tag:blogger.com,1999:blog-10614348.post8286305273757297349..comments2024-01-22T11:26:37.599-08:00Comments on TGD diary: E8 symmetry, harmony, and genetic codeMatti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger16125tag:blogger.com,1999:blog-10614348.post-8182962426523569012016-01-25T16:40:11.415-08:002016-01-25T16:40:11.415-08:00
When I talk about p-adic prime I talk about prim...<br />When I talk about p-adic prime I talk about prime as prime characterizing p-adic number field. <br /><br />The number of prime is very general and defined not only for rationals but also for their algebraic extensions. One of<br />them is complex rationals: in this case algebraic extension consists of complex integers m+in and Gaussian primes are primes for this number fields. There is infinity of other extensions and all of them have also p-adic variants. The number of number fields is<br />really huge. <br /><br />Primes are well-defined also for quaterions and octonions.Matpitka6@gmail.comhttp://tgdtheory.com/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-76512758319998592392016-01-25T12:49:28.104-08:002016-01-25T12:49:28.104-08:00Why must the primes be p-adic? You also use Mersie...Why must the primes be p-adic? You also use Mersienne primes.<br />Note that these small primes are mostly 'virtual' roots?<br /><br />Here a good monopole link http://dl.bsu.by/file.php/534/Lecture4.pdfUllahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-59100884829695831332016-01-19T19:24:41.195-08:002016-01-19T19:24:41.195-08:00The small primes 3,5,7, that you assign with E7 ha...The small primes 3,5,7, that you assign with E7 have nothing to do with p-adic primes. Symmetry groups and p-adic length scale hypothesis are totally unrelated. <br /><br />%%%%<br /><br />p-Adic primes of course appear in p-adic coupling constant evolution. This involves 3 conjectures: here I am little bit ashamed since I know that most conjectures made by human kind have been wrong. So: hereby I confess all my potential crimes against serious science;-):<br /><br />Conjecture 1: The values of alpha_K analogous to critical temperature are conjectured to be labelled by p-adic primes near prime powers of two (p= about 2^k, k prime: zeros in increasing order for imaginary part<-->primes in increasing order. Every p-adic length scale identified in this manner corresponds to its own critical temperature. This allows to realize coupling constant evolution (physical fact) with vanishing loop corrections and thus also vanishing divergences). One could ask: why not all p-adic length scales, why not p-adic length scales for which k is integer?<br /><br />Conjecture 2: Number theoretical universality (NTU) motivates the conjecture that primes labels zeros of zeta: exponents p^iy for imaginary parts y of zeros of zeta define roots of unity. <br /><br />NTU derives from the vision about adelic physics. Various p-adic physics serve as cognitive representations for real physics. Strong form of holography making string like objects and partonic 2-surfaces basic objects realizes this vision at space-time level. Coupling constant evolution would be number theoretical and reflect the hierarchy of algebraic extensions of rationals at fundamental level. <br /><br />Two conjectures are involved: this is of course dangerous!! <br /><br />Prediction: The identification of spectrum of 1/alpha_K with zeros of zeta predicts an evolution which looks realistic and the prediction for value of alpha_U(1) is excellent at electron length scale. <br /><br />Conjecture 3: The spectra of *all* gauge coupling constants in coupling constant evolution correspond to zeros of zeta(M(s), where M is some Mobius transformation s-->as+b/cs+d, a,b,c,d real, mapping which is holomorphic in upper half plane and maps its to itself. <br /><br />Prediction: The evolution of 1/alpha_W, the weak coupling strength is obtained in this manner and the integers a,b,c,d are very simple: one of them is 137 (magic number!) and the values of Weinberg angle is correct and fine structure constant are correct at electron's p-adic length scale. At ultra high energies the predictions differ dramatically from those of standard model.<br />Matpitka6@gmail.comhttp://tgdtheory.com/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-57304133055718555702016-01-19T11:03:22.835-08:002016-01-19T11:03:22.835-08:00"For instance, critical values could correspo..."For instance, critical values could correspond to primes near to prime power of two: when p-adic length scale is scaled by suitable power of two, alpha_K changes. Coupling constant evolution would be discrete."<br /><br />As instance E7 has primes 3,5 and 7 inherent in its symmetry, so that 7 is bosonic, 3 and 5 fermionic (Pythagoras?)? But is the commutative part giving massivation/condensation also between 3 and 5 (compare DNA?), in fact a small part of the whole non-commutative Lie group. Actually like a 'surface' (compare Josephs simulation video), but that 'surface' can bulge out much? (Compare to arXiv: 1410.8447v1<br />http://irfu.cea.fr/Phocea/Vie_des_labos/Ast/ast.php?t=fait_marquant&id_ast=3533s)and 'sea quarks' necessary to have involved? Also twin primes interesting. This is why I asked about primes and/as thermodynamics.<br /><br />Also, what is a hadron seems varying. Also 'annihilation' of whole hadron possible, and consequent 'popping up'. http://arxiv.org/abs/1406.7425 and the 'compactification' of sheets at higher N.Ullahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-83957391438466842152016-01-19T04:42:57.343-08:002016-01-19T04:42:57.343-08:00
Kahler coupling strength requires some explanatio...<br />Kahler coupling strength requires some explanations.<br /><br />*Kahler coupling strength alpha_K is the only coupling parameter of TGD and appears in Kahler action which defines the classical theory. alpha_K analogous to critical temperature: this if one accepts that TGD Universe is quantum critical. <br /><br />*The question is whether alpha_K has just single critical value or large number of critical values. For instance, critical values could correspond to primes near to prime power of two: when p-adic length scale is scaled by suitable power of two, alpha_K changes. Coupling constant evolution would be discrete.<br /><br />* This would allow to have non-trivial coupling constant evolution (albeit in discrete sense): this is forced by experimental facts. But alpha_K would also have trivial local coupling constant evolution lasting for few octaves for given prime satisfying this condition: alpha_K and other couplings would be piecewise constant functions of length scale. <br /><br />* All radiative corrections would vanish and theory would be like N=4 SUSY in this respect: extremely simple. Also number theoretical considerations demand discrete coupling constant evolution.<br /><br /> *By symmetry arguments alpha_K analogous to weak U(1) coupling strength, which is not quite the same as fine structure constant alpha_em but near to it.<br /><br />*The hypothesis that the values of 1/alpha_K interpreted in this manner correspond to zeros of zeta works so nicely that I tend to believe that this interpretation is correct. U(1) coupling constant evolution would reduce to number theory. Same would happen to other coupling strengths. <br /><br />%%%%<br /><br />I have considered many options. I had to give up the assumption that alpha_K at electron length scale corresponds to the value of alpha_em, fine structure constant. I have also been considering the possibility that alpha_K has just one value independent of p-adic length scale and considered also other formulas for alpha_K.Matpitka6@gmail.comhttp://tgdtheory.com/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-35824396291598001972016-01-19T04:03:45.176-08:002016-01-19T04:03:45.176-08:00You say:
Newton's constant [G?] is geometrize...You say: <br />Newton's constant [G?] is geometrized to CP_2 size scale and one can take CP2 size as fundamental length unit.<br /><br />Only Kahler coupling strength remains as dimensionless parameters, which cannot be eliminated by choice of units. It has a spectrum since it is inversely proportional to h_eff. The proposal is that this spectrum reduces essentially to the spectrum of zeros of zeta. Same would happen to other coupling strengths related to alpha_K.<br /><br />Kähler coupling as c.c. or alpha? Also about the G seen as that, are there any links?<br />Forgive my stupidity...Ullahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-52648979757610777072016-01-18T10:52:25.646-08:002016-01-18T10:52:25.646-08:00http://arxiv.org/abs/1601.01797
This paper is exc...http://arxiv.org/abs/1601.01797<br /><br />This paper is excellent is astounding, I did not know that the H=xp Hamiltonian of Berry-Keating has interpretations in terms of general relativity and Rindler spacetimes. It goes into detail the interpretation of the "smooth Riemann zeros" that is, the zeros without the correction of the argument/phase of zeta.. and shows how the "missing spectral lines" interpretation of Connes is not entirely correct... the correct interpretation is that the argument provides a finite sized correct to the exact location of the zeros.. anyway, massive and massless fermions appear and they suggest that one could construct a system of reflecting moving mirrors that generates the zeros in its spectrum. Pretty cool<br /><br />--crowAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-10614348.post-86235925959170273922016-01-17T22:34:58.834-08:002016-01-17T22:34:58.834-08:00To Ulla:
The mentioning of Kosterlitz-Thouless fo...To Ulla:<br /><br />The mentioning of Kosterlitz-Thouless forced me to Wikipedia to look summary about thermal phase transitions and this in turn to ask how TGD description could generalise the description of thermal and quantum phase transitions (quantum TGD as square root of thermodynamics). The reply however grew to entire posting so that I will not attach it to here.Matpitka6@gmail.comhttp://tgdtheory.com/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-4830220304032986992016-01-17T22:30:26.926-08:002016-01-17T22:30:26.926-08:00To Anonymous:
I do share the feelings of the ...<br />To Anonymous: <br /><br />I do share the feelings of the authors of stochastic papers;-). <br /><br />In the case of Planck constant it is however important that its spectrum is discrete and it reduces to group theory: the levels of fractal hierarchy of isomorphic subalgefbras of conformal algebra are labelled by integers n =h_eff/h. h van be taken to h=1 by a suitable choice of units.<br /><br />Light velocity c can be reduced to c=1 by suitable choice of units when signal propagating with light-velocity is geometrize to the notion of light-like geodesic. <br /><br />Newton's constant is geometrized to CP_2 size scale and one can take CP2 size as fundamental length unit.<br /><br /> Only Kahler coupling strength remains as dimensionless parameters, which cannot be eliminated by choice of units. It has a spectrum since it is inversely proportional to h_eff. The proposal is that this spectrum reduces essentially to the spectrum of zeros of zeta. Same would happen to other coupling strengths related to alpha_K.<br /><br /> Matpitka6@gmail.comhttp://tgdtheory.com/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-82031822115401250172016-01-17T20:27:30.910-08:002016-01-17T20:27:30.910-08:00Reminds me of the stochastic papers where I read a...Reminds me of the stochastic papers where I read a footnote that says "every occur ance of the constant C represents a different variable that changes with time"Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-10614348.post-42609077197573614542016-01-17T13:52:34.174-08:002016-01-17T13:52:34.174-08:00The link left out, sry.
http://rsta.royalsocietypu...The link left out, sry.<br />http://rsta.royalsocietypublishing.org/content/370/1981/5718Ullahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-19594031759761281602016-01-17T13:50:26.322-08:002016-01-17T13:50:26.322-08:00Also link this to Wilson loops?Also link this to Wilson loops?Ullahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-75923247817408322892016-01-17T13:49:19.515-08:002016-01-17T13:49:19.515-08:00In spin ice with short-range interactions up to se...In spin ice with short-range interactions up to second neighbours, there is an intermediate critical phase separated from the paramagnetic and ordered phases by Kosterlitz–Thouless (KT) transitions. In dipolar spin ice, the intermediate phase has long-range order of staggered magnetic charges. The high- and low-temperature phase transitions are of the Ising and 3-state Potts universality classes, respectively. <b>Freeze-out of defects in the charge order produce a very large spin correlation length in the intermediate phase.</b> As a result of that, the lower-temperature transition appears to be of the KT type.<br /> <br />spin correlations decay with the distance algebraically rather than exponentially [logaritmic perpendicularly between different phases?] so spin is the slowest transition, always only 1/2 (fermion) and this should be the 'condensation phase' of the E8, of which most is non-commutative, and 'virtual'. What part of E8 is splitted and why? It must be the center, if I understand right, hence the creations of microBH and 'wormholes'are also possible. What role play the long correlation lengths? In Josephs simulations we saw it as a 'clock-function' of pulses.<br /><br />You refer to gravitational couplings (and gravitational interaction?) but the use of constant G is a bit bothersome here in quantum level. Also it is normally eliminated by the hbar=c=G as 1, so it cannot be seen so well.<br /><br />At the same time this describes different time scenarios and strong tensions. Ullahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-49255794918801946162016-01-15T21:24:14.658-08:002016-01-15T21:24:14.658-08:00Glass Bead Games with things like MacKay correspon...Glass Bead Games with things like MacKay correspondence are dangerous (I might destroy my entire career;-) since my technical skills are so meagre. The only guide line is physical intuition and generalised common sense and I dare trust to them. Matpitka6@gmail.comhttp://tgdtheory.com/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-50511157160337121392016-01-15T13:42:15.830-08:002016-01-15T13:42:15.830-08:00Matti, welcome back to the Glass Bead Game. Matti, welcome back to the Glass Bead Game. L. Edgar Ottohttps://www.blogger.com/profile/00525169618204198073noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-57777408752789510142016-01-15T06:55:09.651-08:002016-01-15T06:55:09.651-08:00Matti, what an entertaining post, very cool. MacKa...Matti, what an entertaining post, very cool. MacKay. I remember something about moonshine and the MacKay-Thompson series. https://en.m.wikipedia.org/wiki/Monstrous_moonshine<br /><br />The number 137 pops up again and again because it's the first time that the argument of zeta is not on the principal branch of the logarithm, also the numbers 3,4,8 etc also pop up after some relatively standard manipulations in my paper on hardy z function . I should have known Michael Berry is a cranky old man, he totally missed my point about about what I was suggesting and claimed "some of us discovered those graphs years ago" yet provided no evidence or references.. it's hard to find people to work with<br /><br />--crowAnonymousnoreply@blogger.com