tag:blogger.com,1999:blog-7307840825023135484.post7556441869528760894..comments2023-04-16T03:44:23.949+12:00Comments on Arcadian Pseudofunctor: Greek Trinity IIKeahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-7307840825023135484.post-27421925337558632152011-11-10T18:20:45.741+13:002011-11-10T18:20:45.741+13:00Great, Tony. Well, we shall soon know if your T-Tb...Great, Tony. Well, we shall soon know if your T-Tbar condensate is relevant for LHC observations. Personally, I still favour the full Massive realm for all LHC phenomenology. Either way though, it's you and I against everyone else, it seems!Keahttps://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-31495116656722356792011-11-10T17:00:13.901+13:002011-11-10T17:00:13.901+13:00The democratic mixing matrix for the Massless Real...The democratic mixing matrix for the Massless Realm is a nice idea. <br /><br />In Z. Phys. C - Particles and Fields 45, 39-41 (1989) Koide said: "... <br />the mass matrix of the type ... 1/3 x m x <br /><br />1 1 1<br />1 1 1 <br />1 1 1 <br /><br />... has name... "democratic" family mixing ... <br />the ... democratic ... mass matrix can be diagonalized <br />by the transformation matrix ... <br /><br />1/sqrt(2) -1/sqrt(2) 0 <br /><br />1/sqrt(6) 1/sqrt(6) -2/sqrt(6) <br /><br />1/sqrt(3) 1/sqrt(3) 1/sqrt(3) <br /><br />as <br /><br />0 0 0<br />0 0 0<br />0 0 m <br /><br />...". <br /><br /><br />Up in the Massless Realm you might just say that there is no mass matrix, <br />just a democratic mixing matrix of the form <br />1/3 x<br /><br />1 1 1<br />1 1 1 <br />1 1 1 <br /><br />with no complex stuff and no CP violation in the Massless Realm. <br /><br />When go down to our Massive Realm by ElectroWeak Symmetry Breaking <br />then <br />you might as a first approximation use m = 1 <br />so that all the mass first goes to the third generation as <br /><br />0 0 0<br />0 0 0<br />0 0 1 <br /><br />which is physically like the Higgs being a T-Tbar quark condensate. <br /><br />The subsequent distribution of mass down to the other quarks <br />might be determined by octonion combinatoric symmetries <br />with the third generation quarks being triples of octonions, <br />the second generation being pairs, <br />and the first being single octonion basis elements. <br /><br />Koide applied something like the above reasoning to <br />get a lepton mixing matrix (which does not have the color force <br />so the combinatorics would differ from the quark case). <br /><br />TonyTony Smithhttps://www.blogger.com/profile/06997411020615409522noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-3865498062052080322011-11-09T15:51:03.309+13:002011-11-09T15:51:03.309+13:00Alternatively, Tony, putting all CKM entries to $u...Alternatively, Tony, putting all CKM entries to $ud$ suggests the <i>democratic mixing matrix</i>, of all equal amplitudes. This too is a kind of identity, which is the natural (infinite product) limit of any complex magic mixing matrix.Keahttps://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-78027411031755331892011-11-08T16:33:52.968+13:002011-11-08T16:33:52.968+13:00Interesting thoughts, Tony. I think the appearance...Interesting thoughts, Tony. I think the appearance of quark gluon plasma physics at CMS, for instance, is already one hint that the LHC could see a shift in the mixing. But without a detailed analysis of the parameter shifts, it is really anyone's guess what will happen, at this point.Keahttps://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-33061537911105451362011-11-08T14:04:24.126+13:002011-11-08T14:04:24.126+13:00As to "... the massless mixing has to be the ...As to "... the massless mixing has to be the identity matrix ..."<br /><br />you have there a very interesting and important idea <br />(you should put it on vixra to establish credit). <br /><br />It makes physical sense: <br /><br />The massive Z0 and massless photon will in the Massless Realm <br />become massless W0 plus the massless high-energy QED gauge boson <br />and <br />the Weinberg angle will not be relevant in the Massless Realm. <br /><br />if all fermions are massless <br />there is no energy to be gained in any decay chain <br />like <br />tauon to muon to electron <br />or <br />tau-neutrino to mu-neutrino to electron neutrino<br />or <br />Tquark to charm to up (by W0)<br />or <br />Bquark to strange to down (by W0)<br />or <br />Tquark to strange to up (by W+/-) <br />or <br />Bquark to charm to down (by W+/-) <br /><br />so <br /><br />any lepton or quark fermion will just stay as it is <br />until it has interactions that bring its energy down <br />below the ElectroWeak Mass Generation threshold. <br /><br />Maybe experiments in the Massless Realm will not show <br />anything that distinguishes the second and third generation fermions <br />from the first generation (mass having gone away)<br />and <br />so theoretical physics models will only need to have <br />one fermion generation at high energies (Massless Realm). <br /><br />As to why nothing like the Massless Realm has yet been seen at the LHC, <br />note that <br />the LHC beams have only been operating at 7 Tev for protons <br />and<br />protons are not elementary particles but are complicated <br />bags of quarks and gluons. <br /><br />If the ElectroWeak transition to the Massless Realm takes place <br />at 300 GeV (about as low as you could go)<br />the 3 valence gluons would carry 1 TeV <br />and <br />since gluons (and maybe virtual sea quarks) might carry the remaining 6 TeV <br />(in Lagrangian QCD most of the proton mass is gluon binding energy) <br />it may be that the LHC has yet to reach the Massless Realm. <br /><br />If the ILC collides electrons at 500 GeV to 1 TeV <br />it might be that the ILC would not see much Massless Realm phenomena <br />(especially if each electron is seen as one valence electron <br />plus a cloud of virtual electron-positron pairs and photons <br />among whom the total energy must be divided). <br /><br />If the CLIC collides electrons up to 5 TeV <br />then it might be a good bet to see some Massless Realm phenomena. <br /><br />It would be interesting to estimate what effect Massless Realm phenomena <br />might have on muons in a Muon Collider. <br /><br />TonyTony Smithhttps://www.blogger.com/profile/06997411020615409522noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-6705178014313753922011-11-08T08:52:43.521+13:002011-11-08T08:52:43.521+13:00Re massless quarks: we could take a punt and use (...Re massless quarks: we could take a punt and use (1) the tribimaximal form for neutrino mixing (probably broken by $\theta_{13}$) along with (2) a quark lepton complementarity ansatz to reduce the three quark parameters to a two parameter form. But which one? Using $(-0.231,24)$ we obtain an almost-CKM form with a zero entry in place of the smallest entry, like for the TBM matrix. <br /><br />BUT, since the TBM is definitely associated to mass for charged leptons, via the Koide rule, and all $3 \times 3$ qutrit operators are closely related to mass, I would guess that massless mixing has to be the identity matrix. Could the LHC see something closer to the identity? That would be my bet.Keahttps://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-88373015976937247212011-11-08T08:42:08.932+13:002011-11-08T08:42:08.932+13:00Interesting, Tony. Of course, in those centuries (...Interesting, Tony. Of course, in those centuries (1200-1600) there would have been many European and Eastern scholars with access to ancient works that have since been lost. We have the <a href="http://en.wikipedia.org/wiki/Vedas" rel="nofollow">Vedas</a>, and so on, but just imagine what was in all those destroyed libraries! <br /><br />Re the CKM: as my blog shows, I have been struggling with these parameters for some years now. First, since the continuum fields are constructed from categorical algebra, we need to find the right 'series' of discrete data from the motivic point of view. This would probably be incredibly easy for a good mathematician, which is why it is so frustrating thinking about it on my own.Keahttps://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-23123093074593619172011-11-08T06:50:26.613+13:002011-11-08T06:50:26.613+13:00Bruno may have only been an intermediary.
The Wik...Bruno may have only been an intermediary. <br />The Wikipedia entry on Ramon Llull says: <br />"... Around 1275, Llull designed a method, which he first published in full in his Ars generalis ultima or Ars magna ("The Ultimate General Art", published in 1305) ... It is believed that Llull's inspiration for the Ars magna came from observing Arab astrologers use a device called a zairja. ...<br />Llull also invented numerous 'machines' for the purpose. <br />One method is now called the Lullian Circle, each of which consisted of two or more paper discs inscribed with alphabetical letters or symbols that referred to lists of attributes. The discs could be rotated individually to generate a large number of combinations of ideas. ... These combinations were said to show all possible truth about the subject of the circle. Llull based this on the notion that there were a limited number of basic, undeniable truths in all fields of knowledge, and that we could understand everything about these fields of knowledge by studying combinations of these elemental truths.<br />...<br />The idea was developed further by Giordano Bruno in the 16th century, and by Gottfried Leibniz in the 17th century for investigations into the philosophy of science. Leibniz gave Llull's idea the name ars combinatoria, by which it is now often known. Some computer scientists have adopted Llull as a sort of founding father, claiming that his system of logic was the beginning of information science. ...". <br /><br />Tony <br /><br />PS - As I have said on my web site, <br />I think that it goes back even further to ancient African IFA divination. <br /><br />PPS - On another matter, the 3x3 Kobayahsi-Maskawa matrix: <br />If Electroweak Symmetry Breaking and Mass Generation occurs around 300 GeV or so<br />then <br />quarks etc should be massless at higher energies <br />and<br />the LHC should be able to do experiments at those higher energies at which quarks should be massless <br />so <br />the LHC should be able to measure Massless Realm Kobayashi-Maskawa matrix parameters. <br /><br />It will be interesting to see whether the Massless Realm K-M parameters are the same as or different from the K-M parameters we measure in the low-energy Massive Realm. <br /><br />Since my model calculations of K-M parameters are based on fermion mass ratios<br />my calculation method is not applicable to the Massless Realm. <br /><br />Therefore, I am very interested in alternative fundamental ways to calculate K-M parameters, <br />and your work on circulants (such as vixra 1008.0015) seems an interesting approach. <br />What ideas do you have for fundamental derivation of the parameters you use in section 4 of that paper ? <br /><br />Have you presented ideas for calculations of Massless Realm phenomena that might be experimentally testable to LHC people ?Tony Smithhttps://www.blogger.com/profile/06997411020615409522noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-34879581359198498002011-11-06T17:09:26.083+13:002011-11-06T17:09:26.083+13:00Once upon a time, I often said that the 19th centu...Once upon a time, I often said that the 19th century American philosopher <a href="http://www.peirce.org/" rel="nofollow">C. S. Peirce</a> was the founder of Category Theory, with his work on diagrammatic logic. But <a href="http://books.google.com/books/about/Giordano_Bruno_and_the_geometry_of_langu.html?id=3AwiNeYULfwC" rel="nofollow">Bruno himself</a> deserves this honour. And if Bruno, then we must respect the long murky chain of history, backwards to ancient times.Keahttps://www.blogger.com/profile/05652514294703722285noreply@blogger.com