tag:blogger.com,1999:blog-10614348.post2393107101260787262..comments2024-05-16T00:26:22.599-07:00Comments on TGD diary: About Fermi-Dirac and Bose-Einstein statistics, negentropic entanglement, Hawking radiation, and firewall paradox in TGD frameworkMatti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger15125tag:blogger.com,1999:blog-10614348.post-15542456259533242422015-11-19T10:33:39.023-08:002015-11-19T10:33:39.023-08:00
Condensed matter is certainly not 10-D: this I am...<br />Condensed matter is certainly not 10-D: this I am saying. String theorists however want some use for their methods;-)! So that it is not so big deal to decide that it is 10-D! A lot of papers and long curriculum vitae: this is after all more important than physics;-). <br /><br />Condensed matter gives a lot of applications for the high levelled mathematical physics: I have been developing them for more than decade. <br /><br />I have explained again and again that the problem of string theory approach is that the realisation of holography is doomed to fail because conformal invariance is too restricted. The extended conformal invariance of TGD requires 4-D space-time and 4-D Minkowski space. This is physics. <br /><br />Maldacena has done nice mathematical work but unfortunately it has very little to do with physics of any kind. <br /><br />Matpitka6@gmail.comhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-48640406746185004122015-11-19T09:56:43.777-08:002015-11-19T09:56:43.777-08:00The most promising support of this theory is the A...The most promising support of this theory is the AdS/CFT correspondence [25], which explicitly connects via a one-to-one correspondence the framework of a 5D string theory in anti-deSitter space with a conformal quantum field theory on the 4D boundary.<br />Maldacena, J., Adv. Theor. Math. Phys.2 (1998) 231; <br />Maldacena, J., Int. J. Theor. Phys.38 (1998) 1113; <br />Petersen, J. L., Int. J. Mod. Phys. A 14(1999) 3597; <br />+ additional introductions to and overviews of the AdS/CFT<br />+ http://arxiv.org/abs/hep-th/0309246Ullahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-2244791400002180582015-11-19T08:22:59.128-08:002015-11-19T08:22:59.128-08:00This is a book, http://users.physik.fu-berlin.de/~...This is a book, http://users.physik.fu-berlin.de/~kleinert/kleiner_reb1/pdfs/1.pdf<br />gauge fields in condensed matterUllahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-40172912113311041132015-11-19T08:14:46.875-08:002015-11-19T08:14:46.875-08:00AdS is a mathematical representation of holography...AdS is a mathematical representation of holography but with too small conformal symmetry. One cannot actually forget that space-time is 10-D in it and this makes condensed matter applications questionable. <br /><br />This I don't get, condensed matter is not in 10D? Ullahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-44143987348368646552015-11-19T08:08:57.446-08:002015-11-19T08:08:57.446-08:00https://books.google.fi/books?id=hyx6BjEX4U8C&...https://books.google.fi/books?id=hyx6BjEX4U8C&pg=PR9&hl=sv#v=onepage&q&f=false<br />A Quantum Approach to Condensed Matter Physics<br /> AvPhilip L. Taylor,Olle Heinonen, 2002Ullahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-20126659434315060612015-11-18T18:16:55.027-08:002015-11-18T18:16:55.027-08:00
Thank you. A lot of reading. I hope that I had ti...<br />Thank you. A lot of reading. I hope that I had time. The notion of distortion is new to me. It looks interesting. I did not understand what antisymmetry in this context could mean. <br /><br />AdS is a mathematical representation of holography but with too small conformal symmetry. One cannot actually forget that space-time is 10-D in it and this makes condensed matter applications questionable. For instance, in applications one must assume that the additional dimensions are large. This makes no sense. One cannot take just some features of the system and forget things like actual space-time dimension. This is typical left-brainy thinking plaguing the theoretical physics today.<br /><br />One could see AdS an alternative description for 2-D conformal theory with 2-surfaces imbedded in 10-D spacetime with boundary. This is purely mathematical approach and personally I see the attempts to describe condensed matter as 10-D blackholes as a horrible waste of time. AdS has made no breakthroughs where it has been applied. There is diplomatically incorrect bread and butter view about this and I cannot prevent my alter ego from stating it;-). string theory was a failure but string theorists have a lot of methods and they want to apply them and receive also funding for this activity: why not condensed matter! <br /><br />To get something better one must generalise the notion of conformal symmetry from 2-D to 4-D. Light-bone boundary allows hugely extended superconformal symmetry and supersymplectic symmetry. Now 10-D space is replaced with 4-D space-time surface in M^4xCP_2 and also twistors essential for conformal invariance enter the game. Holography becomes strong form of holography. <br />In holography 3-D surface could could for 4-D physics. Now 2-D partonic 2-surfaces and string world sheets do it. Strings are of course essential also now and in TGD inspired quantum biology and thermodynamics of consciousness the Hagedorn temperature seems to be a key player. I must also mention the magnetic flux tubes which are everywhere. <br /><br />If I were a dictator or Witten, it would took five minutes and people would be busily making TGDt;-). <br /><br />Matpitka6@gmail.comhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-612611372389988722015-11-18T13:16:37.456-08:002015-11-18T13:16:37.456-08:00http://www.nature.com/ncomms/2015/151117/ncomms981...http://www.nature.com/ncomms/2015/151117/ncomms9818/full/ncomms9818.html The new way to look at symmetry and deformation. Compare to<br />http://scitation.aip.org/content/aip/magazine/physicstoday/article/68/11/10.1063/PT.3.2980 and the older<br />http://scitation.aip.org/content/aip/magazine/physicstoday/article/62/1/10.1063/1.3074260<br />and http://motls.blogspot.fi/2015/11/fq-hall-effect-has-vafa-superseded.html<br />Moreover, the big strength of Chern-Simons and topological field theories is that you may put them on spaces of diverse topologies so even the weaker topological claim about the AdS space can't be considered an absolute constraint for the theory.<br /><br />What is your opinion of AdS space other than y don't understand it :) How then interpret results gained with it?Ullahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-11594693335729651272015-11-09T00:35:36.550-08:002015-11-09T00:35:36.550-08:00It would be interesting to look the behavior of in...<br /><br />It would be interesting to look the behavior of inverse of complex temperature defined by zeros of zeta and its pole: this for for fermionic partition function.<br /><br />I have assumed the Kahler coupling strength is real but one might consider in spirit of electric magnetic duality also complex values. This would allow to consider the identification as poles of fermionic zeta as values of 1/alpha_K. Just for fun of course!<br /><br />Trivial zeros would correspond to p-adic temperatures T=-1/n in the convention defined by strict formal correspondence of p-adic Boltzmann weight with real Boltzmann weight. I have earlier defined p-adic temperature as T=1/n. <br /><br />The inverse of real critical temperature correspond to 1/alpha_K=T=1 (pole of Riemann zeta), p-adic temperatures T=1/n, and inverses of complex temperatures to inverses of non-trivial zeros of zeta which approach to zero at the limit y--> infty. This could have interpretation as asymptotic freedom since alpha_K would go to zero. At infrared 1/alpha_K approach to the lowest zero 1/2+iy, y=14.1.. so that it does not diverge anywhere.<br /><br />The very naive guess would be that the real or imaginary part of some nontrivial zero corresponds to fine structure constant: this guess might be wrong of course The first estimate shows that this cannot be the case very accurately although zeros . The smallest value of alpha_K would correspond to 1/14: color coupling strength?<br /><br />One obtains also alpha_K = about 127 for one of the zeros - fine structure constant at electroweak scale. Could the values of 1/alpha_K be identified imaginary parts of zeros of zeta and assigned with p-adic length scales?<br /><br /> Magnetic coupling would correspond to real part and be equal to -1/2,-1, and n=1,2,3,.... Kahler electric coupling would have values vanishing for real zeros and pole and imaginary part of zero at critical line. Does this make any sense? Difficult to say! <br /><br />If this crazy conjecture makes sense then both super-symplectic conformal weights and complex inverse of Kahler coupling strength would have poles of zeta_F as their value spectrum. The different values for zeros of zeta could in turn naturally correspond to number theoretical coupling constant evolution with values of coupling strength associated with different algebraic extensions of rationals.<br /><br /><br /><br /><br /><br /> Matpitka6@gmail.comhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-36128156956259270092015-11-08T23:52:20.028-08:002015-11-08T23:52:20.028-08:00Corrected version of the comment which contained s...Corrected version of the comment which contained something which should not belong to it.<br />########<br /><br />I was thinking further about the idea that physically the poles of fermionic zeta are the appropriate notion. The partition function for poles would diverge as intuition suggests. I want to explain more precisely this intutiion.<br /><br /> Since the temperature interpreted as 1/s is not infinite this means that one has analog of Hagedorn temperature in which degeneracy of states increases exponentially to compensate exponential decreases of Boltzman weight so that partition function is sum of infinite number of numbers approaching to unity. Hagedorn temperature relates by strong form of holography to magnetic flux tubes behaving as strings with infinite number of degrees of freedom. One would have quantum critical system. Supersymplectic invariance, etc..<br /><br />The real part of temperature is real part of 1/s and given by T_R= 1/2/(1/4+y^2) and approaches zero for large y as it should. Also imaginary part T_Im approach zero. One has infinite number of critical temperatures.<br /><br />An interesting question is whether zeros of zeta correspond to critical values of Kahler coupling strength having interpretation as inverse of critical temperature?!<br /><br />But what about negative values of poles of z_F at n=-1,-2,...? They would correspond to negative temperatures -1/n. No problem! In p-adic thermodynamics p-adic temperatures has just these values if one defines p-adic Boltzmann weight as exp(-E/T)---> p^(-E/T), with E=n conformal weight!! The condition that weight approaches zero requires T negative! Trivial poles would correspond to p-adic thermodynamics and non-trivial poles to ordinary real thermodynamics! <br /><br />This would be marvellous connection between TGD and number theory. Riemann zeta would code basic TGD and of course, all of fundamental physics! ;-)<br />Matpitka6@gmail.comhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-30013467264516668882015-11-08T19:54:37.772-08:002015-11-08T19:54:37.772-08:00o?
More talk here http://empslocal.ex.ac.uk/peopl...o?<br /><br />More talk here http://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/physics2.htmAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-10614348.post-58233635740783666302015-11-08T17:16:31.649-08:002015-11-08T17:16:31.649-08:00This comment has been removed by a blog administrator.Matpitka6@gmail.comhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-46481490112426327412015-11-08T16:56:08.695-08:002015-11-08T16:56:08.695-08:00
Mellin transform representation is of course comp...<br />Mellin transform representation is of course completely ok mathematically but the physical interpretation in terms of fermionic c statististics seems utterly wrong. Fermionic partition function is sum n^-s where n is square free integer and I cannot see a connection with representation.<br /><br />Matpitka6@gmail.comhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-69351247766743775352015-11-08T11:10:48.509-08:002015-11-08T11:10:48.509-08:00yes... if the authors would have done the same ana...yes... if the authors would have done the same analysis with the Hardy Z function (it is totally real valued when its parameter is real) they would have gotten farther or made even deeper insights. <br /><br />I will think more about the Mellin transform aspect, I am quite comfortable with them by now. <br /><br />[MP] *The finding that by writing zeta as WKB wave function as a product of modulus and phase with phase given by exponent of action defined by the function S(z) giving the number of zeros at critical line is very interesting since at zeros of zeta S(z) as number of zeros is quantized action!<br /><br />[SC] Yes, it is quite cool! I am adding more content related to the Hamilton-Jacobi equations to my paper on this topic at http://vixra.org/abs/1510.0475<br /><br />p.s. see page 5 of the paper at http://www.math.waikato.ac.nz/~kab/papers/zeta2.pdf the flow near the zeros is graphed... I think, if u look on the appendix of my paper at http://vixra.org/abs/1510.0475<br /><br />I suggest an extension of the Berry-Keating Hamiltonian H(x(t))=((x(t)x'(t)+x'(t)x(t)))/2=-i(x(t)x'(t)+1/2) to something like <br />𝒥^(2,+)x(t)={(p,X)|x(t+z)⩽x(t)+p⋅z+(X:z⊗z)/2+o(|z|^2) as z→0}<br />and<br /> 𝒥^(2,-)x(t)={(p,X)|x(t+z)⩾u(x)+p⋅z+(X:z⊗z)/2+o(|z|^2) as z→0}<br /><br />which are sets called the second-order superjets and subjets of x(t) where p∈ℝ^n is the Jacobian of x(t∈Ω)∈C^0(Ω⊆ℝ^n) and X∈𝕊^n is the Hessian of x(t) where 𝕊^n is the set of n×n symmetric matrices. The main idea being that the canonical momentum x˙(t) is replaced with the generalized pointwise derivative which can be written as 𝒥^2x(t) in case both the superjet and subjet exist and actually define the same set.<br /><br />The "X" in that superjet and subjet definition should really be X_n where n is the n-th Riemann zero, I think that the flow around each zero can be specified in terms of a symmetric operator X... it would algebrically/numerically encode the flow around each zero. <br /><br />anyway... I'm not personally that interested but it would be something someone else could do.. I really want to work with the Hamilton-Jacobi aspects some more and try applying their analysis to the Z function, since that will get rid of some of the objects you stated. Hardy's Z function is most clearly expressed as<br /><br />Z(t)=exp(I*(-I*(lnGAMMA(I*t*(1/2)+1/4)-lnGAMMA(1/4-I*t*(1/2)))*(1/2)-(1/2)*ln(Pi)*t))*Zeta(1/2+I*t)<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-10614348.post-85697535000965639622015-11-07T23:29:47.028-08:002015-11-07T23:29:47.028-08:00A nice paper written in such a manner that physici...<br />A nice paper written in such a manner that physicist understands. <br /><br />*The finding that by writing zeta as WKB wave function as a product of modulus and phase with phase given by exponent of action defined by the function S(z) giving the number of zeros at critical line is very interesting since at zeros of zeta S(z) as number of zeros is quantized action! <br /><br />*The authors propose interpretation of zeros as conformal weights: this is natural since angle is generalized to complex coordinate z and the integrals INT p.dq along closed classical orbit with residue integral over S interpreted as complex 1-form. The interpretation of zeros as conformal weights is also the TGD interpretation. <br /><br />*The authors mention also the doubling formula of zeta and deduce that Riemann zeta is proportional to Mellin transform of fermionic zeta function. Here I did not understand at all. I see it as Mellin transform of **inverse** of the inverse 1/(1+exp(x)) of fermionic zeta , not fermionic zeta 1+exp(x)!! My first reaction is that they have made a mistake. I cannot hope that I am wrong since in this case I myself had made a horrible blunder!;-).<br /><br />Let me explain why I believe that I am right. I have proposed different interpretation for the fermionic zeta based on the fact that fermionic zeta zeta_F equals to Z_F=Prod_p (1+p^s) and Riemann zeta to Z_B= Prod 1/(1-p^s) as formal partition functions of a number theoretic many-fermion/many-boson system with energies coming as multiples of log(p) (for fermions only n=0,1 is of course possible, for bosons all positive values of n are possible and this the form of Z_F). Product involves all primes. <br /><br /> In this framework **poles**(not zeros!!) of fermionic zeta zeta_F(s)= zeta(s)/zeta(2s)) (this identity is trrivial to deduce, do it!!) correspond trivial zeros of zeta, the pole of zeta at s=1, and to trivial poles at negative integers. <br /><br />The interpretation of **poles** (much more natural in physics, and even more so in TGD, where fundamental particles involve only fermions!) of z_F as conformal weights associated with the representations of extended super-conformal symmetry associated with super-symplectic algebra defining symmetries of TGD at the level of "world of classical worlds" is natural. <br /><br />"Conformal confinement" stating that the sum of conformal weights is real is natural assumption in this picture. <br />The fact that superconformal algebra has a fractal structure implies direct connection with quantum criticality: infinite hierarchy of symmetry breakings to sub-symmetry isomorphic to original one!! Needless to say the conformal structure is infinitely richer than the ordinary one since the algebra in question has infinite number of generators given by all zeros of zeta rather than a handfull of with conformal weights n=-2,...+2). Kind of Mandelbrot fractal realized physically.<br /><br />*The problem of all attempts to interpret zeros of zeta relate to the fact that zeros are **not** purely imaginary, they have the troublesome real part Res)=1/2. This led me for long time ago to consider coherent states instead of eigenstates of Hamiltonian in my proposal for a strategy to prove Riemann hypothesis. <br /><br />Also the interpretation as partition function suffers from the same disease: genuine partition function should be real.<br /><br />In TGD framework the solution of the problem is zero energy ontology (ZEO). Quantum theory is "complex square root" of thermodynamics and means that partition function indeed becomes complex entity having also the phase. Ordinary partition function is modulus squared for it.<br />Matpitka6@gmail.comhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-45641859421171140692015-11-07T10:27:51.415-08:002015-11-07T10:27:51.415-08:00See section 4 entitled "Physical Perspectives...See section 4 entitled "Physical Perspectives" of http://arxiv.org/abs/0903.4321 "Eigenvalue Density, Li's Positivity, and the Critical Strip" where the Hamilton-Jacobi (no Bellman here!! :) conditions of classical mechanics form the basis of the quantization conditions. The idea is related to "H=xp" Hamiltonian, with a twist. From the paper also "This tells us that the<br />Riemann ξ-function (symmetrized Zeta function), up to a factor which does not vanish in the critical strip, is the Mellin transform of a Fermi–Dirac distribution"<br /><br />Can you please have a look and comment?<br /><br />--crow<br />Anonymousnoreply@blogger.com