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Calculation of particle masses without string theory is implausible

...or any comparably deep advance in fundamental physics...

Anna V has mentioned a seemingly interesting March 10th Greek talk about a paper that claims to calculate the elementary particle masses with 1% precision out of some gravitational attraction between objects matching the ideas of a schoolkid at an elementary school.

Off-topic, experiment: the gravitational force has been measured down to 50 microns (the distance between the two masses), Newton may relax, he is still OK.

Usefulness of colliders outside HEP: accelerators' superconducting RF cavities may be helpful to build quantum computers. Also, quantum information theorists talk to quantum gravitists about wormholes which is right although I don't quite understand what's the new insight here
The paper is childish nonsense, of course. You can't answer difficult questions like that with the elementary school algebra (and ideas). The authors have obviously not understood the difficulty of the problem – which is not far from the completion of a theory of everything – even at some vague qualitative level. To derive particle masses, you almost surely need to use the Standard Model gauge group, the representation theory for the particles, non-diagonal mass matrices and their eigenvalues, and probably also the renormalization group running, aside from many other hard components. It's almost guaranteed that very simple formulae with the 1% precision can't exist and even if the final low-energy masses could be given by a miraculously simple formula, you can't possibly derive or justify such a formula from some understanding of particle physics which seems absent in the paper.

As far as I can see, the authors haven't even understood the vast range that the masses span i.e. the hierarchy. They're described by various hierarchies, including the hierarchies in the Yukawa couplings and, in their case, also the standard hierarchy between the weak scale and the Planck scale (which they claim to use). And even a qualitative answer to the question "why those parameters seem so vastly different" seems extremely difficult.

The hierarchy problem has been studied by a huge fraction of theoretical particle physicists for half a century, they have used a lot of ideas and difficult tools, and there's no "clearly winning" solution to explain the hierarchy, not even qualitatively. Would you really believe that some elementary formula written down by Greeks suddenly answers these questions? Then you're a gullible victim of anti-scientific populism. Trivial formulae for hard problems could be nice for you but they're wrong – or it's impossible for them to be right.

The paper also makes some specific statements that just look self-evidently wrong. Like the claim that the neutrino mass is dictated by "gravitational confinement". Nice but two nearby neutrinos still have a much higher force from the exchange of Z-bosons etc. Gravity is the weakest force, you know, and may be neglected, especially for the lowest-mass fermions in Nature.

It seems almost absolutely implausible to me that such questions may be answered without some usage of string theory; I will justify and reiterate this point at the end of this text. Soon, I will also turn my attention to a today's stringy paper that says something about the particle masses calculated from a string theory model.

You know, I have an advantage. I know what it means to be a part of the group that has some expertise and believes that this expertise is needed to answer questions from some ambitious enough class; but I also know damn well what it means to be an absolute outsider and a research solitaire. In contrast with all the lies about "group think" of string theorists, I have had no one in Czechoslovakia or Czechia whom I could meaningfully talk to about string theory – up to my undergraduate years. But I still independently converged to the conclusion that it's at least a necessary step towards the complete theory of everything and wrote some papers as an undergrad.

Without pretending that I am not bragging, if you know another physics paper written by one undergrad and no one else that has over 300 cits, let me know. ;-)

But I have been trying to calculate the elementary particle masses since the age of 9 or so. At the beginning, I was intrigued by the tables of those masses and considered protons and electrons elementary (screw QCD). Numerology was good enough for me so I also independently found the formula \(m_p/m_e\approx 6\pi^5\approx 1836.15\). The naivite of such attempts became increasingly clear when my understanding of fundamental physics was getting deeper.

While the non-existence of the absolute final answer as of 2020 may be discouraging, there are some aspects of the problems that we need to solve on one side; and the tools and abilities of string theory on the other side – that almost completely match. It's only string theory where the 4D gauge groups but also global symmetries may be derived from a deeper starting point, where you may interpolate between effective QFTs that have totally different groups, spectra, and other properties. And string theory manages to produce models that have all the required particle types and interactions at energies well below the Planck scale – Higgs-like and inflaton-like scalars, spin-1/2 fermions including the chiral ones, gauge bosons, but also gravitons (plus their superpartners in the intriguing cases).

Some 10-20 years ago, people who couldn't produce any valuable insights in physics started to spread the left-wing memes that we always need "alternatives" or "diversity" and doing nothing convincing, writing no papers that other scientists consider promising (plus writing essays that just sling mud on successful colleagues), is on par with writing profound string theory papers. Lots of laymen are hopelessly stupid sheep and they completely missed the point that this left-wing propaganda was just a trick for some unproductive useless people to justify their being funded despite the absence of any results that would be worth mentioning. These people never knew any world level science and they never cared about it; they only cared about their sources of funding. Sorry but doing nothing useful isn't on par with doing groundbreaking things. Egalitarianism or "diversity at any cost" is always wrong and it is particularly wrong in meritocratic disciplines like physics.

During the Covid-19 hysteria, I noticed some (widely considered) "rightwingers" in the Academia who celebrate the market crash and I realized that they still think like the leftists in the Academia – people who don't produce values directly, who are dependent on funding from others and who don't sell products for consensual prices – when it comes to all these fundamental economic and similar questions. Why not destroy capitalism? Parasites always correctly (in the short run) think that it won't affect them! Indeed, they don't own and manage the means of productions (including stocks), they are not responsible for them, and they believe that some money will always get to them no matter what. And yes, I realized that even folks like Paul Joseph Watson and Tucker Carlson – despite their being "opponents of political correctness" – are leftists in the sense of the "previous left-right confrontations". They just don't have any significant respect for individual rights against those of the government, for capitalism, the freedom to do business, free trade, the vital importance of wealth inequality, and similar things and this is really behind their otherwise shocking Covid-19 hysteria.

Among the 13 new hep-th preprints today, most are about AdS/CFT or string theory. The most phenomenological one is
Quark and lepton mass matrices from localization in M-theory on \(G_2\) orbifold
by Gonzalez, Kane, Nguyen, and Perry (51 pages). It's probably a good choice that it was posted on hep-th although it's "phenomenology". The disappearance of ambitious papers from hep-ph may mean that I will stop following that archive altogether at some point. Cutely, the task they ordered themselves to solve is pretty much the same as the task that the Greek alternative physicists at the top claimed to solve. But you can hopefully see the deep difference between a paper on this topic that is just childish nonsense; and a paper that is promising and that can't be reliably identified as childish by an expert, at least not too quickly.

Gonzalez et al. must start within some framework. Such deep questions may be settled in the string vacua and there are five or so major classes. Kane and pals have M-theory on the \(G_2\) manifolds as their most promising group of string vacua. The seven-dimensional \(G_2\) holonomy manifold has to be singular for the chiral (left-right-asymmetric) fermions to exist. Moreover, they choose the singularity to come from an \(E_8\) singularity which is resolved in a geometric way. That is equivalent to breaking the \(E_8\) symmetry to a smaller group, a similar operation that you do in the \(E_8\times E_8\) heterotic strings. At least vacua with the conceptually identical building blocks of these heterotic and M-theory types are related by a duality.

OK, they study the masses of elementary fermions in this setup and conclude that the masses, or the Yukawa couplings that they are proportional to, come from "the exponentiated volumes of 3-cycles" on the \(G_2\) manifold. It should be analogous to the exponentiated volumes of 2-cycles in the D6-braneworlds of type IIA string theory (from world sheet instantons that are triangles between three intersections, i.e. topologically disks), a famous case that qualitatively explains the hierarchy of the Yukawa couplings out of nothing.\[

y_{\text{Yukawa coupling}} = n_{ABC} \frac{\exp(-Vol_{ABC})}{\Lambda_{ABC}^{\sim Vol(G_2)}}

\] For some breaking of the \(E_8\) singularity to smaller nearby singularities, they may do a fit that is compatible with the observed masses. As always with these string-inspired papers, it's annoying that they have free parameters to adjust because the full string/M-theory should ultimately dictate and stabilize all the scalar fields and determine these parameters and therefore 3-volumes, right?

We don't know the final theory of everything including the right vacuum (or string construction) and there is absolutely no guarantee that we will know it in 20 years, 50 years, 1,000 years, or ever. With the declining "difficult parts" of our civilization, the answer may very well become "almost certainly no" very soon if it hasn't been turned to "no" yet. However, there is a different way to formulate the question about the correctness of string theory. We may ask whether a truly deep advance in similar questions (e.g. the calculation of fermion masses that I have spent a lot of time with in my life, with some unpublished results, although I never worked on it "professionally") may occur outside string theory. Can there be a similarly or more convincing paper that ignores all stringy constructions, the stringy extra dimensions, and all these characteristically stringy tools?

I am pretty sure that the answer is No. Not even in 1,000 years when you multiply the funding for physics by a factor of 100. String theory is really "almost completely established" at this qualitative level. I am convinced that every person who asks for funds to look for such non-stringy answers to questions where string theory seems to be needed is either incompetent or a downright scammer and nothing valuable can possibly ever come out of these things.

On the other hand, the paper by Gonzalez et al. is fun. The exponential geometric formula for the Yukawa couplings is extremely attractive and the transition from type IIA to M-theory with the \(G_2\) holonomy manifolds arguably makes it even more appealing because M-theory is "more geometric" or "more strongly coupled" and therefore more generic in the moduli spaces etc. If curious people aren't suppressed and eliminated, I think that sometime in the future people will find the complete solution, visualize quite some nice higher-dimensional geometries that produce the particles species and masses that we know, and they will look back at some of these papers (like today's Gonzalez et al.) as papers that were very close to the final answer but failed to do some last important steps.

Concerning hep-ph, I really think that the degree of excitement on that archive has dropped hugely, close to zero. I think that this is what the left-wing activists have always wanted – to ban anything that has a potential to be "big" (oppressors!) and turn the paper industry into a meaningless exercise to support some mediocre people's jobs.

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