Outsider theories of interest

So far this year, I have taken a particular interest in Eric Weinstein's Geometric Unity. At this point it's probably the kingpin of unified theories from outside the academy. I have a whole blog about it. 

I am also at an early stage of studying Jenny Nielsen's "Topological Unified Field Theory". 

Finally, there is GIFT. This is the most interesting thing I've seen come out of the world of amateurs (non-physicists) using AI. Just to be clear, as of this writing, it does not hold together. But it's like a simulacrum of someone studying a string theory vacuum and getting predictions. The author even has machine learning code trying to approximate compactification metrics! Given the improvement in AI chronicled here over the past few years, it's possible that GIFT could become something fully rigorous, if the author keeps at it. 

One way that could happen, is if via incremental change, it evolved into genuine string theory. "What part of the phenomenologically relevant string landscape is closest to GIFT?" is a legitimate question. Formally it might be closest to something downstream of this paper. However, the author also started with some "numerological" or pure-number intuitions, and it's not so clear what the upshot of that aspect will be. 

The multitude of independent researchers now using AI is a step forward for that whole demimonde, the way that Vixra was, when it first appeared. At the same time, in the West it's the era of DOGE cuts to state-funded research, and populist skepticism regarding experts of all sorts. From the perspective of the academy, it might seem like an intellectual apocalypse in which actual science is being drowned out by AI-generated nonsense. (On X, "String King" suggests that China and Europe will be the centers of good science for the foreseeable future.) 

However... At one point, when she was still alive, Marni Sheppeard wrote that she and various physics dissidents that she knew, seemed to be converging on some common ideas. This was dubbed a "crackpot condensate". In today's world in which millions of diverse independent experiments in human-AI collaboration are being carried out, there's a serious chance that AI will play a role in finally elevating something true out of the babel of would-be theories of everything. 

P.S. I am also engaged in some pure-math studies with T.L., which I will post about when we're ready. 

Artificial numerology

AI produces many different feelings in people. But while I can, let me express the amazement that it is now  possible to go to an AI, feed it this paper and tell it to devise ways in which an absurd numerological connection could actually be the case, and in 1 minute 12 seconds it will propose seven outlandish but still sophisticated proposals. If anyone was paying me to do outlandish physics numerology, I'd be out of a job. 

Zenodo is the new vixra

It's been so long, that the last time I posted here was before the rise of "reasoning models" in AI, which have revolutionized the world of psychoceramics and fringe physics by being able to write the whole paper for you. 

There's much to be said, but I will mention only that Zenodo, as I understand it, was developed as a way for EU researchers to comply with "open science" requirements that they share their data, etc. But it has become a favorite of everyone engaged in "vibe physics" too. 

Alpha-prime arithmeticoids

Kirti Joshi has claimed a proof of the abc conjecture - based on Mochizuki's work. 

@stringking42069 on X-Twitter attacks complacency and corruption in the string theory establishment, from the point of view of a young string theorist who wants to get on with discovery. 

Incidentally, Joshi's work (again building on Mochizuki) involves "arithmetic Teichmuller spaces" that remind me of the moduli spaces of perturbative string theory. 

Earlier thoughts on Mochizuki. 

"Unconceived Teleportation Technology"

 A discussion with ChatGPT reminded me of an earlier post. (And here is the relevant post by Lubos.) 

GPT physics papers, the next generation

This blog began with the idea of treating snarxiv.org's fake physics papers seriously. 

Last year I found a powerful language model on the web (GPT-J), and tried generating whole papers using titles and abstracts generated by snarxiv.org. This was my first attempt; then this was my repeated exploration of a particular topic. 

Five months later, the era of ChatGPT began. (At the same time, the free web version of GPT-J stopped working.) Like millions of other users, I have been conducting many experiments with ChatGPT and Bing. 

But I only just thought of returning to the snarxiv challenge, using this new generation of tools. Here's my first attempt: "Quintessence at the Intermediate Scale Extremizes the Strong CP Problem"

The resulting "paper" has a palpably different flavor to those generated by GPT-J-6B. But first, let me describe how the paper was generated. The paper is too big for a single output from ChatGPT, so first I gave it the title and abstract, and asked it to generate a table of contents, then I manually asked it to generate each item listed in the table of contents, one after the other. 

You will note that it doesn't actually contain any equations or references. The style of the whole paper, in fact, resembles an abstract - merely declaring that certain things will be explained or shown, but not actually delivering on anything promised. 

On the other hand, the texts produced by GPT-J regularly contained both equations and references, but were far less coherent than what ChatGPT has written. 

The difference between GPT-J and ChatGPT is that ChatGPT, after being "pre-trained" on a vast corpus of writings, has then been conditioned so as to consistently present itself in the persona of a helpful assistant. GPT-J, on the other hand, was (I assume) a raw language model with pre-training only: presented with an input, it would immediately attempt to continue in the style and structure implied. As a result, GPT-J would directly output a (fictitious, incoherent) arxiv paper, complete with LaTeX markup. 

ChatGPT is far more logical and coherent in its output, thanks to intensive fine-tuning. As a result, its paper has a genuinely logical structure, but it also doesn't spontaneously produce equations and references, the way that GPT-J did. However, I'm sure it has the capacity to do so, if prompted appropriately. 

In June 2022, I wrote: 

"I suspect that in less than ten years, you'll be able to input a snarxiv abstract into an AI, and almost instantly get back an essay which really does its best to deliver coherently on the promised content."

It's now nine months later, and I think that a little experimentation with the ChatGPT API would rapidly yield papers combining the logical coherence of ChatGPT with the detailed creativity of GPT-J. How close one could come to the quality of a good arxiv paper is a deep question. 

Antipodes of the standard model

The Feynman diagrams employed in perturbation theory represent particular contributions to the quantum sum over histories. Mathematically, they are integrals full of zeta functions and "polylogarithms" and many other interesting numbers and functions. There is even an algebra of ways to combine the diagrams, since particles exiting one scattering process can enter another; this allows two or more diagrams to be combined into one... In recent decades, this hidden world of mathematical relationships has been intensively studied, under the name of amplitudeology. 

One tool used to simplify these very complicated integrals is the "symbol" of the integral. This is something like a list of the elementary variables and functions appearing in the integral. From this list alone, one can reconstruct a significant part of the integral. 

Late last year, it was discovered that the symbol of one scattering process is the reverse of the symbol of another scattering process. That is, the variables and functions appearing in the path integral of the first process, appear in reverse in the path integral of the second process. This was deeply unexpected. The operation of reversing a symbol is formally a part of the "Hopf algebra" of the Feynman diagrams - there is an "antipode" operator that does this - but no one had envisaged that it might be physically meaningful. 

The scattering processes involved come from supersymmetric Yang-Mills theory. However, they have counterparts in the standard model, and the standard model counterparts of the antipodally dual amplitudes are also perplexing. One process is just gluons in, gluons out, but the other one has a Higgs involved along with the gluons. Gluons come from QCD, but the Higgs is associated with the electroweak sector and doesn't carry color charge - what is it doing in there? 

At this point I have nothing to say about the pure math of the antipodal duality, but I shall record a few thoughts about the appearance of the Higgs. 

First, let me clear about how this works in super-Yang-Mills theory. The fields in the "N=4" (fourfold extended supersymmetry) super-Yang-Mills theory studied by the amplitudeologists, can be called gluon, gluino, and sgluon. The gluon is a vector field, the gluino is a fermion field, and the sgluon is a scalar field. When this is mapped to the standard model, I assume that gluinos correspond to quarks, and that it's the sgluon which corresponds to the Higgs. 

Second, I'll mention how a Higgs boson is produced by "gluon fusion", in actual interactions that occur in the hadron collider. Basically, gluons fuse to create one side of a top quark loop, and a Higgs is emitted from the opposite vertex... One may approximate this interaction via a direct "gluon-gluon-Higgs" vertex, and I believe this corresponds to a gluon-gluon-sgluon vertex in super-Yang-Mills. \

OK, so, why would an amplitude with a Higgs in it, have a relationship to a pure QCD process? 

In this blog, I have occasionally touched on ways that strong interaction may be related to the electroweak interaction (in ways different from the usual grand unification of both gauge symmetries into a larger simple group). The idea that electroweak interactions could come from gauging the chiral symmetry of the strong interactions, and that this might naturally be so from a higher-dimensional perspective, is one of which I'm very fond. 

Another possibility is that the Higgs is actually toponium, top quark and top antiquark bound by something. Alejandro Rivero's observation that Z0 decay behaves a little like pion decay may be a point in favor of this, given that the Z0 gets its mass from a component of the Higgs field. 

Matti Pitkänen has suggested that the apparent color/electroweak duality implied by antipodal duality, might have something to do with the famous electric-magnetic duality of super-Yang-Mills. In this regard, I would draw attention to another idea of Alejandro's that has been mentioned many times in this blog, the "sBootstrap" which aims to derive all the fermions of the standard model, as fermionic superpartners of mesons and diquarks made of the five light flavors of quark. 

Out of many attempts to implement this combinatorial idea within a robust theoretical framework, one of my favorites has been Seiberg duality, in which high-energy N=1 super-QCD, resolves at low energies to a different N=1 gauge theory, in which an extra meson superfield has emerged. The idea here is something like this, that at high energies one has N=1 super-QCD with one heavy quark (the top) and five massless quarks, and that at low energies one has six massive quarks, and an emergent electroweak sector, with the leptons arising as mesino components of the meson superfield... But Seiberg duality is itself a form of electric-magnetic duality. 

All of these might serve as starting points, in a quest to confirm and understand, the possible presence of antipodal duality within the standard model. 

"Three Fermion Generations from Octonions": another experiment

On the forums, there is a discussion about papers which try to get the three fermion generations "from octonions", somehow. I decided to seed GPT-J just with the title, "Three Fermion Generation from Octonions". In the end I ran the experiment eight times (in honor of the eight-ness of octonions), seven times at temperature 0.95, and once at temperature 0 (which makes the model deterministic). Here is my distillation of the most coherent ideas in the eight incomplete papers that were generated... 

1: each generation is associated with a different irreducible representation of SU(2), or maybe SU(3)

2: particles are classified by a spinor representation of octonions; generations have a quantum number 0, 1/2, 3/2 

3: links to 'Quantum gravity and charge renormalization' by David Toms

4: electroweak unification 'by considering octonions as the base ring'; quarks and leptons described by complex octonions 

5: in an octonionic free fermion system with three chiral generations, there are fermions with spin 1/2 and fermions with spin 0, and the masses come from 'the imaginary units of the octonions in the appropriate group representations', which are constructed using Young tableaux 

6: 'introduces an important ingredient, crucial for the stability of the compactification, namely a non-polynomial superpotential with a new “hair” for the complex structure of the Calabi-Yau manifold'

7: consider fermions in 4d space deformed by 'the co-product algebra of the octonions'

8 (temperature 0): 'the octonionic algebra is the algebra of the three generations of fermions'

"(P,q) Instantons" by O. H. Silverstein

snarxiv.org was launched in March 2010: a site which generates random imitations of arxiv abstracts. 

This blog was launched in June 2011 with an experiment: What happens if you take snarxiv abstracts seriously? What might the paper accompanying a given abstract, actually be about? 

In June 2020, OpenAI began to make GPT-3 available to the world: a "language model" trained on Internet text, which could write a whole essay, or other verbal production, given a short "prompt" to set it off. 

Now in June 2022, I have used GPT-J, another model inspired by GPT-3, to write a whole fictitious physics paper, using a snarxiv abstract as the prompt. Here is the result. 

The individual sentences make sense, but the resulting paper is not coherent on scales greater than a paragraph. But somehow I suspect that in less than ten years, you'll be able to input a snarxiv abstract into an AI, and almost instantly get back an essay which really does its best to deliver coherently on the promised content. 

A pole star becomes invisible

That Lubos Motl's famous blog, "The Reference Frame", is now closed to the public, deserves comment, since it is the best physics blog there is; the only place you see a physicist of his level, offering frank, intuitive, technical commentary on topics from the perennial (e.g. what is quantum spin) to the misguided (whether that's fads among his peers, or among fans of alternative physics) to the truly new and promising. 

Apparently he had monetized the blog with Google's AdSense; just before he closed it, AdSense kept telling him that various posts on climate, Covid, etc, were no longer acceptable. So it seems he's taken the whole thing private while he decides what to do, and/or has a break from the stresses of maintaining it. 

Maybe he'll be back, maybe not, but the disappearance of such a valuable resource needs to be recorded. 

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. 

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. 

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.  

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.

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.

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"...

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.

Atiyah

Sir Michael Atiyah came out of left field and made sensational claims (proved the Riemann hypothesis, calculated the fine-structure constant) more characteristic of a vixra physicist. And indeed, his Riemann preprint has been uploaded to vixra, though I don't know if it came from him.

I started a forum thread on the physics of his claims. I have not succeeded in properly deciphering his procedure to produce the value of 1/α. The integer part is Eddington meets Bott, but no-one has been able to motivate the next few digits.

But one interesting thing came up in that thread. Atiyah speaks of an iterated process that he calls renormalization, and "Auto-Didact" remarked that it resembles something out of bifurcation theory. And as I have posted here previously, 1/α is approximately equal to 2π times the square of Feigenbaum's constant.

So if - against the odds - there is anything to Atiyah's baroque conceptions, I think it would involve the Feigenbaum connection. But for now, I expect nothing. It was stimulating, it stirred things up, but I think it's a blind alley.

Historical interlude

Yet another subgenre of parodic scholarship has made its first appearance on vixra. An author whose name is Korean for "true history" overturns existing theories of the "Hwan-Suomi hyperwar", a clash of ancient supercivilizations unknown to normies and mundanes, but known to the cognoscenti of 4chan's "History and Humanities" board. Suomi means Finland, but these were hyperborean True Finns, superior to any modern stock; while the Hwan were the ancestral Korean master race, known to us thanks to the Handan gogi, a 20th-century work of "nationalist pseudohistory" (so say the killjoys at RationalWiki). Sometimes, fiction really is stranger than truth.

Koide from S-duality

1) Crackpot idea of the day: "the bottom quark is S-dual to the rho meson".

Gorsky et al conjecture that holographic QCD has a "flavor S-duality" in which vector mesons are dual to baryons. This is to be realized in string theory by a web of 5-branes.

Quark-hadron duality shows a kind of continuity between properties of quarks and properties of hadrons.

And the mass of the rho meson has been estimated at sqrt(6) times the constituent quark mass; while in the simplest version of Rivero's waterfall, the bottom quark mass comes out as 2 . sqrt(6) . sqrt(6) times the constituent quark mass. Also, the Brannen mass scale of the Koide triple containing the bottom quark equals the mass of the proton, the prototypical baryon.

2) Vague bonus idea: Koide relations are an echo of this S-duality.

This just comes from Brannen and Sheppeard's discussion of the discrete Fourier transform, in the context of circulant matrices (they obtain Koide masses as eigenvalues of a circulant). One might start with the realization of geometric Langlands via S-duality, and then look for analogues over finite fields. Sheppeard has occasionally hinted at something like this.