Monday, April 10, 2017

vixra watch: April fools

arxiv sees a few joke papers on April 1st every year. vixra was created as a repository for papers blocked from arxiv. We may now have the first parody paper posted to vixra because it wouldn't survive on arxiv. It's a proposal for an "Un-collider", that not only mocks numerous aspects of contemporary physics culture, but also today's political and geopolitical situation. The authors are "Snowden" and "Ellsberg" (the latter promoted it at "Not Even Wrong"), and it has all the professionalism of a proper arxiv parody paper.

There was another parody uploaded at the same time, on "gauge theology", but it's merely clever, and doesn't have the sting of the Un-collider.

Finally (for now), yet another paper has appeared, promising "a Hodge-theoretic analysis of reinforcement learning". I thought that one might be real - making such a connection is not beyond the reach of vixra authors, or of arxiv authors, or even of reality. But the paper merely reproduces the abstract, which says "we begin with a diagram" illustrating the connections. That there is no diagram, is perhaps a way of saying that there is no connection. Then talk of inducing entropy in an economy makes it sound fake, and the final straw is that it's classified as "Relativity and Cosmology". So, another joke paper; perhaps someone testing the vixra submission procedure.

Tuesday, March 7, 2017

Two problems

There was unexpected progress, posted at Physics Stack Exchange, on two problems that were low on my list.

First, numerology of the charge radius. See my 2017 update: I ran across a model of the nucleon in which the radius is 4 natural units, divided by the mass. That doesn't explain why the radius comes out a little different for muonic hydrogen compared to electronic hydrogen; but it can explain why dandb's ratio is approximately 4 in both cases.

Second, mystery of the Z0 decay width - that it lies on the same curve as a number of mesons. It's one of @arivero's minor observations, and not one that I spent any time on. I was just going through the motions of investigating it, when to my surprise, something turned up.

Friday, February 10, 2017

tHWZ - latest formulation

During a discussion at PF, I found the following interesting way to think of these quantities:

mH ~ √2 mZ
mt ~ 2 mZ
Hvev ~ 2 √2 mZ
mW ~ √7 / 3 mZ

The last one may look a little odd, but it allows us to approximate sin2 of the Weinberg angle as 2/9.

The impetus was a comment by @arivero in which he pointed out that a tHWZ mass estimate due to Hans de Vries implies

(mW2 - mH2) / (mZ2 - mt2) = 3/8

Now in many GUTs, at the GUT scale, we have that

mW2 / mZ2 = 3/8

So it's as if (mW2 - mH2) / (mZ2 - mt2) is almost invariant under renormalization group flow, with mH = mt = 0 at the GUT scale.

We could even speculate that my set of four approximations above is an infrared fixed point. (The approximations are not exact, but one could think of these as valid at tree level.)

Unfortunately I don't see how any of this makes sense in terms of Hans de Vries's original physical hypothesis.

Anyway, I find that the LC&P formula also works neatly using the four approximations. And I would remark again that mZ is very close to the standard model's μ parameter

Wednesday, August 24, 2016

Multifractal worldsheet

The opinion is spreading that the real discovery of the LHC was that the Higgs boson mass is special. The most impressive prediction was Shaposhnikov and Wetterich 2006, which got the right value from the assumption that gravity is asymptotically safe.

This creates cognitive dissonance for anyone who appreciates the string-theoretic model of quantum gravity. Asymptotic safety isn't even consistent with the holographic principle, is it?

Well, asymptotic safety is one of several heterodox approaches to quantum gravity in which the dimension of spacetime seems to change from 4 to 2 at the smallest scales. Sabine Hossenfelder lists a few others and says, "It is difficult to visualize what is happening with the dimensionality of space if it goes down continuously, rather than in discrete steps".

Fractals can have non-integer dimensionality. But they are typically embedded in a larger space. Meanwhile, in string theory, one has a 2d worldsheet embedded in a "target space" that usually has more than two dimensions. So what if the world sheet embeds in the target space as a multifractal surface that is 4d on large scales but 2d on small scales?

Saturday, July 9, 2016

A formula for α

On page 4 of "Naturally Speaking" by G.F. Giudice, after a short list of numerological formulas for the fine-structure constant α, one finds a formula for α according to physical orthodoxy, i.e. grand unification. I reproduce it here for the edification of passing numerologists: 

α = { αs sin2θW (b1−b3)+3/5 cos2θW (b3−b2) } / (b1−b2) + higher-order terms.

"Here, the fine-structure constant α, the strong coupling constant αs and the weak mixing angle θW are evaluated at the same renormalization scale and b1,2,3 are the gauge β-function coefficients. Higher-order terms cannot be neglected to achieve a prediction that matches the experimental accuracy."

Saturday, May 14, 2016

Higgs, top, 750 GeV II

The idea that the 750 GeV anomaly might be a top-antitop bound state has been taken to a new level by Froggatt & Nielsen, who have sketched a whole phenomenology for their particle. The reasoning is "crude" (their word), but still on a much higher plane than any mere numerology of masses.

So things may be about to get serious there. Meanwhile, I want to enumerate a few relationships which are still just numerology, but have the potential to be part of a genuine theoretical synthesis.

mH ~ mt/√2
Hvev ~ 2 mH
m375 ~ 3 mH
m750 ~ 6 mH

mH is the Higgs boson mass, mt is the top quark mass, Hvev is the Higgs field vev. m750 is the mass of the 750 GeV particle. m375 is the mass of a 375 GeV particle that Lubos may have found in the data. 

The picture I get is that the Higgs field is a top quark condensate, the 750 is a sort of loose bound state of 6 Higgs bosons (that is a "1S" toponium when analyzed at the level of quarks), and the 375 is like the 750 but with only half of the available top states occupied.

Wednesday, May 11, 2016

Higgs, top, 750 GeV

It is a long-standing idea that the Higgs might be a top-antitop bound state. (I have proposed a bootstrap version of this idea.)

My credence for that idea has just gone way up, now that I have discovered another long-standing proposal, that there might be a light bound state of 6 tops and 6 anti-tops. The number 6 appears because the top quark has two spin states and three color states, so this is the maximum number of tops in the same wavefunction that is allowed by the Pauli exclusion principle.

I had already wondered if the LHC bump at 750 GeV was somehow 6 Higgs bosons bound by top loops, since 750 GeV = 6 x 125 GeV, the Higgs mass. But if the Higgs is already a top-antitop bound state...