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Free PDF : Isospin, Hypercharge and Fermat's Last Theorem
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richard miller
Aug 20, 2019, 12:54:18 PM8/20/19
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Isospin, Hypercharge and Fermat's Last Theorem
Free PDF at:
http://www.urmt.org/urmt_isospin_hypercharge.pdf
If you don't want to click the link, just go to www.urmt.org (if you trust it, that is) and look at the front page.
If you don't want to click any link anyway, here is the Abstract and Conclusions:
Abstract
This paper shows how the quark Hypercharge values, in integer form, for the SU(3), Up, Down and Strange Quark flavour model, are given by the eigenvalues of a special eigenvector solution to a generalised form of Fermat's Last Theorem, which has integer solutions for arbitrary odd exponent greater than two. Upon reduction of the order of the equation to a quadratic exponent, and hence Pythagorean in form, the eigenvalues become those of the third component of Isospin. The associated eigenvectors representing the Up and Down quarks are seen to algebraically differentiate themselves from that of the Strange quark, and this is noted as indicative of the relative stability of nucleons formed from the Up and Down quarks compared with that of the Strange quark, which forms unstable particles.
Conclusions
It has been shown that a generalised version of Fermat's Last Theorem, known as the Coordinate Equation
(0 =x^n + y^n - z^n + kxyz, integers k,x,y,z),
has two very special solutions:
1) a Pythagorean solution (0 =x^2 + y^2 - z^2) for the smallest possible, zero Potential energy V=0 , where the Coordinate Equation reduces to a quadratic exponent with integer Isospin eigenvalues +1,0,-1;
2) The z=x+y solution, which gives the integer Hypercharge eigenvalues (+1,+1,-2) and is valid for any arbitrary odd exponent n>=3. This latter solution is obtained for the next smallest magnitude, integer Potential energy solution V=-2. Alternatively stated, the two smallest magnitude Potential energy values gives two of the most general and simple solutions to a modified form of Fermat's Last Theorem.
It has been noted that the Up and Down quarks, forming relatively stable particles, i.e. the nucleons, are represented by eigenvectors that algebraically differentiate themselves from the Strange quark, which forms unstable particles.
On a more general historical note
It is now 40 years since the triumph that is the Standard Model was crowned with a Nobel award to Weinberg, Glashow and Salam - strictly speaking their award was for the Electroweak. Nice work chaps. W,Z and Higgs is CERN's crowning glory.
But nearly 50 years since string theory (Nambu, 1970) and nowt to show. Any progress yet guys? Nambu deserves some credit though.
URMT has been going 10 years - its premise that the laws of nature are discrete and those of number theory remain incredibly unpopular in the academic world, but then you get a recent paper like the following, where a remarkable conversion seems to have taken place, especially since one of the authors has won an essay prize rebutting Integers in Physics! Funny that.
Nakarin Lohitsiri, David Tong
Hypercharge Quantisation and Fermat's Last Theorem
arXiv:1907.00514v2 [hep-th] 12 Jul 2019
Enjoy
Richard Miller
http://www.urmt.org
Free PDF at:
http://www.urmt.org/urmt_isospin_hypercharge.pdf
If you don't want to click the link, just go to www.urmt.org (if you trust it, that is) and look at the front page.
If you don't want to click any link anyway, here is the Abstract and Conclusions:
Abstract
This paper shows how the quark Hypercharge values, in integer form, for the SU(3), Up, Down and Strange Quark flavour model, are given by the eigenvalues of a special eigenvector solution to a generalised form of Fermat's Last Theorem, which has integer solutions for arbitrary odd exponent greater than two. Upon reduction of the order of the equation to a quadratic exponent, and hence Pythagorean in form, the eigenvalues become those of the third component of Isospin. The associated eigenvectors representing the Up and Down quarks are seen to algebraically differentiate themselves from that of the Strange quark, and this is noted as indicative of the relative stability of nucleons formed from the Up and Down quarks compared with that of the Strange quark, which forms unstable particles.
Conclusions
It has been shown that a generalised version of Fermat's Last Theorem, known as the Coordinate Equation
(0 =x^n + y^n - z^n + kxyz, integers k,x,y,z),
has two very special solutions:
1) a Pythagorean solution (0 =x^2 + y^2 - z^2) for the smallest possible, zero Potential energy V=0 , where the Coordinate Equation reduces to a quadratic exponent with integer Isospin eigenvalues +1,0,-1;
2) The z=x+y solution, which gives the integer Hypercharge eigenvalues (+1,+1,-2) and is valid for any arbitrary odd exponent n>=3. This latter solution is obtained for the next smallest magnitude, integer Potential energy solution V=-2. Alternatively stated, the two smallest magnitude Potential energy values gives two of the most general and simple solutions to a modified form of Fermat's Last Theorem.
It has been noted that the Up and Down quarks, forming relatively stable particles, i.e. the nucleons, are represented by eigenvectors that algebraically differentiate themselves from the Strange quark, which forms unstable particles.
On a more general historical note
It is now 40 years since the triumph that is the Standard Model was crowned with a Nobel award to Weinberg, Glashow and Salam - strictly speaking their award was for the Electroweak. Nice work chaps. W,Z and Higgs is CERN's crowning glory.
But nearly 50 years since string theory (Nambu, 1970) and nowt to show. Any progress yet guys? Nambu deserves some credit though.
URMT has been going 10 years - its premise that the laws of nature are discrete and those of number theory remain incredibly unpopular in the academic world, but then you get a recent paper like the following, where a remarkable conversion seems to have taken place, especially since one of the authors has won an essay prize rebutting Integers in Physics! Funny that.
Nakarin Lohitsiri, David Tong
Hypercharge Quantisation and Fermat's Last Theorem
arXiv:1907.00514v2 [hep-th] 12 Jul 2019
Enjoy
Richard Miller
http://www.urmt.org
alie...@gmail.com
Aug 20, 2019, 5:28:09 PM8/20/19
to
On Tuesday, August 20, 2019 at 9:54:18 AM UTC-7, richard miller wrote:
> Isospin, Hypercharge and Fermat's Last Theorem
>
> Free PDF at:
>
> http://www.urmt.org/urmt_isospin_hypercharge.pdf
>
> If you don't want to click the link, just go to www.urmt.org (if you trust it, that is) and look at the front page.
>
> If you don't want to click any link anyway, here is the Abstract and Conclusions:
>
> Abstract
>
> This paper shows how the quark Hypercharge values, in integer form, for the SU(3), Up, Down and Strange Quark flavour model, are given by the eigenvalues of a special eigenvector solution to a generalised form of Fermat's Last Theorem, which has integer solutions for arbitrary odd exponent greater than two. Upon reduction of the order of the equation to a quadratic exponent, and hence Pythagorean in form, the eigenvalues become those of the third component of Isospin. The associated eigenvectors representing the Up and Down quarks are seen to algebraically differentiate themselves from that of the Strange quark, and this is noted as indicative of the relative stability of nucleons formed from the Up and Down quarks compared with that of the Strange quark, which forms unstable particles.
Uh huh. How about charm, top and bottom quarks?
> Isospin, Hypercharge and Fermat's Last Theorem
>
> Free PDF at:
>
> http://www.urmt.org/urmt_isospin_hypercharge.pdf
>
> If you don't want to click the link, just go to www.urmt.org (if you trust it, that is) and look at the front page.
>
> If you don't want to click any link anyway, here is the Abstract and Conclusions:
>
> Abstract
>
> This paper shows how the quark Hypercharge values, in integer form, for the SU(3), Up, Down and Strange Quark flavour model, are given by the eigenvalues of a special eigenvector solution to a generalised form of Fermat's Last Theorem, which has integer solutions for arbitrary odd exponent greater than two. Upon reduction of the order of the equation to a quadratic exponent, and hence Pythagorean in form, the eigenvalues become those of the third component of Isospin. The associated eigenvectors representing the Up and Down quarks are seen to algebraically differentiate themselves from that of the Strange quark, and this is noted as indicative of the relative stability of nucleons formed from the Up and Down quarks compared with that of the Strange quark, which forms unstable particles.
Mark L. Fergerson
richard miller
Aug 21, 2019, 12:14:41 PM8/21/19
to
http://www.urmt.org/urmt_quark_paper.pdf
The short paper was largely written in response to the arXiv paper.
Richard Miller
www.urmt.org
alie...@gmail.com
Aug 21, 2019, 6:43:54 PM8/21/19
to
On Wednesday, August 21, 2019 at 9:14:41 AM UTC-7, richard miller wrote:
> On Tuesday, 20 August 2019 22:28:09 UTC+1, nu...@bid.nes wrote:
> > On Tuesday, August 20, 2019 at 9:54:18 AM UTC-7, richard miller wrote:
> > > Isospin, Hypercharge and Fermat's Last Theorem
> On Tuesday, 20 August 2019 22:28:09 UTC+1, nu...@bid.nes wrote:
> > On Tuesday, August 20, 2019 at 9:54:18 AM UTC-7, richard miller wrote:
> > > Isospin, Hypercharge and Fermat's Last Theorem
> > Uh huh. How about charm, top and bottom quarks?
>
>
> The paper is SU(3) only, there is an earlier (and free PDF) quark paper
> covering all six under an SU(6) quark flavour model, at web site.
>
> http://www.urmt.org/urmt_quark_paper.pdf
>
> The short paper was largely written in response to the arXiv paper.
Mmm. Let me know when you decide to address flavor-changing in neutrinos.
> covering all six under an SU(6) quark flavour model, at web site.
>
> http://www.urmt.org/urmt_quark_paper.pdf
>
> The short paper was largely written in response to the arXiv paper.
As far as I know, *nobody* else seems to want to.
Mark L. Fergerson
por...@gmail.com
Aug 22, 2019, 2:04:50 AM8/22/19
to
physics is physics
and
mathematics is mathematics
nothing more
=================
Y.P
===========
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