Is the Yang-Mills mass-gap problem already solved?

A World Formula or Theory of Everything Perspective

Jan 06, 2022

I recently read a Nature article [1] on solving the Yang-Mills mass gap problem in view of Gödel’s incompleteness theorems being connected to unsolvable calculations in quantum physics.

A logical paradox at the heart of mathematics and computer science turns out to have implications for the real world, making a basic question about matter fundamentally unanswerable [1].

Knowing that the ‘World Formula’ provides the most complete toolbox known to mankind at this time in understanding physics, it got me thinking that Gödel’s incompleteness theorems might just be a problem of bias, ideology, and groupthink (see my prior article). Such bias might then prevent one from shifting to a different paradigm [2]. Once I realized this, I immediately started connecting some pieces together that I have seen in Norbert’s writings that link to the Yang-Mills question.

“The mass-gap problem relates to the observation that the particles that carry the weak and strong nuclear force have mass. This is also why the weak and strong nuclear forces have limited range, unlike gravity and electromagnetism, and why quarks are only found as part of composite particles such as protons or neutrons, never in isolation. The problem is that there is no rigorous mathematical theory which explains why the force-carriers have mass, when photons, the carriers of the electromagnetic force, are massless [1].”

And I now believe Dr. Schwarzer may, in principle, already have the template to solve the Yang-Mills mass-gap problem, and in reviewing the work, one only needs to pull it all together!

Problem solved?

He has already derived electromagnetism (EM) directly out of the Einstein Hilbert action in the vacuum case 4D-space-times without any add-ons [3,4,5]. As Hilbert had done the job for gravity over 100 years ago, we can conclude that the situation for both, gravity and EM is clear… no masses.
The other stuff (like mass) requires either curvature or compactified add-on dimensions [4, 5].

Such dimensions – of course – also lead to additional interactions but – due to the compactification, they cannot be of 1/r^2-character like EM and gravity [5].
Hence the low range.
Klein-Gordon and Dirac derivations are important parts of the mass-gap question, and while these are already covered in the references, they can be briefly explored in the linked videos below.

Something to consider if you want to win a cool 1 Million and have access to some decent computing power. You know where to find us.

Thank you for reading A World Formula or Theory of Everything Perspective. This post is public so feel free to share it.

The Theory of Everything (part 1) - Origin of Matter

The Theory of Everything (part 2) - Metric Origin of the Klein-Gordon Equation

The Theory of Everything (part 3): The Metric Origin of the Dirac Equation

It is important that we also consider Dirac, as this completes (for many) the proof that QT truly already resides in Einstein’s GTR.

References

[1] D. Castelvecchi, “Paradox at the heart of mathematics makes physics problem unanswerable”. Nature (2015). https://doi.org/10.1038/nature.2015.18983

[2] T. Bodan, “The Eigth Day”, Amazon (March 2017), ISBN-10:1520908474, ISBN-13:978-1520908472, ASIN: B094Y8J2Q9

[3] N. Schwarzer, "The World Formula: A Late Recognition of David Hilbert ‘s Stroke of Genius", Jenny Stanford Publishing (2022), ISBN: 9789814877206
https://www.jennystanford.com/9789814877206/the-world-formula/

[4] N. Schwarzer, “Masses and the Infinity Options Principle - Can We Explain the 3-Generations and the Quantized Mass Problem?”, Part 5 of “Medical Socio-Economic Quantum Gravity”, Self-published, Amazon Digital Services, 2020, Kindle

[5] N. Schwarzer: “The Math of Body, Soul and the Universe”, Jenny Stanford Publishing, ISBN 9789814968249

“Quoting Richard P. Feynman—‘I think we can safely assume that no one understands quantum mechanics’—I am convinced that he would have made the following comments: (1) The Theory of Everything by Norbert Schwarzer is a quantum leap forward regarding the understanding of quantum mechanics. (2) There is no more need for the interpretation of the Copenhagen Convention, nor for The Cellular Automaton Interpretation of Quantum Mechanics by Nobel Laureate Gerard ’t Hooft. (3) The derivation of the laws of quantum mechanics as a result of the Einstein field equations is absolutely ingenious.”
~Prof. Hans Leuenberger, University of Basel, Switzerland

Wow, you're still reading! - then this may also interest you

and so might this;

Jan 7, 2022Edited

Norbert’s opinion on the matter was that the Hilbert approach probably solves the mass-gap problem. Only to this he referred to, when suggesting that the Hilbert-path might be the way to go. And then I saw a potential connection to the Yang-Mills millennial problem within the wider "Gödel's incompleteness theorems" via the Nature article I read.

With respect to the millennium prize, however, he wrote the following:

“Moin Troy, I’m afraid the definition of the task is such that the mass-gap problem is not really solving their problem. The theory on which they insist to explain it all comes with an intrinsic difficulty, perhaps even an inconsistency, namely the one they want to have solved. This is not a task, but a catch 22 and I have no time to play mill, right now. Could well be that I misunderstood the task, but in its current formulation I doubt that.

So again, I think that the Hilbert approach would help to solve the mass-gap problem, but I do not see that this answers their intrinsic question.

About your question how to get started:

a) Apply a metric Higgs formalism by using the usual scaling function F[f[x0,x1,…]] to the metric tensor

b) Evaluate the Ricci scalar R for this and see that you obtain the right Higgs fields with a setting of f*(4*F*F’’+(6-n)*F’*F’)/4=F’/F, because this gives you F=(f^2+Cf)^2 in the case of n=4

c) Solve the resulting differential equation for f when demanding R=0, which will give you wave functions

d) With this Einstein-Hilbert-Higgs approach move on

e) …

Not sure, but at least we have a metrically derived Higgs field with the expected Mexican hat structure and this I’d consider a not too bad of a start."

So it seems the millennium prize is likely asking the wrong question, but that does not mean the mass-gap problem is unsolvable, only a paradigm shift is required.

By leveraging this paradigm shift that western society appears to be blind too, enormous project opportunities are available to jump to the next evolutionary growth curve. If these opportunities interest you, please get in touch.

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