tag:blogger.com,1999:blog-4167378123314341202023-01-29T15:55:03.575-08:00theorynot endorsed by snarxivUnknownnoreply@blogger.comBlogger90125tag:blogger.com,1999:blog-416737812331434120.post-52117693569936471052022-08-28T15:40:00.001-07:002022-08-28T15:40:27.801-07:00Antipodes of the standard model<p>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. </p><p>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. </p><p><a href="https://arxiv.org/abs/2112.06243">Late last year</a>, 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 - <a href="https://4gravitons.com/2022/08/26/why-the-antipode-was-supposed-to-be-useless/">but no one had envisaged that it might be physically meaningful</a>. </p><p>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? </p><p>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. </p><p>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. </p><p>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. \</p><p>OK, so, why would an amplitude with a Higgs in it, have a relationship to a pure QCD process? </p><p>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. </p><p>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. </p><p><a href="http://matpitka.blogspot.com/2022/08/antipodal-duality-and-tgd.html">Matti Pitkänen has suggested</a> 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. </p><p>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. </p><p>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. </p>Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-416737812331434120.post-88761546172083215972022-07-02T20:07:00.000-07:002022-07-02T20:07:22.941-07:00"Three Fermion Generations from Octonions": another experiment<p>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... </p><p><a href="https://pastebin.com/XDBBimfQ">1</a>: each generation is associated with a different irreducible representation of SU(2), or maybe SU(3)</p><p><a href="https://pastebin.com/fKBT2EYA">2</a>: particles are classified by a spinor representation of octonions; generations have a quantum number 0, 1/2, 3/2 </p><p><a href="https://pastebin.com/k7x0yeYt">3</a>: links to <a href="https://arxiv.org/abs/0708.2990">'Quantum gravity and charge renormalization'</a> by David Toms</p><p><a href="https://pastebin.com/sFeqZZR8">4</a>: electroweak unification 'by considering octonions as the base ring'; quarks and leptons described by complex octonions </p><p><a href="https://pastebin.com/BAbEvCGg">5</a>: 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 </p><p><a href="https://pastebin.com/PF7Q8zce">6</a>: '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'</p><p><a href="https://pastebin.com/fRe1aQUm">7</a>: consider fermions in 4d space deformed by 'the co-product algebra of the octonions'</p><p><a href="https://pastebin.com/6zwpAxmp">8</a> (temperature 0): 'the octonionic algebra is the algebra of the three generations of fermions'</p><div><br /></div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-416737812331434120.post-8409702372073866592022-06-03T05:45:00.000-07:002022-06-03T05:45:03.785-07:00"(P,q) Instantons" by O. H. Silverstein<p>snarxiv.org was launched in March 2010: a site which generates random imitations of arxiv abstracts. </p><p>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? </p><p>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. </p><p>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. <a href="https://pastebin.com/GeLBMt0v">Here is the result.</a> </p><p>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. </p>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-416737812331434120.post-60285265268499767492022-04-20T06:17:00.001-07:002022-04-20T06:17:10.517-07:00A pole star becomes invisible <p>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. </p><p>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. </p><p>Maybe he'll be back, maybe not, but the disappearance of such a valuable resource needs to be recorded. </p>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-416737812331434120.post-12293003005089494812021-07-16T23:23:00.001-07:002021-07-16T23:23:26.298-07:00Serendipitous sum rules<p>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. </p><p>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). </p><p>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. </p><p>In other news, I will mention that snarxiv.org <a href="https://twitter.com/snarXiv/status/1414555143908044800">tweeted out</a> 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. </p>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-416737812331434120.post-12108824598895775552021-06-27T06:43:00.002-07:002021-06-27T06:43:55.056-07:00Ideas, right and wrong<p>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. <a href="https://sheppeardnotes.wordpress.com/">I blog about her when I can.</a> </p><p>There is also a backlog of ideas, waiting to be analysed and sorted. Today I just wanted to mention two lines of thought. </p><p>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. </p><p>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. </p><p>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<i> imaginary</i> 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. </p><p>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. </p>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-416737812331434120.post-64876198674631921252020-09-01T20:15:00.001-07:002020-09-01T20:15:59.910-07:00Rule of three<p>This blog <a href="http://snarxivblog.blogspot.com/2011/06/another-bad-idea.html">started life</a> 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? </p><p>In the previous post, I posed the question, why is <span style="background-color: white; color: #444444; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px;">𝜋</span> near the number 3? We may actually have the beginning of an answer. <a href="https://golem.ph.utexas.edu/category/2020/08/chasing_the_tail_of_the_gaussi.html">As John Baez discusses</a>, the geometric mean of e and <span style="background-color: white; color: #444444; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px;">𝜋</span> 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. </p>Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-416737812331434120.post-64988881472373482642020-04-18T22:39:00.000-07:002020-04-18T22:39:23.180-07:002020 so farIt 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:<br /><br />At vixra, Deep Jyoti Dutta, who I think was 19 when he wrote this paper, took <a href="https://vixra.org/abs/1906.0518">a ratio of masses in deuterium-tritium fusion</a> 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.<br /><br />Also at vixra but not under physics, a serious-but-joking-but-serious made-up religion, <a href="https://vixra.org/abs/2004.0242">"Harmonology"</a>. Spoiler warning, the explanation is at the end.<br /><br />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.<br /><br />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 <a href="https://theportal.wiki/wiki/A_Portal_Special_Presentation-_Geometric_Unity:_A_First_Look">transcript</a>, 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.<br /><br />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.<br /><br />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"<br /><br />Nh ≈ h and q^N ≈ q<br /><br />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.<br /><br />But another intriguing thing I found, in <a href="http://www.kurims.kyoto-u.ac.jp/~motizuki/Alien%20Copies,%20Gaussians,%20and%20Inter-universal%20Teichmuller%20Theory.pdf">Mochizuki's recent expository article</a> (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.<br /><br />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.Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-416737812331434120.post-14577666601382256542019-11-08T16:59:00.001-08:002019-11-08T16:59:28.901-08:00The vixra of politicsI 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 (<a href="http://inspirehep.net/author/profile/P.E.Gibbs.1">Phil Gibbs</a>, <a href="https://www.unz.com/author/ron-unz/topic/theoretical-physics/">Ron Unz</a>).<br /><br />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.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-416737812331434120.post-82592626685261857702019-04-17T22:11:00.003-07:002019-04-17T22:11:39.521-07:00Vixra oddities of 2019Obviously I focus on physics here, but sometimes I like to sample some of the other oddities that show up on vixra...<br /><br />2800+ pages of <a href="http://vixra.org/abs/1903.0499">"a novel hermeneutical science"</a>, 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.<br /><br />200+ <a href="http://vixra.org/author/colin_james_iii">"refutations"</a> of everything under the sun, apparently derived by a system of logic original to the author.<br /><br />Glimpse of the <a href="http://vixra.org/abs/1901.0363">neo-Vedic world civilization</a> that could exist 500 years from now, latest work of <a href="http://vixra.org/author/sai_venkatesh_balasubramanian">S.V. Balasubramanian</a>, himself a glimpse of the kind of ideas that contemporary India can produce.<br /><br />A numerologically rich <a href="http://vixra.org/abs/1904.0218">revision of today's physics from small to large</a>, 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"... Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-416737812331434120.post-84317275859060022262019-01-11T15:37:00.000-08:002019-01-11T15:37:14.511-08:00Uncanny dualLubos Motl just posted an essay, <a href="http://motls.blogspot.com/2019/01/quantum-gravity-from-self-collisions-of.html">"Quantum gravity from self-collisions of the configuration space"</a>. 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.<br /><br />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.<br /><br />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!<br /><br />Furthermore, there's no reason why these connections should be purely spacelike... For more details, see these <a href="http://snarxivblog.blogspot.com/2028/03/fractal-order-beneath-spatio.html">future thoughts of mine</a>. Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-416737812331434120.post-30569506386014361512018-09-28T04:49:00.000-07:002018-09-28T04:50:41.715-07:00AtiyahSir 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.<br /><br />I started <a href="http://www.physicsforums.com/threads/atiyahs-arithmetic-physics.956055/">a forum thread on the physics of his claims</a>. 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.<br /><br />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.<br /><br />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. Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-416737812331434120.post-85161851220413748992018-09-05T22:53:00.001-07:002018-09-05T22:53:06.602-07:00Historical interludeYet 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 <a href="http://vixra.org/abs/1809.0081">"Hwan-Suomi hyperwar"</a>, 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 <i>Handan gogi</i>, a 20th-century work of "nationalist pseudohistory" (so say the killjoys at RationalWiki). Sometimes, fiction really is stranger than truth. Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-416737812331434120.post-46047350225411822062018-06-13T00:46:00.003-07:002018-06-13T00:46:58.610-07:00Koide from S-duality1) Crackpot idea of the day: "the bottom quark is S-dual to the rho meson".<br /><br />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.<br /><br />Quark-hadron duality shows a kind of continuity between properties of quarks and properties of hadrons.<br /><br />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.<br /><br />2) Vague bonus idea: Koide relations are an echo of this S-duality.<br /><br />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. Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-416737812331434120.post-62394228866683445192017-09-05T22:29:00.003-07:002017-09-05T22:29:58.645-07:00Various news III would divide my physics development into two stages, one in which I was studying general frameworks like quantum theory, and another in which I was interested in the details of particle physics. As discussed <a href="http://snarxivblog.blogspot.com/2014/01/numerology-from-m-theory.html">here</a>, it was Marni Sheppeard who really set me on the second road, when she exhibited her decomposition of the CKM matrix in terms of circulants, and I wondered if this could be obtained from F-theory. But it was Alejandro Rivero who ended up being my biggest stimulus in that way - trying to implement his ideas and constructions led me to learn a lot of orthodox theoretical physics.<br /><br />Two weeks after Carl Brannen returned to vixra, Sheppeard has come out with her first <a href="http://vixra.org/abs/1709.0035">phenomenology paper</a> in years. <a href="http://sheppeardnotes.wordpress.com/2017/09/06/neutrino-phenomenology/">My thoughts:</a> I disagree with most of the details, but the spirit of it is something to emulate.<br /><br />Meanwhile, <a href="http://a.rivero.nom.es/families-from-so32/">Rivero's constructions</a> have reached the point where they all but single out <a href="http://www.thespectrumofriemannium.com/2017/08/11/log196-superbootstrap/">specific string vacua</a> for investigation. For me, the most valuable ideas are still some of the earlier versions, but it's impressive that he has come this far. Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-416737812331434120.post-53530819100862713842017-08-23T05:23:00.001-07:002017-08-23T05:23:32.136-07:00Various news1) Carl Brannen once made a <a href="http://www.brannenworks.com/MASSES2.pdf">great discovery</a>: the circulant representation of the Koide relation, with parameters a phase of 2/9 radians, and a mass scale of about 313 MeV. Koide <a href="http://arxiv.org/abs/0706.2534">acknowledged</a> (section 3.1) the phase relation, but deemed it too difficult to explain for now.<br /><br />Brannen has now <a href="http://vixra.org/abs/1708.0267">returned to the subject</a>. His overall philosophy may be seen at <a href="http://brannenworks.com/">his site</a>, especially in the "Operator Guide". I do not endorse his framework, but it may help the reader understand his latest paper, and whether it does contain any new progress.<br /><br />2) There was a <a href="http://www.physicsforums.com/threads/effective-mass-to-charge-ratio-of-electroweak-or-qed-vacuum.919032/">PF thread</a> on gravitational vacuum polarization in which the author attributed significance to the sum of the squares of all particle masses. That is the LC&P formula for the square of the Higgs vev. <br /><br />In the "General physics" category at arxiv (its counterpart of vixra), two papers (<a href="http://arxiv.org/abs/1705.11068">1</a> <a href="http://arxiv.org/abs/1708.05612">2</a>) on obtaining the fine-structure constant from consideration of "virtual parapositronium in the vacuum". It could be bogus but it reminds me of various speculations here about the criticality of <span lang="grc">α<sub>em</sub>. </span>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-416737812331434120.post-4213055876280655162017-05-25T17:41:00.002-07:002017-05-25T17:41:46.913-07:00Feigenbaum meets Feynman III am skeptical about the relationship described in the previous post, but it would be beautiful if true. And there has been progress towards making it plausible.<br /><br />Perhaps the clearest way to classify the available theoretical approaches is how they interpret the doubling cascade. Feigenbaum's constant has the rather abstract meaning, of describing "how quickly" a dynamical system goes from a regime of stasis, to switching between two states, to switching between four states (and so on through powers of two, until chaos is reached), as a control parameter is adjusted. How could that be relevant to the probability that an electron emits a photon?<br /><br />Angel Garces Doz (who has already appeared many times in this blog) in effect <a href="http://vixra.org/abs/1705.0355">proposes</a> to identify the doubling cascade with the cloud of virtual particles - iterated creation of virtual pairs. He points out that the size of the bulbs budding from the Mandelbrot set also diminishes according to Feigenbaum's constant, and says, let's think of spherical wavefunctions in the virtual cloud in this way. It's a brilliantly vivid intuition.<br /><br />Meanwhile, I found that Mario Hieb's discovery had already appeared (in a different form) in papers by Vladimir Manasson (<a href="http://arxiv.org/abs/nlin/0609043">2006</a>, <a href="http://arxiv.org/abs/0803.3300">2008</a>). His idea is that there is a prototypical self-organizing system (e.g. think of a soliton), that has 1-state, 2-state, 4-state... forms according to the value of some parameter, as in the doubling cascade. His idea is that the different elementary particles correspond to the different states, and that the levels of the cascade correspond to the fundamental forces. The Feigenbaum ratio, describing how the control parameter changes from one level to the next, maps to the relative strength of the forces!<br /><br />Finally, I take inspiration from <a href="http://arxiv.org/abs/1608.06638">Sergei Gukov</a>, for whom the doubling cascade describes the proliferation of fixed points in a renormalization group flow, as some property of a QFT varies. I am also intrigued by the criticality of the Higgs boson mass in this regard.<br /><br />I am wondering whether - for example - you could have dissipative "hypermagnetization" (hypercharge magnetization) of the QCD vacuum in the early universe, passing through a doubling cascade of dynamical regimes, and ending in a top quark condensate that breaks electroweak symmetry, leaving only the familiar electromagnetic interaction, with Feigenbaum's constant somehow imprinted on the size of the electromagnetic coupling. Unknownnoreply@blogger.com3tag:blogger.com,1999:blog-416737812331434120.post-2829870837050390642017-04-28T05:05:00.001-07:002017-04-28T05:05:38.676-07:00Feigenbaum meets FeynmanIn quantum field theories, virtual particles cause quantities like the couplings to "run" with energy scale. Amateur physics numerologists find formulas for the low-energy values, but the professionals expect that these quantities will take their simplest form in some high-energy unified theory, so professional physics numerology involves the high-energy values.<br /><br />The low-energy values - which are the quantities that are measured and listed in the physics databooks - are therefore regarded as being equal to "simple high-energy value + messy correction full of logarithms etc". However, there is the phenomenon of the "infrared fixed point". This occurs when the dynamics of the running (as described by a beta function) converges on the same low-energy value, for a range of starting values at high energy. In the language of dynamical systems theory, this means that the beta function enters an attractor at low energy.<br /><br />This strikes me as one of the few ways in which amateur physics numerology might be realized within an actual quantum field theory: an attractor might dictate simple relations between the low-energy values. I have no examples of low-energy numerology being realized in this way, but it's a possibility.<br /><br />It is therefore exceptionally intriguing to see some low-energy numerology which utilizes a famous constant from dynamical systems theory, Feigenbaum's constant. <a href="http://vixra.org/abs/1704.0365">Mario Hieb has noticed</a> that<br /><br />(2 pi) times the fine-structure constant ~= 1 / (Feigenbaum's constant squared)<br /><br />to 1 part in 1000.<br /><br />It's a very attractive formula. It's simple, "2 pi" is a very "physical" factor, and the fine-structure constant is the epitome of what we would like to explain. Still, I wonder how mathematically difficult it is to obtain this within a QFT.<br /><br />Feigenbaum's constant describes the approach to chaos - the rate at which a point attractor bifurcates, as a control parameter varies. It does show up in the theory of phase transitions, which sounds like QFT, but so far I only see it appearing in an indirect way, as part of a formula for some Lyapunov exponents.<br /><br />It's unclear how one would go from that, to the constant appearing with such simplicity, in a formula for a coupling. Also, I have not found any work on infrared fixed points in which a weak U(1) coupling is part of the attractor.<br /><br />But I admit that my survey of the possibilities so far is preliminary and superficial. So, maybe it has a chance of being true. Unknownnoreply@blogger.com19tag:blogger.com,1999:blog-416737812331434120.post-43840559199110372842017-04-10T13:16:00.000-07:002017-04-10T13:16:13.202-07:00vixra watch: April foolsarxiv 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 <a href="http://vixra.org/abs/1703.0300">"Un-collider"</a>, 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 <a href="http://www.math.columbia.edu/~woit/wordpress/?p=9187&cpage=1#comment-225395">promoted</a> it at "Not Even Wrong"), and it has all the professionalism of a proper arxiv parody paper.<br /><br />There was another parody uploaded at the same time, on <a href="http://vixra.org/abs/1704.0001">"gauge theology"</a>, but it's merely clever, and doesn't have the sting of the Un-collider.<br /><br />Finally (for now), yet another paper has appeared, promising <a href="http://vixra.org/abs/1704.0106">"a Hodge-theoretic analysis of reinforcement learning"</a>. 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.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-416737812331434120.post-51253310029942511872017-03-07T03:00:00.000-08:002017-03-07T03:17:13.802-08:00Two problemsThere was unexpected progress, posted at Physics Stack Exchange, on two problems that were low on my list.<br /><br />First, <a href="http://snarxivblog.blogspot.com/2016/05/proton-charge-radius.html">numerology of the charge radius</a>. See my <a href="http://physics.stackexchange.com/a/254114/1486">2017 update</a>: 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.<br /><br />Second, <a href="http://snarxivblog.blogspot.com/2013/08/weak-interaction-bootstrap.html">mystery of the Z0 decay width</a> - 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, <a href="http://physics.stackexchange.com/a/316947/1486">something turned up</a>. Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-416737812331434120.post-51081388516329976342017-02-10T02:45:00.000-08:002017-02-10T02:45:12.959-08:00tHWZ - latest formulationDuring a discussion at PF, I found the following interesting way to think of these quantities:<br /><br />m<sub>H</sub> ~ √2 m<sub>Z</sub><br />m<sub>t</sub> ~ 2 m<sub>Z</sub><br />H<sub>vev</sub> ~ 2 √2 m<sub>Z</sub><br />m<sub>W</sub> ~ √7 / 3 m<sub>Z</sub><br /><br />The last one may look a little odd, but it allows us to approximate sin<sup>2</sup> of the Weinberg angle as 2/9.<br /><br />The impetus was <a href="http://www.physicsforums.com/threads/top-higgs-higgs-vev-relation-from-conformal-symmetry.768598/#post-5684753">a comment by @arivero</a> in which he pointed out that a tHWZ mass estimate due to Hans de Vries implies<br /><br />(m<sub>W</sub><sup>2</sup> - m<sub>H</sub><sup>2</sup>) / (m<sub>Z</sub><sup>2</sup> - m<sub>t</sub><sup>2</sup>) = 3/8<br /><br />Now in many GUTs, at the GUT scale, we have that<br /><br />m<sub>W</sub><sup>2</sup> / m<sub>Z</sub><sup>2</sup> = 3/8<br /><br />So it's as if (m<sub>W</sub><sup>2</sup> - m<sub>H</sub><sup>2</sup>) / (m<sub>Z</sub><sup>2</sup> - m<sub>t</sub><sup>2</sup>) is almost invariant under renormalization group flow, with m<sub>H</sub> = m<sub>t</sub> = 0 at the GUT scale.<br /><br />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.)<br /><br />Unfortunately I don't see how any of this makes sense in terms of Hans de Vries's original physical hypothesis.<br /><br />Anyway, I find that the LC&P formula also works neatly using the four approximations. And I would remark again that m<sub>Z</sub> is very close to <a href="http://snarxivblog.blogspot.com/2016/01/h-z-susy.html">the standard model's μ parameter</a>. Unknownnoreply@blogger.com6tag:blogger.com,1999:blog-416737812331434120.post-71955084038430274202016-08-24T13:25:00.001-07:002016-08-24T13:25:53.440-07:00Multifractal worldsheetThe 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.<br /><br />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?<br /><br />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 <a href="http://backreaction.blogspot.com/2016/08/what-if-universe-was-like-pile-of.html">lists a few others</a> 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".<br /><br />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 <a href="http://snarxivblog.blogspot.com/2014/06/goldfain-on-lc.html">multifractal</a> surface that is 4d on large scales but 2d on small scales?Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-416737812331434120.post-5226969130429911132016-07-09T02:46:00.002-07:002016-07-09T02:46:32.236-07:00A formula for αOn page 4 of <a href="http://arxiv.org/abs/0801.2562">"Naturally Speaking"</a> 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: <br /><br />α = { α<sub>s</sub> sin<sup>2</sup>θ<sub>W</sub> (b<sub>1</sub>−b<sub>3</sub>)+3/5 cos<sup>2</sup>θ<sub>W</sub> (b<sub>3</sub>−b<sub>2</sub>) } / (b<sub>1</sub>−b<sub>2</sub>) + higher-order terms. <br /><br />"Here, the fine-structure constant α, the strong coupling constant α<sub>s</sub> and the weak mixing angle θ<sub>W</sub> are evaluated at the same renormalization scale and b<sub>1,2,3</sub> are the gauge β-function coefficients. Higher-order terms cannot be neglected to achieve a prediction that matches the experimental accuracy."Unknownnoreply@blogger.com4tag:blogger.com,1999:blog-416737812331434120.post-51609747650472327162016-05-14T04:02:00.000-07:002016-05-14T04:02:32.231-07:00Higgs, top, 750 GeV IIThe idea that the 750 GeV anomaly might be a top-antitop bound state has been taken to a new level by <a href="http://arxiv.org/abs/1605.03909">Froggatt & Nielsen</a>, 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.<br /><br />So things may be about to get serious there. Meanwhile, I want to enumerate a few relationships which <i>are</i> still just numerology, but have the potential to be part of a genuine theoretical synthesis.<br /><br />m<sub>H</sub> ~ m<sub>t</sub>/<span class="st">√2</span><br /><span class="st">H<sub>vev</sub> ~ 2 m<sub>H</sub></span><br /><span class="st">m<sub>375</sub> ~ 3 m<sub>H</sub></span><br /><span class="st">m<sub>750</sub> ~ 6 m<sub>H</sub></span><br /><span class="st"><br /></span><span class="st">m<sub>H</sub> is the Higgs boson mass, m<sub>t</sub> is the top quark mass, H<sub>vev</sub> is the Higgs field vev. m<sub>750</sub> is the mass of the 750 GeV particle. m<sub>375</sub> is the mass of a 375 GeV particle that Lubos may have found in the data. </span><br /><br /><span class="st">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. </span>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-416737812331434120.post-16786207231056419092016-05-11T05:36:00.000-07:002016-05-11T05:36:43.951-07:00Higgs, top, 750 GeVIt is a long-standing idea that the Higgs might be a top-antitop bound state. (I have proposed a <a href="http://www.physicsoverflow.org/35142/higgs-as-toponium-bootstrap">bootstrap version</a> of this idea.)<br /><br />My credence for that idea has just gone way up, now that I have discovered another long-standing proposal, that there might be <a href="http://www.physicsforums.com/threads/higgs-top-resonances.856586/#post-5470425">a light bound state of 6 tops and 6 anti-tops</a>. 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.<br /><br />I had already wondered if the <a href="http://snarxivblog.blogspot.com/2015/12/lhc-bump.html">LHC bump</a> 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...Unknownnoreply@blogger.com4