PeterDonis said:
Summary:: The referenced paper discusses a "rotating lepton model" as a proposed mechanism for generating the mass of hadrons. However, the basic premise looks wrong to me, and I am wondering how it will strike others.
I just came across a 2016 paper [1] that claims to have computed reasonably accurate masses for hadrons using what it calls a "rotating lepton model" and "the relativistic Newton equation". An earlier 2001 paper by two of the same authors [2] appears to be the first introduction of the general type of model they are using.
The basic premise of this model appears to be to postulate that hadrons are composed of ultrarelativistic neutrinos in a bound state generated by their mutual gravitation. Unfortunately, they appear to be modeling the mutual gravitation using Newton's gravitational law with the relativistic masses of the neutrinos simply plugged in. This looks obviously wrong to me, since the source of gravity is not relativistic mass but the stress-energy tensor, and you can't just plug relativistic mass into Newton's gravitational equation and get correct answers
Keep in mind that there is nothing exceptional about a model that takes into account special relativity but not general relativity.
The entire Standard Model does that, and
special relativity distinct from uniquely GR effects is the primary contributor to relativistic mass in most circumstances. Relativistic Newtonian Gravity could be "Special Relativistic Newtonian Gravity" and not "General Relativistic Newtonian Gravity."
It is hardly unusual for approximations in physics to disregard factors that have a small impact on its predictions for sake of expediency and a deeper understanding of the primary and most important parts of a physical system.
Also, while general relativity has the stress-energy tensor as an input, rather than relativistic mass, there are a wide variety of physical systems in which the non-mass components of the stress-energy tensor are either zero, or are negligible in magnitude relative to the mass component. Pressure, electro-magnetic flux, and linear momentum, for example, are often negligible in particular physical systems that come up frequently and are important.
Among other things, weak field gravitation in large N-body systems like simulated galaxies, are routinely done using Newtonian gravity rather than GR, despite the fact that it is known to be wrong, because the systemic error introduced in that kind of simplification is surprisingly small compared to a true GR analysis, and is computationally profoundly easier. (A couple of outlier papers argue that MOND-like effects are due to these systemic errors but I don't think that their analysis is correct and other papers have criticized those papers.)
Likewise, there are lots of circumstances in Earth bound or solar system scale considerations of gravity in which non-mass contributions to the stress-energy tensor are immaterial.
More generally scalar graviton approximations of GR (which is essentially what a Newtonian gravity approximation is one example of) can reproduce lots of GR phenomena. See, for example, the abstract and reference of the following paper:
We construct a general stratified scalar theory of gravitation from a field equation that accounts for the self-interaction of the field and a particle Lagrangian, and calculate its post-Newtonian parameters. Using this general framework, we analyze several specific scalar theories of gravitation and check their predictions for the solar system post-Newtonian effects.
Diogo P. L. Bragança, José P. S. Lemos “
Stratified scalar field theories of gravitation with self-energy term and effective particle Lagrangian” (June 29, 2018) (open access) (pre-print
here).
Presumably, in a rotating lepton model, the angular momentum contribution to the stress-energy tensor would not be negligible, but if the angular moment contribution from the stress-energy tensor is captured in magnitude in their definition relativistic mass appropriately, you could have a quite decent approximation of GR without the full stress-energy tensor source considered expressly.
A "relativistic Newton's equation" for gravity also doesn't sound so far afield from the well established (and more accurate in practice than theory guarantees that it should be),
Post-Newtonian Expansion tool for approximating GR effects with less burdensome calculations than a full fledged rigorous exact GR solution.
This isn't to say that I am endorsing the paper by any means. There are all sorts of other potential issues with it, and all laws of gravity including GR are really beyond their experimentally proven domains of applicability in any case, when you are talking about gravitationally bound leptons at subatomic distance scales. I would worry, for example, about Z boson mediated weak force interaction between leptons swamping any gravitational effect at these scales without first running numbers of confirm whether or not that is an issue.
Similarly, I have real doubts that a gravitationally bound structure works for this purpose, and a gravitationally bound system is hard to reconcile with the W boson mediated flavor changing interactions occur that the SM posits which works to extreme degrees of accuracy. It also isn't obvious where you get an electromagnetic charge from a system of gravitationally interacting neutrinos without making some pretty unorthodox assumptions.
But, I don't see the particular objection you note as being the particularly troubling ones with a theory along these lines.
Finally, even if there are deep flaws in the reasoning (and the analysis is honestly quite shallow, probably too shallow to be a truly correct result), I don't think it is appropriate to simply dismiss the results of this toy model as mere numerology, particularly as they are using the theory to get fairly close to half a dozen different fundamental and composite particle masses. It wouldn't be too surprising if something they were doing was, perhaps in an unintended fashion, capturing a key insight of some deeper theory that leads to these reasonably close predictions, even if they have a lot of details wrong. Any phenomenological theory that is a decent fit to the data helps you understand at some heuristic level how those otherwise seemingly random numbers are related to each other, even if a true answer had to employ some far more rigorous and sophisticated string theory type mathematics, for example.
