Talk:Koide formula

message: ::Please read Wikipedia:No original research. You are misunderstanding how Wikipedia works. --mfb (talk) 14:23, 21 March 2015 (UTC)
replies: text:  Hmm, the argument is that if it would not ever go to the main page, it does not deserve even a discussion in Talk. I tend to agree, but the problem I see is that the state-of-the-art of this topic will most probably include always some "sourced but unpublished" observations and that visitors of the page are very likely to rediscover them, so perhaps Talk can act as a kind of buffer, citing the -usually web- sources of the unpublished observations. Arivero (talk) 18:39, 21 March 2015 (UTC)
thread_title:  Unpublished developments 

message: This is a thing I have mentioned in a thread of physicsforums which collects most of the speculation on the topic and also in some talks, but I am afraid it is not going to be published in journal literature. 
Some mechanism should give mass first to an unbroken Pati-Salam or GUT group, with a mass for each of three generations that we can call
    M3 = e up bottom
    M2= tau charm down
    M1= mu top strange
If the masses of the this unified system agree with Koide equation, K(M1,M2,M3)=0, we have really nine Koide equations:
    K(tau,mu,e)=0 
    K(up,charm,top)=0, K(up,charm,strange)=0, K(up,down,top)=0, K(up,down,strange)=0
    K(bottom,charm,top)=0, K(bottom,charm,strange)=0, K(bottom,down,top)=0, K(bottom,down,strange)=0
Then something breaks the unification group in a way that not all the Koide equations are broken. The ones in bold somehow survive, and link all the quarks at the
cost of recovering the old idea of an initial zero mass for the up quark.    Arivero (talk) 19:00, 21 March 2015 (UTC)
thread_title:  Some idea from symmetry 

message: The formula allows one to estimate the masses of a hypothetical fourth generation of leptons. It gives a mass of 43GeV for a 4th generation lepton (yet this is ruled out otherwise it would be produced in W boson decay which have a mass around 90GeV, unless the fourth generation neutrino is very heavy) , and quark masses of 3.5TeV and 84TeV for down and up-type quarks. Continuing in this way one can have a maximum of 9 generations below the Plank Mass scale. The sequence settles into one where each mass is 22.956 =(23+5 \sqrt{21} )/2 larger than the last.  — Preceding unsigned comment added by 87.216.217.210 (talk) 02:22, 21 March 2015 (UTC)
thread_title: Mass Predictions

message: Consider an xyz Cartesian coordinate system and the vectors (1, 1, 0), (1, 0, 1) and (0, 1, 1), the projections of the vector (1, 1, 1) onto the xy, xz, and yz planes respectively.  Modify the projection vectors so that they have the lengths, respectively, that correspond to the masses of the electron, muon, and tau particle in units of eV/c2.  Applying the pythagorean theorem to each of the projection vectors, we have the system of equations
	x2 + y2 = (0.000511)2,  
	x2 + z2 = (0.1057)2,  
	y2 + z2 = (1.777)2.  
The solution to this system is given by
	x2 = -1.5732,           
	y2 = 1.57327,            
	z2 = 1.58445.           
The input data only has three place accuracy, so the solutions can not be relied upon beyond three significant figures. But it is interesting (and perhaps only coincidental) that  these values cluster about the value of pi/2 = 1.57079... .  Samdhatte (talk) 00:14, 19 February 2008 (UTC)
thread_title: Another Interesting Coincidence? 

message: With 3 significant digits.
Q = \frac{m_e + m_{\mu} + m_{\tau}}{(\sqrt{m_e}+\sqrt{m_{\mu}}+\sqrt{m_{\tau}})^2}
Q = \frac{0.511\ \rm{MeV}/c^2 + 105.7\ \rm{MeV}/c^2 + 1777\ \rm{MeV}/c^2}{(\sqrt{0.511\ \rm{MeV}/c^2}+\sqrt{105.7\ \rm{MeV}/c^2}+\sqrt{1777\ \rm{MeV}/c^2})^2}
Q = \frac{1.88 \times 10^3\ \rm{MeV}/c^2}{(7.15 \times 10^1\  \sqrt{\rm{MeV}/c^2} + 1.028 \times 10^2\  \sqrt{\rm{MeV}/c^2} + 4.215 \times 10^2\  \sqrt{\rm{MeV}/c^2})^2}
Q = \frac{1.88 \times 10^3\ \rm{MeV}/c^2}{(5.32 \times 10^1\  \sqrt{\rm{MeV}/c^2})^2}
Q = \frac{1.88 \times 10^3\ \rm{MeV}/c^2}{(5.32 \times 10^1\  \sqrt{\rm{MeV}/c^2})^2}
Q = \frac{1.88 \times 10^3\ \rm{MeV}/c^2}{2.83 \times 10^3\  \rm{MeV}/c^2}
Q = 6.64 \times 10^-1 
:If you had used up to date figures for the masses, or if you had any idea how to use significant digits correctly, this might be interesting. 99.48.75.121 (talk) 04:47, 13 January 2011 (UTC)
thread_title: Actual Result

message: Some interesting discussion has been generated in this period, but it is still too especulative to add to the main entry. Still, the interested reader should pursue the following blog posts:
* http://www.science20.com/quantum_diaries_survivor/alejandro_rivero_fermion_mass_coincidences_and_other_fun_ideas-85187
* http://dispatchesfromturtleisland.blogspot.com/2011/12/more-fun-with-koides-formula.html
* http://motls.blogspot.com/2012/01/could-koide-formula-be-real.html
* http://es.scribd.com/doc/157932274/Koide-equations-for-quark-mass-triplets
* https://johncarlosbaez.wordpress.com/2021/04/04/the-koide-formula/  — Preceding unsigned comment added by Arivero (talk • contribs) 00:49, 18 June 2023 (UTC)
thread_title:  other references online 

message: I put in a "disputed" template to the incomprehensible statement in the lede about a spurious "prediction" of the τ mass mass in an 1981 paper. The heavy lepton was discovered in the early 70s;  and, by 1975, Perl had estimated its mass pretty well.  I have no idea what the baffling assertion is meant to convey, nor where it actually came from. It has a strong whiff of fringe. Cuzkatzimhut (talk) 11:12, 11 April 2018 (UTC)
replies: text: According to page 25 of Perl 1992, for many years the best measurement of the tau mass was a 1978 measurement of 1784 +2 -7 MeV. The next improved measurement, made in 1992, was 1776.9 +.5 -.5 MeV. Koide 1982 had predicted 1777 MeV. Mporter (talk) 06:02, 4 June 2018 (UTC)
replies: text: Granted; however, the 28 March 2018 statement on "prediction" was highly misleading. In 1982, Koide had access to the DELCO 1784 measurement you cite. However, a mere quarter-century drift of the observational value (DELCO-BES)/DELCO by less than 0.4% closer to the subsequent Koide value does not quite meet the standards of "prediction" of the field. WP excessive statements of bogus revelation of this type have been systematically abused by crackpots perpetrating unsound numerological myths, all in the name of "hard facts" furnished by WP in its less than  proud moments. Cuzkatzimhut (talk) 14:18, 4 June 2018 (UTC)
replies: text: Uh, what? The prediction was 1 standard deviation below the measured value, but with a much smaller uncertainty as the electron and muon mass were known much more accurately. The method used to make this prediction is debatable, but the prediction was excellent and spot-on. --mfb (talk) 20:07, 4 June 2018 (UTC)
replies: text: We seem to dissonate on the word "predicted", as used originally in the article. Koide was within a σ of the available observed value then and has an indisputably  better fit now, 36 years thence.  "Predicted" is stretching the term. "Fits the mass of the τ well within error" is indisputable, but that's not what the abusers understand instead of glomming on an imagined history. Cuzkatzimhut (talk) 22:17, 4 June 2018 (UTC)
replies: text: Tons of predictions in particle physics are like that, and they are always called theory predictions, even when they are made after initial measurements exist. They do not depend on the measured value, that is the important point. If you want to use "prediction" differently from everyone else, fine, but do that somewhere else. --mfb (talk) 00:35, 5 June 2018 (UTC)

text: I don't know where you publish, but apparently not in particle physics, otherwise we wouldn't have this discussion. This is a particle physics topic. --mfb (talk) 05:53, 5 June 2018 (UTC)
replies: text: Perhaps we have it because I've been refereeing and editing DPF papers for four decades? Cuzkatzimhut (talk) 13:44, 5 June 2018 (UTC)
replies: text: Then I'm sure you refereed many papers that made "predictions" for things measured before. Based on the SM, based on SUSY, based on whatever. So what is the problem? --mfb (talk) 00:57, 6 June 2018 (UTC)
thread_title: Disputed "prediction" of τ mass

message: The Koide formula in even numbers 0 , 1, (7 + 4 * square root of 3 ) 
https://www.wolframalpha.com/input/?i=%28+0+%2B+1+%2B+a%29%2F%28+sqr+0+%2B+sqr+1+%2B+sqr+a%29%5E2+%3D+2%2F3
Maybe this has meaning to someone?
Answer to above unsigned: yes, the 0 mass Koide triplet was discovered before Koide, it is quoted here and in the main page, as it is a published result Arivero (talk) 11:18, 6 June 2023 (UTC)
thread_title:  Koide formula in even numbers 

message: In 2013 and 2018 (https://en.wikipedia.org/w/index.php?title=Koide_formula&diff=prev&oldid=827675064) we got a couple suggestions from a contributor in Newcastle that while interesting, are unsourced. The main idea here is eigenvalues of some 3x3 matrix. The equations go as mass square roots, but of course they could be uplifted to 6th degree, surely such uplifting is buried somewhere in goffinet thesis. The recipe is obvious:
:(a x^3 + b x^2 + c x + d)(a x^3 - b x^2 + c x - d) = a^2 x^6 + 2 a c x^4 - b^2 x^4 - 2 b d x^2 + c^2 x^2 - d^2
and then the condition b^2=6ac
===Ratio Factor===
Each triple of Koide masses is defined by a mass scale and another variable \gamma given by:
:\frac{ \sqrt{e}^3+\sqrt{\mu}^3+\sqrt{\tau}^3}{(\sqrt{e}+\sqrt{\mu}+\sqrt{\tau})^3} = \frac{1}{2}\left(1+\gamma\right)
which determines along with the Koide relation the mass ratios e:\mu:\tau.
When one of the masses is zero then \gamma=0. For the charged lepton triple we find \gamma\approx \frac{1}{81}.
A problem I have with this is that it does not emerge from a simpler integer relationship nor from a simpler formula. It reminds, and can be confused with, the extra correction Koide did in its original paper Arivero (talk) 00:09, 18 June 2023 (UTC)
replies: text: 2x^3-6x^2n+3xn^2-3=0
A value of n=3 fits the lepton triple, while a value of n=2 fits the (top, bottom, charm) triple. A value of n=2.5 fit's the (strange, down, up) triple only if we give the up-quark mass a value of 0.1MeV. Cubic equations usually arise in symmetry breaking when solving for the Higgs vacuum. This involves finding the eigenvalues of a 3x3 matrix.
NOTE that the author of this contribution seems to forget a dependence on n for the last term, that would justify the explanation and surely also the term 81 in the other contributed formula.   — Preceding unsigned comment added by Arivero (talk • contribs) 15:35, 18 June 2023 (UTC)
thread_title: Anonymous post from Newcastle

message: Each triple of Koide masses is defined by a mass scale and another variable \gamma given by:
:\frac{ \sqrt{e}^3+\sqrt{\mu}^3+\sqrt{\tau}^3}{(\sqrt{e}+\sqrt{\mu}+\sqrt{\tau})^3} = \frac{1}{2}\left(1+\gamma\right)
which determines along with the Koide relation the mass ratios e:\mu:\tau.
When one of the masses is zero then \gamma=0. For the charged lepton triple we find \gamma\approx \frac{1}{81}.
A problem I have with this is that it does not emerge from a simpler integer relationship nor from a simpler formula. It reminds, and can be confused with, the extra correction Koide did in its original paper Arivero (talk) 00:09, 18 June 2023 (UTC)
thread_title: Ratio Factor

message: The following cubic equation's solutions fit the Koide formula for any value of n when considered as square roots of masses up to scale:
:2x^3-6x^2n+3xn^2-3=0
A value of n=3 fits the lepton triple, while a value of n=2 fits the (top, bottom, charm) triple. A value of n=2.5 fit's the (strange, down, up) triple only if we give the up-quark mass a value of 0.1MeV. Cubic equations usually arise in symmetry breaking when solving for the Higgs vacuum. This involves finding the eigenvalues of a 3x3 matrix.
NOTE that the author of this contribution seems to forget a dependence on n for the last term, that would justify the explanation and surely also the term 81 in the other contributed formula.   — Preceding unsigned comment added by Arivero (talk • contribs) 15:35, 18 June 2023 (UTC)
thread_title: As Solutions to a Cubic Equation

message: I had various pieces of 'numerology' related to particle mass and the fine structure constant published in July 7th 1983 edition of Nature. Since that publication I have simplified the various relationships into the following....which I find quite remarkable even if it is coincidence...
The following is the mathematical ‘operation’ table for positive times negative integers
For the range 0 to 2 for positive numbers and 0 to –2 for negative numbers.
      	        	      A	       B	       C
      	       *	0      	        	
-2    	        	       	        	
     X	0       	0      	0       	0
     Y	1       	0      	        	
     Z	2       	0      	        	
Now take the values in the above table and use them as powers to which pi is raised
( i.e pi ^ -1  is pi to the power of minus 1)
      	        	      A	       B	       C
      	       *	0      	        	
-2    	        	       	        	
     X	0       	1      	1       	1
     Y	1       	1      	Pi ^-1  	Pi ^ -2
     Z	2       	1      	Pi ^-2  	Pi ^ -4
The fine structure constant 137.03604 happens to be very close to (4 * pi ^ 3) + pi ^ 2 + pi , or 137.03599
This happens to be  pi ^ 3 times the sum of the values in columns A and B ( or rows X and Y ) in the table. 
If we take the proton mass to be pi ^ 2, then the sum of the values in column B ( or row Y ) gives you the neutral pion mass to extremely close accuracy, and the sum of the values in column C ( or row Z ) gives the Muon mass very closely.  The overall accuracy here is remarkable ! 
Consider this……that a simple operation on a multiplication operator table gives a simple matrix that provides a remarkably accurate relationship between fine structure constant, muon mass, neutral pion mass,
and proton mass. ( The proton mass does not have to be pi ^ 2 but can clearly be scaled up or down as any power of pi along with the matrix itself being scaled up or down by the same power….so all the relationships can be defined as between integral powers of pi .) 
Fine structure constant                                   = 137.03600                         Above table gives 137.036303
Ratio of proton to neutral pion mass              = 6.95230                              Above table gives 6.95223189
Ratio of proton to muon mass                         = 8.87678                              Above table gives  8.87883898
If this is a coincidence, then it is a remarkable one.  Most pieces of ‘numerology’ simply provide single relationships…..such as that the proton electron mass ratio is close to 6 * pi ^ 5 ( six times pi to the power 5 ), which has been known for years. Other than Bode’s law for the planets, no other simple ‘numerological’ formula gives such a remarkable relationship between four fundamental constants of nature.
I might expect, by pure chance, a rough proximity to a few particle masses or constants. But what convinces me that the above very likely does have significance is its amazing overall accuracy and simplicity. It is the combination of those two factors that is most striking. Most ‘numerology’ in this arena is convoluted, includes a lot of arbitrary factors to ‘tweak’ the results, and contains precious little in the way of any patterns.
This ‘matrix’ was first published in July 1983 in Nature ( not in the above form )…….along with an editorial comment that recognised the remarkable nature of the relationships but regarded the matter as ‘numerology’. Whilst I’m quite happy to accept criticism that there’s no explanation or theory as to why such a relationship occurs, I find it extremely hard to accept that the above can lightly be dismissed as just ‘coincidence’. Science is the search for patterns between data, and here you have a pattern that cries out for an answer. Why should four fundamental constants just happen to have such a close fit to so simple a symmetry ? Peter Stanbury (talk) 16:45, 18 March 2024 (UTC)
thread_title:  Some Possibly Related Coincidences ?