Friday, July 16, 2021

Serendipitous sum rules

Today I shall report that I am rather more positive than I was, about the second "wrong" idea in the previous post. The reason is that the sum of all the masses in a multiplet, is a quite natural item to appear in a sum rule! So the relation would be, that the sum of the masses of the charged leptons, considered as a multiplet of a flavor or family symmetry, equals the sum of the neutron and proton masses, with the neutron and proton to be considered as an isospin doublet. 

What I still lack is a mechanism. I believe that (for example, in the linear sigma model), nucleon mass can be regarded as originating in the spontaneous breaking of chiral symmetry. Meanwhile, the Higgs-yukawa interactions in the standard model give the fermions their masses, once electroweak symmetry breaking occurs; so one might consider models in which chiral symmetry breaking triggers electroweak symmetry breaking (something which might also explain the order-of-magnitude similarity between the QCD scale and the Fermi scale). 

On the other hand, since the variations among the fermion masses derive from the yukawas, it might seem that the relevant symmetry-to-be-broken is the family symmetry, not the electroweak symmetry... Then there are other hints, like obtaining electroweak symmetry by gauging part of chiral symmetry (something which is formally common in chiral perturbation theory, I think), and the Rivero idea that the leptons are Goldstone fermions, superpartners of mesons. 

In other news, I will mention that snarxiv.org tweeted out a fictitious paper whose content is serendipitously close to other things I have been thinking about. The very first posts on this blog were discussions of snarxiv papers, and if there was nothing else to blog about, I might have talked more about "Special Lagrangian Branes Wrapped on the Moduli Space of Squashed Lens Spaces". But I'll save that for another time. 

Sunday, June 27, 2021

Ideas, right and wrong

There are many things that I could or should post about here. I must mention the terrible news of Marni Sheppeard's death, which is a loss in so many ways. I blog about her when I can. 

There is also a backlog of ideas, waiting to be analysed and sorted. Today I just wanted to mention two lines of thought. 

One is the potential harmony between Rivero's sBootstrap, Dienes's misaligned supersymmetry, and the Veltman-like sum rule of Lopez-Castro - Pestieau - Garces Doz. 

The other is a cluster of thoughts about how to explain the 313 MeV scale in Brannen's version of the Koide formula. The main thought is: maybe it's a kind of Goldberger-Treiman relation. I think that thought is promising. 

Then there are some other thoughts about it which are surely wrong, but which I shall mention here. One is: what if the charged leptons are different forms of a mesino with a rest mass of 626 MeV, undergoing relativistic periodic motion in compact extra dimensions. You may ask: that's alright for the tauon, but what about the electron and muon, whose mass is less than that? Well, the "answer" is that they have imaginary momentum in the extra dimensions, and that overall there are three complex extra dimensions, like a Calabi-Yau... There's no way this is true, but it was too cute to not mention. 

My other wrong thought is this: If you take the trace of Brannen's mass matrix, you find that the sum of electron, muon, and tauon masses, equals two times a nucleon mass. But what if it's really a proton mass plus a neutron mass - the two members of the nucleon isospin doublet? Again, I think it's a cute idea, but it seems very unlikely that this is where the factor of 2 comes from. 

Tuesday, September 1, 2020

Rule of three

This blog started life with an exercise in taking the fake arxiv-like abstracts generated by snarxiv.org, and looking for meaningful interpretations. Nine years later, it's the age of GPT-3, the AI that can write a small essay given an appropriate "prompt". Could GPT-3 be tuned to produce an entire fictitious physics paper, given a snarxiv abstract as prompt? 

In the previous post, I posed the question, why is 𝜋 near the number 3? We may actually have the beginning of an answer. As John Baez discusses, the geometric mean of e and 𝜋 is very close to 3; and Ramanujan proposed an exact formula for that mean, the sum of an infinite series and an infinite continued fraction, which derives in part from the properties of Gaussian distributions. So there may be a deep reason after all.  

Saturday, April 18, 2020

2020 so far

It feels like a long time since I updated here, and I will surely forget some things I wished to mention. But here are a few items:

At vixra, Deep Jyoti Dutta, who I think was 19 when he wrote this paper, took a ratio of masses in deuterium-tritium fusion and found a factor of 𝜋^2. This struck me as something that might be explained in skyrmion theory, e.g. from integrating over a 4-dimensional solid angle.

Also at vixra but not under physics, a serious-but-joking-but-serious made-up religion, "Harmonology". Spoiler warning, the explanation is at the end.

A few months back I asked Math Overflow if there's any explanation as to why 𝜋 is specifically near 3, but the question was removed. This struck me as an odd failure of imagination, in the age of "the field with one element" and all the elaborate mappings of higher number theory. The question itself was inspired by the Church of Entropy's writings on the subject.

There was a recent flurry of events in mainstream and mainstream-alternative math and physics. The great John Conway died, from coronavirus. Stephen Wolfram and Eric Weinstein (see transcript, between 02:11:07 and 02:12:34) came out with their theories of everything. And it was announced that Mochizuki's disputed proof of the abc conjecture would be published in a Japanese journal.

German ex-wunderkind Peter Scholze has taken the lead in western skepticism about Mochizuki's proof. Mochizuki has a grid of copies of a ring, which is supposed to define an "arithmetic deformation theory" (Fesenko's term) based on separating out addition and multiplication. Scholze claims the grid is redundant, and can be replaced with a single copy of the ring, but then Mochizuki's conclusion doesn't follow.

For my part, rather than just believe that Mochizuki needs to answer Scholze, I am hoping to understand the overall argument whereby abc is reached. Mochizuki himself makes the intriguing assertion that an important step is to obtain the "equations"

Nh ≈ h and q^N ≈ q

where you start with an elliptic curve with certain "q-parameters", and construct a simulated elliptic curve with Faltings height h and q-parameters q^N. The step from q^N to q, sounds like knocking out powers greater than 1 (as when one defines the radical Rad(abc)), and the height might play a role in establishing an upper bound (as the abc inequality requires). So maybe the whole thing is a kind of symmetry or duality of Diophantine equations and their crystalline uplifts... I don't know, it's all very interesting but still way beyond me.

But another intriguing thing I found, in Mochizuki's recent expository article (section 4.4), is the idea that western mathematicians have had trouble understanding his work, because their thinking is guided by certain preconceptions about the nature of progress. He mentions two other paradigms, Grothendieck's pursuit of motives, and the Langlands program; whereas he places himself in a third tradition, anabelian geometry.

Since his antagonist Scholze is known as the discoverer of perfectoids, which have been central to the advance of the Langlands program, one might suppose that from a very high perspective, perhaps in a mathematics of the near future, one will think in terms of relations between three kinds of entities, motives, perfectoids, and - perhaps Mochizuki's frobenioids.

Friday, November 8, 2019

The vixra of politics

I keep an eye on vixra.org. Another site I keep an eye on is unz.com. They are an odd couple, and might seem to have nothing in common, except that both were founded by physicists (Phil Gibbs, Ron Unz).

But both serve as a source of shunned news and views. Vixra, of course, started life as a haven for physics papers that were kept off the arxiv. Unz.com, meanwhile, is "A Collection of Interesting, Important, and Controversial Perspectives Largely Excluded from the American Mainstream Media". The powers have no interest in Vixra, it is left to sink or swim on its own, but Unz.com carries material that is considered genuinely dangerous (mostly from the right, but also from the left), and I would be unsurprised to wake up one day and find that it has been taken down by some politically motivated campaign.

Wednesday, April 17, 2019

Vixra oddities of 2019

Obviously I focus on physics here, but sometimes I like to sample some of the other oddities that show up on vixra...

2800+ pages of "a novel hermeneutical science", written in the dense frantic style of someone overflowing with thoughts. Could it be as significant as Hegel or Heisman? Someone would have to try to read it, to find out.

200+ "refutations" of everything under the sun, apparently derived by a system of logic original to the author.

Glimpse of the neo-Vedic world civilization that could exist 500 years from now, latest work of S.V. Balasubramanian, himself a glimpse of the kind of ideas that contemporary India can produce.

A numerologically rich revision of today's physics from small to large, that incorporates the "Kotov cycle" and the "Sternheimer Biological scale factor". What gets me is that there are nine authors. Usually something like this is the work of one person. Though it's always possible that some of those coauthors are there without their consent; there is a note at the end from Atiyah saying, "please do not use my name in any way other than referencing a published paper"...

Friday, January 11, 2019

Uncanny dual

Lubos Motl just posted an essay, "Quantum gravity from self-collisions of the configuration space". It makes an analogy between a property of strings, and how quantum gravity in the larger world may work. Namely, a string may appear to be a self-contained world, but if the worldsheet fields approach the same values as those on another string - or even elsewhere on the same string - then interaction can occur, because both strings are actually moving in a larger space, and having worldsheet fields with the same values, means the strings are at the same place in the larger space.

So Lubos says, this may be a property of quantum gravity in general, that when quantum fields in different places approach similar values, there is some possibility for the formation of a wormhole connecting them.

What has me in mild shock is that this is the best rationale yet for something like Sheldrake's "morphic resonance", and for any number of alleged paranormal phenomena. The attempt to influence something far away by making a copy of it used to be called sympathetic magic, and is sometimes used as an example of pre-scientific or pre-causal thinking. And here we have the perfect mechanism for it!

Furthermore, there's no reason why these connections should be purely spacelike... For more details, see these future thoughts of mine.