryonic matter to dark matter densities in the present-day universe. (I'd also like to acknowledge that work by A. Hattawi helped to fix this fact in my mind - that the OM/DM ratio is about 1/5.) So my question is, is there some theory in which this is not just a coincidence?