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"Standard Model has no octonions in it" is politically incorrect, too

Left-wing activists stifle the discussion about anything so much that the Inquisition looks like a fresh air in comparison

My essay about Cohl Furey and octonions has been read by some 6,000 people, higher than the average, but the relative increase of insufferable trolls – and bans per article – was much higher than the increase of the number of readers.

Many people often present the medieval Inquisition as a textbook example of an institution that was preventing the people from researching and even talking about scientific matters. Many Christian readers love to defend or lionize the Inquisition or the Catholic Church and its officially sponsored thinkers – and they occasionally attack the likes of Galileo Galilei.

Make no mistake about it, I am squarely on Galileo's side and I would be on the analogous side even in disputes where science was represented by a less shining man than the founder of science.

However, I find it increasingly obvious that the Inquisition represented the freedom of thought and the open-minded approach to arguments relatively to the left-wing activists that have literally contaminated the whole Planet Earth by 2018.

The Inquisition was trying to preserve some Catholic theses, dogmas, and "ways of thinking" that it considered vital for the preservation of the "system of the civilized world". They were just wrong: this suppression of the freedom of thought wasn't really good – or vital – for the preservation of the civilization. But these protected dogmas were rather special – in some sense, there were just several risky statements that researchers should have been careful about.

For example, in March, I was rather persuaded that Giordano Bruno was burned for his belief in exoplanets. The idea that other planets are analogous to Earth and they're just floating somewhere, independently of ours, was (and is) very clearly dangerous for the perceived centrality of Earth and therefore the centrality of the Biblical God, too.

In the Bible, God said that He was focused on the Earth in one way or another. If the Earth is just one many planets that have nothing to do with each other and move in rather random directions, it was rather stupid for God to focus on Earth, right? The whole thing is rather stupid... and people may keep on thinking, it's dangerous, and Giordano Bruno had to be burned.

There weren't really too many scholars analogous to Giordano Bruno who were burned for heresies related to statements about physical sciences. On top of that, Bruno could be said to be an ideologue of a sort, not a pure scientist. But I think that Bruno was a good, scientifically literate scholar and many of his statements about the structure of the Solar System and the Universe were actually (even) more modern than those of Copernicus, Kepler, and others. Some of the missions searching for exoplanets etc. should be named after Bruno – that would be more appropriate e.g. than Kepler.

OK, the Inquisition was really protecting a few theses that were written at a few prominent places of the Bible. Most other things could have been thought about. If you discussed the atomic theory or its details, people wouldn't even have a clue which of the competing views should be considered "the view sponsored by the Catholic Church" and which of them should be viewed as a potential heresy.

Sadly, it seems to me that the contemporary post-truth, mostly left-wing, octopus is significantly more far-reaching and classifies a huge percentage of the possible statements about science as heresies – or, in the modern terms, as politically incorrect propositions. In some corners, including those claiming to be scholarly ones, people can't say that there is obviously no threat posed by the climate change; all predictions of the apocalypse driven by the population growth or climate change or other things have spectacularly failed; that blacks statistically differ from whites, women from men, and pretty much any two groups defined by similar criteria differ from each other in most respects, sometimes dramatically.

People are harassed for saying anything that could be potentially interpreted as the statement \(X\neq Y\) for any \(X,Y\). And there are lots of other forbidden ideas. I think that the percentage of the forbidden statements is higher than it was during the Inquisition because the present replacement of the Inquisition, the set of obnoxious left-wing trolls who occasionally turn a university or a Soros into their key ally, has defined the only politically correct statements about virtually all topics you may imagine.

I could see that their fanaticism is really extreme because even the following innocent statement has been treated as a heresy:

The Standard Model has no octonionic structures in it and existing papers claiming to prove otherwise are wrong.
This statement has apparently nothing to do with the politically correct dogmas that the left-wing trolls defend by spamming the "mainstream" newspapers and comment sections on the Internet. What is the relationship between octonions and egalitarianism? Well, the problem is that:

Everything has something to do with the left-wingers' sensitive points.

The snowflakes are troubled by basically everything you may say. In this particular case, the reason why octonions became a politically sensitive issue is simple. A deceitful article by Natalie Wolchover connected the success of women in science with the presence of octonions in the Standard Model.

The twisted logic of the PC attack dogs therefore is: If you dare to say that octonions in the Standard Model is pseudoscientific rubbish, you're also against the women in science, and therefore you're a sexist chauvinist pig! It sounds incredible that some people are so fudged up to politicize all things in this way but this is where much of the mankind seems to be evolving.

(Before I banned every troll in that thread, I have verified that every single one of them was motivated by identity politics. Cohl Furey is female but a fair person doesn't care and I have spent much more time by deconstructing pseudoscience written by male crackpots than female crackpots so please give me a break with these ludicrous off-topic accusations and this insane politicization of algebra.)

Even if there were octonions in the Standard Model, it wouldn't do much for (the rational appraisal of the role of) women in science because Ms Cohl Furey just copied all these ideas from the likes of Mr M. Günaydin, Mr F. Gürsey, Mr Geoffrey Dixon, and perhaps a few others and everything that she has added is just irrelevant would-be technical gibberish that changes nothing about the story whatsoever. So not only legitimate physical sciences but even this particular corner of pseudoscience is overwhelmingly dominated by men.

But the more important point is that the octonions in the Standard Model are just an erroneous idea. There is nothing octonionic about or inside the Standard Model of particle physics. And there's no \(G_2\), the exceptional Lie algebra that is the automorphism group of the octonion algebra, inside the Standard Model, either.

95% of the commenters at the Quanta Magazine – who were happily persuaded that there were octonions in the Standard Model – are not only scientifically illiterate. They don't really know how to use a search engine on the Internet. Or they just didn't have the idea that they could try. (Well, maybe most of them just don't want to learn the truth – they prefer the lies they are being served because they decided Ms Furey is great as a person – she's impressive, indeed – or as a political cause and the truth about Nature is secondary.) Just look for octonions and the "Standard Model" on Google Scholar. You will get papers that are decades old.

The most famous paper in the search ends up to be one by our (Frank) Tony Smith, a paper with 40 citations. Tony Smith is great, nothing against him, and I have surely described him as a crackpot, and even if I haven't, I will do it right now: Tony Smith is a textbook example of a crackpot. Still, his papers have some standards and you would find reasons to think that he's a counterpart of the researchers who is working outside the Academia.

If you replace the octonions e.g. by \(SO(10)\), you get a vastly more impressive list of papers. This list is 500 times longer and numerous papers on the first page have over 1,000 citations. That's what it looks like when science has found some actual evidence that there could be a relationship between the Standard Model and something else – in this case, the \(SO(10)\) grand unified gauge group.

You wouldn't need to look for Google Scholar. You could read Cohl Furey's CV or anything. You would find out that she's been writing basically identical papers since 2010. No one has ever done followup research on that because the papers clearly don't make sense according to physicists. Recently, one of the copies of these papers penetrated to a journal – because of a referee's mistake or his sabotage – which was enough for her to get a PhD and land a job. The thirst for female researchers and the corresponding affirmative action has become totally extreme, indeed.

But every sane person could easily figure out that the physicists think it's no good, they have no way how to elaborate on these writings, and nothing can realistically change about the status of these papers, just like nothing could change about the crackpot status of Lisi's papers despite the amazing hype he received from the media.

Alternatively, you may know something about group theory and particle physics. When you have a Lagrangian or an equivalent expression defining the laws of physics, it is really a straightforward exercise to determine the unbroken symmetry group. The Standard Model has the \(SU(3)\times SU(2) \times U(1) / \ZZ_6\) gauge group. Sometimes, there may be hidden symmetries that are broken – such as the grand unified group – or hidden symmetries whose action is nonlocal or otherwise advanced – like the Yangian or enhanced gauge groups in string theory. The discovery of such hidden groups requires some ingenious steps. It's manifest that nothing like that is contained in Furey's and similar papers. One needs minutes to check it for a given paper.

Furey's and similar papers are an algebrology, if I use a Mitchell Porter's term – a counterpart of numerology where symbols for algebraic structures, instead of numbers, are religiously worshiped. But just like in the case of numerology, no actual physical role of the worshiped objects is ever found. What she is actually doing is simply counting the number of components and imagining that the fields of the Standard Model are labeled by labels that smell like directions in the octonions or an octonion-like algebra. But if you rename some fields or components and give them names of the puppies, it doesn't mean that you have found a relationship between the Standard Model and dogs. The case of octonions is absolutely identical to the case of dogs.

The actual characteristic properties of dogs and/or relationships between dogs (with each other or the rest of the world) aren't reflected in any properties or relationships inside the Standard Model. And the same is true for octonions in the Standard Model. So there are really no dogs and octonions in the Standard Model.

There are many concise arguments that instantly prove that the efforts to combine the Standard Model with the octonions are nonsensical. First, the Standard Model is a quantum mechanical theory where all the observables are (and must be) linear maps. And maps are associative. A key, pretty much defining, property of the octonions is that they are non-associative. So the observables cannot be octonions. They cannot be functions of octonions, either.

There could hypothetically be octonions outside observables, the octonions could play a different role. But there's really no known reason why physical objects should make non-associative division algebras useful. There's no known possible physical application of the main nontrivial operation inside octonions, the non-associative product. Something could hypothetically change about this negative statement in the future but there's a more down-to-Earth statement we may be certain about: Furey hasn't changed anything about the physical irrelevance of the octonionic product (yet).

So when she uses the tensor products like \(\HHH\otimes \OO\), the product has no physical implications. The tensor product \(\HHH\otimes \OO\) looks spicy but at the end, it's only used as a generic space \(\RR^{32}\). It's just some 32 real components. The tensor product exists but it inherits no interesting properties from the factors. In particular, the tensor product isn't a division algebra. The octonionic product – which is what makes octonions octonionic – is completely forgotten throughout her papers. So the claim that she has used octonions or found octonions somewhere in the Standard Model is just a sleight-of-hand, an illusion designed to impress those who don't look carefully at all.

The octonions have the \(G_2\) automorphism group, a subgroup of \(SO(7)\). Well, \(G_2\) is surely not a symmetry of the Standard Model. In particular, fermionic fields of the Standard Model don't form full representations of \(G_2\). There are many reasons why they don't. The proposal that "\(G_2\) is a symmetry of the Standard Model" is so ludicrously wrong that you may prove it wrong immediately, in many different ways.

For example, \(G_2\), like \(E_8\), only has real representations. So when you decompose it to representations of \(SU(3)\) etc., you will always find \({\bf 3}\) and \(\bar{\bf 3}\) in pairs. For every color triplet, for example, there will be the antitriplet that has the same handedness under the Lorentz group and the same hypercharge. But the Standard Model is chiral. The left-handed and right-handed quarks and antiquarks (and leptons and antileptons) carry different hypercharges. The hypercharge of the fields has a sign correlated with the field's being in \({\bf 3}\) or \(\bar{\bf 3}\), respectively.

The chirality of the weak nuclear force was discovered in a sequence of deep insights in particle physics half a century ago or so (the violation of C,P,CP etc.). Mathematically speaking, these discoveries have also showed that we need complex – i.e. non-real, non-quaternionic – representations to describe the fermionic fields. (There are no octonionic representations at all because representations are those of associative groups while octonions violate the associativity.) This was a (moderate) revolution and there can't be any full-blown counterrevolution because the previous, innocent, left-right-symmetric image of the Universe was falsified and the falsification is irreversible in physics.

So obviously, \(G_2\) was never used as a grand unified group. It's too small, too. It's ludicrously wrong at many levels. The octonions are a rather sophisticated special algebraic structure but that doesn't mean that they're relevant for the Standard Model – or anything else in Nature that someone finds important. They're not.

I have banned roughly five obnoxious trolls who were attacking me personally for saying that the "there aren't octonions in the Standard Model and papers claiming otherwise are wrong or pseudoscience". In fact, I noticed something remarkable (the octonion wars weren't the first context in which I have noticed that). They find the absence of octonions in the Standard Model so incredibly heretical that they are not even able to repeat my simple statement!

In practice, almost all these trolls have distorted – and incredibly softened – my statements because they would probably die immediately if they dared to repeat my simple statements. So they claimed that I wrote that the octonions weren't "fruitful" in the Standard Model and the future may show that the papers weren't important, and so on.

That's not what I wrote and what I say. I say that the papers are complete garbage, they are demonstrably wrong now, no relationship between the Standard Model and octonions has been found in these papers as they exist, and because these are mathematical facts, nothing can possibly change about these facts in the future. You know, that's one of the glorious features of mathematics (and mathematical physics) that one may unambiguously and permanently say that some statements are right and some statements are wrong – instead of the omnipresent would-be diplomatic fog that the folks from the "humanities" prefer at all times. There's simply zero evidence of a relationship in her papers and a competent physicist who is asked to find octonions inside the Standard Model will end up with the answer "there aren't any", whether or not he is allowed to use the existing literature on similar questions.

Well, most actual physics researchers will leave some room for a possible new discovery in the future and they may choose a welcoming language but when they review the existing papers and understand what is being said, they will agree that the discovery hasn't been made yet.

What's going on is that these fanatical, idiotic trolls are – not so subtly – intimidating us all the time. "You can't possibly say that this paper is wrong," we effectively hear. At most, you may say "you are not completely certain whether this brilliant paper will be fruitful in the year 2100", and even that is an unforgivable heresy.

I am sorry, comrades, but your rules don't apply to me. Furey's and Dixon's papers on octonions are pure crackpottery, they are completely wrong, the chance that something will change about this fact in the future is zero, people who suggest that these papers have the same status as big papers on string theory are just psychopaths, and your fanatical and unfriendly defense of the indefensible and your efforts to silence scientists mean that you are a threat for the civilization and the civilization will either die in a slow death or it will have to look for ways to prevent the material like you from spreading on the surface of Planet Earth.

And that's the memo.

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