In the previous post I drew attention to the fact that M12 contains a finite version of SU(3), or more precisely of PSU(3), that contains the binary tetrahedral group that has been the main point of my models of physics in the past few months (or even years). You will have noticed that my efforts to get SU(3) out of the binary tetrahedral group, in order to model the strong force, might appear contrived, and might not be entirely convincing. There might therefore be some point in extending the model to this finite version of PSU(3), or even SU(3), in order to include the strong force in a more “natural” way.
I will start by considering PSU(3), as a subgroup of M12, so that it has an action on 12 fermions, grouped as 3×4 as explained in the previous post, and on 12 bosons, grouped as 3+9, breaking to 3+1+8 on restriction to the binary tetrahedral group. There may be some point in extending to the full SU(3), which can be found inside the Weyl group of E_6, and which may therefore relate to the various E_6 models in the literature. It all depends on how we can interpret the normal subgroup of order 9 in PSU(3), or the normal subgroup of order 27 in SU(3).
First of all, if we interpret the 12 fermions as above, then we do not appear to have any explicit “colours” for the quarks, but we have a group of order 9 that acts as generation symmetries. There is no single element that acts simultaneously as generation symmetries on all four types of particles, but each element acts on three types of particles, and not on the fourth. If you think about it, then something like this is essential, in order to cope with the fact that generations of quarks do not behave in the same way as generations of leptons. So let us take two specific generation symmetries, one that acts on electrons but not on neutrinos, and one that acts on neutrinos but not on electrons. The former changes the mass on the electrons, does nothing to neutrinos, and presumably therefore also changes the mass of the quarks. The latter, on the other hand, does nothing to the electrons (so does not change their mass), and changes the generation (flavour) of the neutrinos (but without a detectable change in mass), so presumably also has an undetectable effect on the quark masses.
Well now, as far as the quarks are concerned, what is the difference between this symmetry and the colour symmetry? Can you see any difference? I can’t. As far as the electrons are concerned, it does nothing, so it is again the same as the colour symmetry on electrons. Only on neutrinos do we see a “flavour” symmetry instead of a “colour” symmetry. Is this a deal-breaker for this model, or is it a hint that the “flavour” of a neutrino is really a “colour”, and that the labels have been accidentally switched at birth? Of course, the Standard Model insists that flavours of neutrinos are really generations and not colours, but where is the experimental evidence for this? I don’t think there is any, because this is just a theoretical assumption built into QCD.
Mathematically, the assumption that there is a “generation” symmetry that acts on all four types of fermions, and a “colour” symmetry that acts on just two, is inconsistent with the existence of the weak force, with an SU(2) gauge group containing the essential isospin symmetry group Q_8. The only way that group theory allows two triplet symmetries of “generation” and “colour” to work together is if each triplet symmetry acts on three of the four triples. Of course, this is not an argument I can win, against the accumulated “might is right” attitude of thousands of mainstream physicists. I know, because I tried it ten years ago, and gave up. But it is an argument that is correct, and strongly supported by experiment, which confirms that neutrinos and quarks have a “colour” symmetry that does not affect the mass, and that electrons and quarks have a “generation” symmetry that does affect the mass.
More importantly, it is essential that neutrinos have a colour rather than a generation, in order to allow the “colour” to leak out of nucleons, without which there can be no (quantum) force of gravity between nucleons. Yes, you heard me right, a quantum theory of gravity is impossible unless the neutrinos have a colour, in order to glue together nucleons across the vast expanses of space and time. The colour of the neutrinos is the gravitational field. I’ve said it before, and I’ll say it again. You can call me a crackpot all you like, and you can try and pretend that my mathematics is not relevant to your physics. But the lesson of history is that physicists who ignore the simple but powerful arguments of mathematics are consigned to history. Mathematics is an imperious queen, and does not brook dissent.
January 1, 2024 at 11:53 am |
Those physicists who treat mathematics as a handmaid instead of a queen have forgotten the story of Cinder Ella. You see, Ella is short for Electron, and the two big fat ugly sisters are called Muon (because she mews like a cat) and Tau(rus), who is obviously a cow (or perhaps a bull in drag, since this is pantomime season).
Don’t believe any of the nonsense about the “glass” slipper, which is a mis-translation of “verret”, assumed to be French but really a dialect version of the English “ferret”, so they were fur slippers, not glass slippers. I am sure you will agree that is much more reasonable.
Slippers come in pairs, like neutrinos and antineutrinos, and so the story is about finding the foot that this neutrino fits. The ugly sisters tried using strong force, but the neutrino didn’t fit. Ella used weak force, and the neutrino fitted perfectly.
The ugly sisters tried the Up, Down and Sideways (or strange) quarks, without success. Ella used the Charm, Truth and Beauty quarks instead. So, you see, the story of Cinder Ella is really the story of particle physics. And the Truth, Beauty and Charm of mathematics win over the Ugly, Stupid and Dysfunctional models of physics in the end.
And they all lived happily ever after.
January 1, 2024 at 2:14 pm |
Not forgetting the Ella-gance of mathematics, of course.
January 1, 2024 at 2:16 pm
Or should that be Cinderellagance?
January 1, 2024 at 10:35 pm |
I didn’t understand your reply comment on the previous post, that symmetry groups are not the way forward, while you use of Mathieu group M12 to model particles. Maybe M12 is related to symmetry groups?
My issue is that the strong interaction is well modelled by SU(3), weak interactions by SU(2). There are problems with mixing, symmetry breaking, masses and other fiddled parameters, and (in my outrageous/outraged view) the issue that there is no symmetry group included for dark energy/gravity, but really there is evidence symmetry groups are part of the big picture.
January 2, 2024 at 8:31 am |
Perhaps I didn’t express myself very well. I agree that symmetry groups are of the essence of the theory. The question is, *which* symmetry groups. I am far from convinced that the Standard Model has got the right groups. The post above is an argument that SU(3) is not the right group, but that it is really PSU(3). This is a subtle change as far as physics is concerned, because both groups have the same Lie algebra, and it is only the Lie algebra that is used in the Gell-Mann matrices in the Standard Model. So I am not sure if anyone has really considered the possibility of using PSU(3) as the symmetry group for the strong force, rather than SU(3).
Certainly the octonion cult is firmly wedded to SU(3), so that they embed SU(3) in SO(8) rather than PSU(3). This doesn’t appear to be a conscious decision, but rather a lack of awareness that there is another possibility. It probably goes right back to Gunaydin and Gursey, and has been followed by everybody else ever since. This is odd, because the initial explorations along these lines, using SU(3) to generalise to Georgi-Glashow SU(5) and Pati-Salam SU(4), clearly failed to produce realistic models of physics. Yet it still goes on, and people like Furey are still working on SO(10) models after half a century of failure, judging by her latest three posts to the arXiv.
So I think I am going to have to write a complete new post about the embedding of PSU(3) in SO(8), explaining how the octonions crowd have got it all wrong.
January 2, 2024 at 12:31 pm |
Furey’s “Algebraic Roadmap of Particle Theories” is a perfectly good map of some perfectly useless theories. She’s looking at the wrong roads.
January 2, 2024 at 1:11 pm
Full of sound and Furey but signifying nothing?
January 2, 2024 at 1:39 pm
Full of math and theory, but signifying nothing?
January 2, 2024 at 11:42 am |
“Nature’s No Match for Maths”
The maths are simply beautiful
And surely *must* be right
And Nature must be dutiful
And prostrate in their sight
It’s simply *inconceivable*
That groupies could be wrong
And Nature ain’t believable
If ugly is her song
January 2, 2024 at 12:04 pm |
There is a powerful lobby that disagrees with this sentiment, of course. Hossenfelder’s “Lost in Math” argues that beauty is an unreliable guide. I would argue, however, that Hossenfelder is an unreliable guide. See my next post, in which I argue that the octonion nuts have got too little beauty in their models, not too much.
January 2, 2024 at 12:06 pm
The problem, of course, is not in the “Math”, it is in the “Lost”.
January 2, 2024 at 12:09 pm
Just as the problem with the Gruppenpest is not the Gruppen but the Pest.
January 2, 2024 at 12:20 pm
The problem is not the groups, but the groupies.
If Nature plays grunge but the groupies like classical, never the twain shall meet.
January 2, 2024 at 12:31 pm
The Nature of Nature” (riffing on Forest Gump)
Nature gist?
Or “Nature” buzz?
Nature is
What Nature does
“Nature” = the magazine, of course
January 2, 2024 at 12:37 pm
I say magazine, you say journal
Magazine, journal
Let’s call the whole thing buzz
January 2, 2024 at 1:05 pm
Beauty is in the lie of the beholder.
January 2, 2024 at 1:32 pm
I don’t really follow Hossenfelder, but Is Sabine part of the Fossil Physics lobby?
January 2, 2024 at 12:26 pm |
Quite. The groupies only consider classical (Lie groups). Nature is not interested in Lie groups.
January 2, 2024 at 12:34 pm |
“Nature” plays only classical music. Nature is not subject to such arbitrary rules.
January 2, 2024 at 12:40 pm |
Nature is natural,
“Nature” is nurtural,
“Relativity” is special,
Relativity is spatial.
January 2, 2024 at 12:54 pm
Nice.
By the way, did you know that C. elegans is a hermaphroditic roundworm?
Quite the dancing partner at a ball, I imagine
January 2, 2024 at 1:43 pm |
I don’t follow Hossenfelder much either. She’s certainly dabbled in non-fossil topics like super-determinism and emergent gravity, but I stopped reading her blog after a while as it seemed rather too fossilised for my taste. I heard she came down on the side of “GR/DM is correct and the wide binary tests prove nothing”, which pretty much confirmed that I had made the right decision.
January 2, 2024 at 1:52 pm |
“Full of math and theory but signifying nothing” is a stone that could be thrown at many things, but perhaps my house is made of glass…
January 2, 2024 at 1:53 pm
…unlike Cinderella’s slipper, of course.
January 2, 2024 at 3:19 pm
One thing is certain: C. elegans is as slippery as glass
January 2, 2024 at 3:34 pm |
Don’t you mean as slippery as a ferret?
January 2, 2024 at 3:14 pm |
Nature’s Twisted Nature”
It’s claimed “assisted twistor”
Is Nature’s basic beat
But Nature’s “Twisted Sister”
And maths are in defeat
January 2, 2024 at 4:49 pm |
There once was a fellow called Witten,
Who by the theory of strings was smitten,
(“That’s not even wrong” –
The refrain of Woit’s song.)
Not once shy, but twice bitten.
There once was a fellow called Woit,
Who said “This cannot be roight,
This string isn’t strong,
It’s not even wrong.”
Lee Smolin agreed: “Quoite roight!”.
January 2, 2024 at 7:25 pm
Isn’t it spelled “Quoit Woit”?
As in “Spacetime is Woit-handed”
January 2, 2024 at 7:27 pm
Oops, there went my news years revolution.
Oh, well, there’s always next year
January 2, 2024 at 7:57 pm |
Ah yes. You’re quoite woit. Moy mistike.
January 2, 2024 at 11:31 pm |
OK, so you suggest PSU(3) which is a subset of M12. The problem here is that a google search for PSU(3) and M12 produces one paper by Larry Finkelstein written in 1979 which might as well be in double Dutch (or a contribution to Bertrand Russell’s “Principia mathematica” (I’ve always thought he reversed the title of Newton’s work to make clear his book was the exact opposite…). I’m not familiar with this.
In looking at standard model particles in terms of how to how to unify leptons (like neutrinos) and quarks, and what charges or masses they have, I’d suggest taking a look at fig 24 at the bottom right of p30 and fig 34 on p44 of https://vixra.org/pdf/1111.0111v1.pdf (ignore the remainder of the paper for the present). (This paper is a compilation of decades of collecting useful insights, it’s not off the cuff conjecture/speculation.)
The key thing is to start by ignoring the fractional “electric charges” of quarks because they’re emergent from the very large vacuum polarization shielding of a pair or triplet of quarks. The Rosetta is the Omega Minus is a triplet of strange quarks with the electric charge -1, so the strange quarks are all -1/3.
But look at the maths in this: the you have in close proximity THREE similar electric charges, which must physically produce a vacuum polarization (pairs of charged virtual fermions which align to shield the core charge within) THREE times stronger than a single charge would produce. Hence, the strange quarks hypothetical isolated electric charge is 3 x (-1/3) = -1, the same as the electron.
Sure, you can’t isolate a quark, but my point is that the theory used to get “fractional charges” is bunk because it doesn’t take account of the difference between the strength of the vacuum polarization shielding electric charges of a single lepton like the electron, and a triplet like the omega minus, a triplet of identical electric charges! So there’s your quark-lepton unification.
What happens to the missing “shielded” energy? The virtual particles acquire this energy, adding to their survival time beyond the Heisenberg’s t = ℏ/E (virtual fermions only exist between UV and IR cutoff energies, which translate into distances out to ~33 fm). So this acquired electric field energy allows them to briefly behave like real particles, obeying Pauli’s exclusion principle and thus gaining a quasi nuclear shell structure (near the UV cutoff where virtual quark pairs exist) and a quasi electron structure further out (nearer the IR cutoff where electron-positron pair production occurs). Simple calculations prove this predicts particle masses: Table 1 in https://vixra.org/pdf/1408.0151v1.pdf
Now back to https://vixra.org/pdf/1111.0111v1.pdf at Fig 34 in the middle of p44 (this figure should be in colour, but isn’t, follow the grey lines). Conventionally, Fermi’s point theory of beta decay says a muon decays into an electron, and strange quarks decay into upquarks. But when the W- propagator was added to Fermi’s theory, an anomaly emerged (compare top half of diagram to bottom half): if a muon decays into an electron, then the corresponding Feynman diagram shows a strange quark decaying also into an ELECTRON. I rest my case, your honour. Beware mainstream self-contradictory quackery.
January 3, 2024 at 5:02 pm |
I don’t know what to make of this at all. But there is something very odd going on in the mathematics, which makes it look as though the up/down/strange triplets that gave rise to the original 8-fold way should really be up/down/muon triplets. This doesn’t make much sense to me, but maybe it makes sense to you? Certainly the muon mass and the sum of the strange+down+down quark masses are equal to within experimental uncertainty, so maybe the strange quark is just what’s left when you try and subtract a couple of down quarks from a muon? Just something “virtual”, rather than a real particle? I don’t know.
January 3, 2024 at 5:19 pm
What it needs is someone to take a fresh look at the actual evidence for standard model particle charges (which depends on how you calculate them regarding vacuum polarization shielding), masses (does the polarized vacuum contribute most of the mass?), what happens to the energy of fields that are screened by vacuum polarization (it’s becomes short-ranged field quanta, e.g. the nucleus is held together by virtual pions as in Yukawa’s model, in a very simple way like air pressure forces are down to bombardment by air molecules, so “quantum tunnelling” is just the stochastic nature of the field quanta).
Woit kindly sent me an email suppling his 1980s papers, but didn’t reply on this topic, about correcting interpretational errors in SM orthodoxy before trying to see what the real experimental data is (nobody has ever seen a -1/3 charged quark directly; it’s value is simply implied by a faulty analysis only). Prof. Clifford Johnson (a string theorist) replied that he “hadn’t thought about” such mechanisms of the vacuum polarization. Distler tried to make complex numbers in the optical theorem of QFT an excuse to ignore physical mechanisms entirely (note my mass gap paper https://vixra.org/abs/1408.0151 uses the Laplace transform not the complex Fourier transform). Warren Siegel (string theorist) replied on nuclear physics, but only trying to obfuscate the simple virtual pion mediated nuclear binding energy by arguing that there are loads of different virtual mesons etc at higher energy (which are simply not relevant for the nucleus distance scale, where pions dominate), etc.
January 3, 2024 at 5:28 pm |
You could well be right about that – but I’m now out of my depth in physics and can’t contribute meaningfully to that part of the discussion.
January 3, 2024 at 9:57 pm
It’s up to you, but as a mathematician, you may have an advantage in not being brainwashed by data-alloyed-to-ad hoc theory, if you ever decided to investigate in the future. It’s not as if there’s mountains of stuff out there anyway, the anomalies stick out like sore thumbs even when wallpapered over or covered up
January 3, 2024 at 10:05 pm |
Yes, that is true. There are quite a few anomalies that do indeed stick out like sore thumbs, and that I have put serious thought into. There may well be some others that it would be worth my while to think about, but I’m not aiming to resolve all of them at once. However, it seems clear that the problems are so deep that it is probably impossible to solve one of them without essentially solving them all.
January 3, 2024 at 10:23 pm |
I noticed that you pointed to a “joke” suggestion that the W/Z mass anomaly might be a US/Europe geographical anomaly. I took this suggestion a little more seriously, because at some point one or other of these anomalies is going to be a smoking gun for quantum gravitational interference. So in my book, every anomaly must be investigated for the possibility of interference from QG. Which means, since we haven’t got a theory of QG, investigating mysterious correlations with classical gravity. In this particular case, I didn’t find the smoking gun I was looking for. But that doesn’t necessarily mean it isn’t there, and it doesn’t mean we shouldn’t look for it.
January 3, 2024 at 9:10 am |
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