Exploring Rotating Lepton Model for Hadron Masses

[PeterDonis]

TL;DR 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.

I'm wondering if anyone else has seen these papers, or similar models, before, and what others' reactions are to the models described in the papers linked to here.

[1] https://iopscience.iop.org/article/10.1088/1742-6596/738/1/012080/pdf

[2] https://arxiv.org/abs/2001.09760

 

[sysprog]

The first article seemed to me to be vague about what was meant by "relativistic Newtonian", so I looked at another iopscience paper that goes into greater detail about what it calls "Relativistic Newtonian Dynamics": https://iopscience.iop.org/article/10.1088/1742-6596/845/1/012028/pdf

 

[Vanadium 50]

I'd wait for a peer reviewed paper to come out. These are conference proceedings.

 

[PeterDonis]

I'd wait for a peer reviewed paper to come out. These are conference proceedings.

Conference proceedings from 2016 (or 2017 for the one @sysprog linked to). I cannot find any peer-reviewed papers since then, which in itself makes the claims seem questionable.

 

[PeterDonis]

I looked at another iopscience paper that goes into greater detail about what it calls "Relativistic Newtonian Dynamics"

This one raises just as many red flags as the other one. For example:

"SR considers the influence of kinetic energy on spacetime." Huh? In SR spacetime is flat and non-dynamical; there is no "influence" on it of anything.

"For non-gravitational fields energy conservation and Planck's equation predict a time dilation based on position in space." Not something I've seen in any GR textbook.

"None of the relativity theories considers the influence of non-gravitational potential energy on spacetime." Ever heard of the stress-energy tensor?

And, once again, the "Relativistic Newtonian Dynamics" just means plugging some expression for "energy" into Newton's gravitational law. Which was known not to work in 1907.

 

[ohwilleke]

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.

 

[PeterDonis]

there is nothing exceptional about a model that takes into account special relativity but not general relativity

Taking into account SR but not GR would be fine for a theory that is not intended to cover domains where gravity is significant. However, this model is specifically proposing that gravity is significant.

In any event, taking into account SR but not GR is not what this model does. Newton's gravitational equation is not part of SR. Plugging relativistic mass into that formula isn't either.

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.

Your statement is correct, but irrelevant to this discussion, as that is not what these papers are doing.

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.

And even in those systems, the source of gravity is not relativistic mass. You will find plenty of threads here on PF discussing exactly this point. Only a brief point is worth making here: in any system whose relativistic mass is much larger than its rest mass, the momentum components of the stress-energy tensor are certainly not negligible, since by construction they are similar in magnitude to the relativistic mass.

weak field gravitation in large N-body systems like simulated galaxies, are routinely done using Newtonian gravity rather than GR

For systems where nothing has relativistic speeds, yes. Not for systems containing components that have relativistic speeds. Newtonian gravity is not a good approximation in those cases.

scalar graviton approximations of GR (which is essentially what a Newtonian gravity approximation is one example of) can reproduce lots of GR phenomena

"Lots of", but not all. An again, this is irrelevant to this thread, since the papers I linked to in the OP are not proposing a scalar graviton approximation or anything like it.

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

It does the way these particular papers are using the term "relativistic Newton's equation". What they are doing is nothing like the perfectly valid post-Newtonian expansion that is commonly used to make approximations in weak field gravity.

There are all sorts of other potential issues with it

The two specific issues you raise are indeed additional valid concerns--but to even get to that point one has to accept the basic theoretical framework, which is already highly questionable for the reasons I stated.

I don't see the particular objection you note as being the particularly troubling ones with a theory along these lines

You should think again. See above.

 

[ohwilleke]

Taking into account SR but not GR would be fine for a theory that is not intended to cover domains where gravity is significant. However, this model is specifically proposing that gravity is significant. In any event, taking into account SR but not GR is not what this model does. Newton's gravitational equation is not part of SR. Plugging relativistic mass into that formula isn't either.

Obviously, it isn't trying to fit into the existing SM + GR core theory. It is seeing how toying with ideas inspired by those theories that use them in a very different manner might work out compared to observation.

And even in those systems, the source of gravity is not relativistic mass. You will find plenty of threads here on PF discussing exactly this point. Only a brief point is worth making here: in any system whose relativistic mass is much larger than its rest mass, the momentum components of the stress-energy tensor are certainly not negligible, since by construction they are similar in magnitude to the relativistic mass.

The point of their theory, I think, is that lots of angular momentum plus rest mass in GR might be reasonably well approximated by their relativistic Newtonian mass concept, which you seem to acknowledge is similar in magnitude.

For systems where nothing has relativistic speeds, yes. Not for systems containing components that have relativistic speeds. Newtonian gravity is not a good approximation in those cases. "Lots of", but not all. An again, this is irrelevant to this thread, since the papers I linked to in the OP are not proposing a scalar graviton approximation or anything like it. It does the way these particular papers are using the term "relativistic Newton's equation". What they are doing is nothing like the perfectly valid post-Newtonian expansion that is commonly used to make approximations in weak field gravity.

First of all, I would say that pretty much any Newtonian starting point model is quite similar to a scalar graviton approximation. Newtonian gravity is basically a scalar graviton approximation of GR without self-interacting gravitons.

The point of the other examples is simply to note that using Newtonian gravity as a starting point to an approximation of true GR is not infrequently valid in well accepted approximations. Those approximations have different domains of applicability, but it isn't an unreasonable starting point for a sensible theory.

Using Newtonian gravity as a starting point might also be valid in this case, but, if it is, it is obviously valid for reasons different than in those other cases, since it is not a weak field or low velocity case.

Probably what I would see as the biggest red flag is its application to baryons and mesons, where we already know where the mass of the composite particles come from, i.e. gluon energy for the most part. I wouldn't be surprised if the apparent success in those cases is due to the fact that gravity has a lot of properties of "QCD squared".

 

[PeterDonis]

The point of their theory, I think, is that lots of angular momentum plus rest mass in GR might be reasonably well approximated by their relativistic Newtonian mass concept

No, it isn't, because "lots of angular momentum plus rest mass in GR" does not look anything like "plug relativistic mass into Newton's gravitational formula". It looks like a near-extremal Kerr spacetime.

Newtonian gravity is basically a scalar graviton approximation of GR without self-interacting gravitons.

No, it isn't. You really need to spend some time working through a GR textbook that treats these issues, such as MTW, which has a good detailed treatment in a series of worked problems in a fairly early chapter.

The point of the other examples is simply to note that using Newtonian gravity as a starting point to an approximation of true GR is not infrequently valid in well accepted approximations.

Sure, but none of those examples work for the specific domain proposed in the papers I linked to, namely, ultrarelativistic particles.

 

[Trifractaloid]

the thing that I find the most questionable about it is how such formations would occur naturally (neutrinos orbiting positrons, electrons or electron and positron pairs at relativistic speeds)

 

[arivero]

the thing that I find the most questionable about it is how such formations would occur naturally (neutrinos orbiting positrons, electrons or electron and positron pairs at relativistic speeds)

boundaries of an open string?

btw, how did you find this thread?

https://www.sciencedirect.com/science/article/abs/pii/S0378437114002404 seems related

 

[Trifractaloid]

boundaries of an open string?

btw, how did you find this thread?

https://www.sciencedirect.com/science/article/abs/pii/S0378437114002404 seems related

I'm not y any means well-versed in string theory, but if it's allowed in it then maybe so.

I was looking for more about rotating lepton model since it's not very well-known but despite it's flaws is pretty interesting model I think. So I just went searching for anything about it and found this.
I'm guessing this is an old thread that no-one has been in for a while XD

I actually don't remember how I found out about this particular model in the first place come to think of it XD

 

[arivero]

Really, once we are aware of see-saw models for neutrino mass, someone is going to try to use Newton constant to put the Planck mass into the game at a classical level, hoping that it is the tree-level of something. I myself did some speculations in 2006 https://arxiv.org/abs/gr-qc/0603123 and even one formula had the trouble of a gamma factor. So it is easy, once you are in the ballpark, to try small configurations to adjust the final result; at the end it is more of Eddington but without the alpha. See https://www.jstor.org/stable/41134170

The amusing thing in the papers is the use of longitudinal mass. According wikipedia,https://en.wikipedia.org/w/index.ph...l_relativity#Transverse_and_longitudinal_mass it is a concept already abandoned after 1906

 

[Paul Colby]

It seems to me that the model should supply excited state masses using shorter wave lengths over the circular orbits. No mention seems to be made of this. Did I miss something?

 

[ohwilleke]

Really, once we are aware of see-saw models for neutrino mass, someone is going to try to use Newton constant to put the Planck mass into the game at a classical level, hoping that it is the tree-level of something. I myself did some speculations in 2006 https://arxiv.org/abs/gr-qc/0603123 and even one formula had the trouble of a gamma factor. So it is easy, once you are in the ballpark, to try small configurations to adjust the final result; at the end it is more of Eddington but without the alpha. See https://www.jstor.org/stable/41134170

The amusing thing in the papers is the use of longitudinal mass. According wikipedia,https://en.wikipedia.org/w/index.ph...l_relativity#Transverse_and_longitudinal_mass it is a concept already abandoned after 1906

Is there any theory work out there opposing see-saw models for neutrino mass?

 

[arivero]

Is there any theory work out there opposing see-saw models for neutrino mass?

I am afraid that an opposing model would at the end be named Type IV see-saw or whatever