tag:blogger.com,1999:blog-10614348.post1425341176630964850..comments2024-01-22T11:26:37.599-08:00Comments on TGD diary: Class field theory and TGD: does TGD reduce to number theory?Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger17125tag:blogger.com,1999:blog-10614348.post-21683959475829430602014-02-19T04:19:44.197-08:002014-02-19T04:19:44.197-08:00
I think that the misunderstanding is following.
...<br />I think that the misunderstanding is following.<br /><br />In ZEO WCW is space of all 3-surfaces: consisting of pairs of 3-surfaces at boundaries of given CD. <br />At each boundary 3 surface as several disjoint components. This kind of multicomponent 3-surface represents a single point in WCW. <br /><br />WCW decomposes to sectors labelled by the numbers of 3-surfaces at the two boundaries of CD and the moduli characterising the CD. Your thought experiments means only moving from a sector of WCW to another one and having different numbers of 3-surfaces at the boundaries of CD.<br /><br />Locally the given sector of WCW is Cartesian product of sectors containing only single 3-surface. Just as in many particle physics one effectively has configuration spar (E^3)^n. This approximation fails when the 3-surfaces touch.<br />This is however improbable since 3-surfaces in 7-D space delta M^4_+xCP_2 are in question. Intersection disappears with arbitrary small deformation.<br /><br /><br />Matti Pitkanenhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-7384173929576733482014-02-18T22:14:32.749-08:002014-02-18T22:14:32.749-08:00Dear Matti,
Suppose there is an electron in a sys...Dear Matti,<br /><br />Suppose there is an electron in a system. In standard QFT, in really there is not just this electron, but there are a lot of particles when one goes to higher and higher energies.<br /><br />In TGD, there is space of 3-surfaces. But is there any different between high and low energy? When 3-surface like particle is replaced with point like particle, this is similar to high energy QFT, that there are a lot of point like particles?<br /><br /><br />In macroscopic, when there is a system of gas with atoms of gas as smaller 3-surfaces glued to space-time sheet of the system, one can say in the viewpoint of TGD, there is space of 3-surfaces. These 3-surfaces corresponded to atoms of the gas. <br />Now!, Let’s we pick up the particles of the object one after one. Hence the number of 3-surfaces in the WCW reduced in the process. <br />But I think the number of 3-surfaces in WCW, is a mathematical property of WCW and is not related to how many atoms of gas there is in the system in the external world.<br />What is my misunderstanding?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-10614348.post-77185074174666602032014-02-17T08:29:24.026-08:002014-02-17T08:29:24.026-08:00
To Ulla:
Certainly not. I cannot why this sho...<br />To Ulla: <br /><br />Certainly not. I cannot why this should be the case.<br />Matti Pitkanenhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-39594296333737806642014-02-17T01:44:31.336-08:002014-02-17T01:44:31.336-08:00"What is important are not details, but the i... "What is important are not details, but the idea of bosonic emergence. Only fundamental fermions exist. From these one can engineer observed fermions and bosons."<br /><br />Charge conservation when bosons are carriers for the gauge field???? This means that the charge conservation IS false dogma? Ullahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-46348169397440015372014-02-16T21:52:34.710-08:002014-02-16T21:52:34.710-08:00To Ulla:
I am sorry that my answers are not easy...<br />To Ulla: <br /><br />I am sorry that my answers are not easy to grasp. This not my or anyone else's fault. There is so much context lacking and I have only words which have strongly context dependent meaning. <br /><br />Bosons in the simplest - not yet quite correct - description is pair of massless fermion and antifermion which however do not move quite parallel so that boson can become massive. What is important are not details, but the idea of bosonic emergence. Only fundamental fermions exist. From these one can engineer observed fermions and bosons. <br /><br />Strings as such are not massless: dominant part of weak boson mass would come from the stringy contribution to mass.<br /><br />Detailed understanding of weak boson masses and Higgs has been the most difficult exercise in application of TGD, which are of course amateurish when seen from the Godly CERN perspective. <br /><br />My views have been fluctuation between all imaginable alternatives. Thank for LHC making end of this fluctuation! Theoreticians would be totally helpless without the helping had of experimentalist!<br /><br /><br /> Matti Pitkanenhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-40425058490990304382014-02-16T07:11:05.656-08:002014-02-16T07:11:05.656-08:00I have studied TGD in so many years, and I thought...I have studied TGD in so many years, and I thought now, after reading about other models, I would finally be ready to understand it a bit better. I am sorry if my questions are not easily grasped.<br /><br />I want to have a more clear view of the analog to Bohr model. The preferred extremals come from it. Are in your texts a good description of this analog. I have searched but when there is so much text.<br /><br />Also about how the criticality and stability is done in TGD I would be happy to have a better text.<br /><br />Bosonic strings are massless. Seen in a wormhole or Dirac fermione, how is that mechanism between fermions and bosons made?<br /><br />You know I am no enemy, at least you should know. I have helped you what I can.Ullahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-52793498936592756852014-02-15T19:13:54.859-08:002014-02-15T19:13:54.859-08:00This comment has been removed by a blog administrator.Matti Pitkanenhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-20861835042124925942014-02-15T18:53:35.193-08:002014-02-15T18:53:35.193-08:00
Hi,
it is lonely at the top;-). Personally I am...<br />Hi,<br /><br />it is lonely at the top;-). Personally I am driven by the passion to understand. Basically it does not matter much to me whether I am the only one who understands my life work. I am of course happy that there are at least few who have some idea about the importance of my work. I do my best to share my work. <br /><br />It is really wonderful to develop a new world view and know that it will be the world view of future. <br />What makes me sad is that recent academic science is to high extent CV production. But what else Big Science could be. The degeneration of our society is taking place both in economy, academies, and society in general, and one can make only guesses about how long the new Middle Age lasts. People like me are for science what mystics are for religion. We keep it alive over the dark periods. <br /><br />Concerning your questions. One class of open questions relates to the mathematical side. All this is very technical and personally I can develop only overall view. I develops slowly.<br /><br />*More detailed understanding of WCW geometry would be needed: I am now going through the entire existing material to update it and considerable progress has occurred. <br /><br />*I have a handful of characterisations of preferred extremals. Are they equivalent? <br /><br />*Adelic formulation of the theory seems to be very promising and here also much could be done. But people handling the needed enormously complex mathematics would be needed. I can provide only the physical insight.<br /><br />*More detailed understanding of stringy twistor approach to TGD would be needed: here I am too old to do anything detailed: just the understanding of the general vision would be enough for me.<br />Very fascinating result is that M^4 and CP_2 are the only 4-D manifolds allowing twistor space with Kahler structure. What does this imply?<br /><br />*One should go through p-adic thermodynamics by applying the recent model of elementary particles as pairs of wormhole contacts. I am too old to carry out the calculations again.<br /><br />Concerning particle physics.<br /><br />* LHC will probably provide new interesting findings and here M_89 hadron physics is the<br />most interesting issue.<br /><br />*Massivation of gauge bosons and Higgs should be understood better. The basic difference between TGD is that Higgs is there but Higgs mechanism is replaced with p-adic thermodynamics and Higgs couplings to fermions are just gradient couplings: this gives naturalness automatically.<br /><br />*TGD view about SUSY is something that I do not<br />understand well enough. Progress probably requires rather new insights which as such could be rather trivial. All revolves around right handed neutrino: I have pieces but I am unable to put them together.<br /><br /><br />In consciousness theory and quantum biology I am rather happy with the recent situation. The hardest problem has been the understanding of time and now I can safely say that it is understood. The recent model for microtubuli gave fantastic insights to how topological quantum computation (TQC) like processes form the core of quantum biology. Even understanding of the origin of genetic code might be possible. One new element is generalisation TQC using 1-braids to that using 2-braids: string world sheets are knotted in 4-D space-time! <br /><br />Matti Pitkanenhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-27146464565961866832014-02-15T13:02:04.478-08:002014-02-15T13:02:04.478-08:00Matti, I "understood" all of that... nic...Matti, I "understood" all of that... nice work... I am continually amazed by your<br />, but I am also a bit dismayed that I understand because it seems useless to understand if no else does? or not many rather. like, it is deemed "weird" to understand ... but that's more of a social issue I guess. Peace' can u summarize the current set of open questions in TGD? also yes... preferred... lol... by who...crowhttps://www.blogger.com/profile/14715663185910266616noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-56819777329272853192014-02-14T20:07:41.145-08:002014-02-14T20:07:41.145-08:00To Ulla:
1. Perelman's proof of Poincare con...<br />To Ulla:<br /><br />1. Perelman's proof of Poincare conjecture is accepted. It involves volume flow for a metric defined by its Einstein tensor and this leads to<br />constant curvature spaces asymptotically. The analog was well-known in 2-D case: sphere, torus,etc allows constant curvature metric too. <br /><br /> One could say that the flow as irreversible process does what approach to thermal equilibrium does: all irrelevant details are polished out and the simple constant curvature metric remains.<br /><br />What is also physically interesting that the constant curvature metric of manifold classifies it topologically and that most 3-manifolds allow this kind of metric. There would be a deep connection between Riemannian geometry and topology. In TGD framework preferred externals - analogs of Bohr orbits- could also define 4-D topological invariants since one can hope that for given space-time topology the preferred extremal is unique. <br /><br />[It can actually happen, that the preferred externals are not quite unique but this is a delicacy.]<br /><br />Constant curvature hyperbolic 3-manifolds might be relevant for TGD too. One can take the proper time constant hyperboloid of M^4: t^2-x^2y^2-z^2=a^2, choose one, call it G, of the infinite number of discrete subgroups of Lorentz group L acting in this space and form a coset space L/G. <br /><br />The resulting space is hyperbolic constant curvature manifold. The subgroups of Lorentz group acting in 3-D hyperbolic space could be completely analogous to lattice groups in Euclidian 3-space. The constant curvature spaces would be analogous to cubic lattice cells. <br /><br />The Lorentz boosts in the subgroup of Lorentz group in turn would be analogous to the discrete lattice of translations. There are indications that <br />cosmic redshifts are quantized: my proposal is that the allowed redshifts correspond to the analog of lattice defined this subgroup. The distant objects would recede with quantized velocities. Astrophysical objects would form lattice like structure. This is a testable proposal.<br /><br /><br />2. Preferred extremal is purely TGD based notion. <br />It is analogous to Bohr orbit and forced by the condition that the WCW Kahler metric in the space of 3-surfaces has general coordinate invariant in 4-D sense. <br /><br />This is possible only if the very definition of Kahler function assigns to 3-surface a unique 4-surface. Kahler function is the Kahler action for a preferred extremal (space-time surface) connecting 3-surfaces at the ends of causal diamond. Kahler action in turn has direct physical interpretation so that classical physics is coded by WCW Kahler function.<br /><br /><br />3. That manifold has both Kahler metric and Einstein metric expresses only the fact that Kahler manifold as Ricci tensor proportional to metric tensor. This is true for instance for constant curvature spaces/symmetric spaces. <br /><br />4. I do not believe that http://suess.sdf-eu.org/website/lang/en/research.php gas anything to do with Zeeman effect or physics.<br />This high specialised and technical algebraic geometry: a luxury to which physicists trying to achieve something during this lifetime cannot afford;-).<br /><br />To sum up, most of the questions have basically rather trivial answer: the problem is the lack of context which makes it very difficult to explain what it involved in an understandable manner: you see that I am forced to introduce additional notions which are standard but would require a further explanation so that the explanation would grow to a two-semester course in basic mathematics;-). To answer understandably without the context would be a Muenchausen trick;-).<br />Matti Pitkanenhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-81695410898154665332014-02-13T13:37:45.876-08:002014-02-13T13:37:45.876-08:00http://iopscience.iop.org/0264-9381/25/22/222002/f...http://iopscience.iop.org/0264-9381/25/22/222002/fulltext/ Ricci flows and wormholes. I guess the ERR model is outdated?Ullahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-40108489201853272882014-02-13T12:43:28.271-08:002014-02-13T12:43:28.271-08:00This is an example of what I mean. http://suess.sd...This is an example of what I mean. http://suess.sdf-eu.org/website/lang/en/research.php<br />"I became interested in the question of the existence of Kähler-Einstein metrics on Fano T-varieties." see the fig. How is the Zeeman effect realized, and the different 'shells' and sizes of atoms, as seen as ions (momentum change, Cooper-pairs?) etc. It cannot be only an effect of hbar or p-adics seen as hierarchy (maybe the n-shells are a hierarchy?)? <br /><br />You have talked of cyclotron-frequencies, but I don't quite grasp that... <br /><br />Maybe these are too complex questions?Ullahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-70666173612018823372014-02-13T12:20:23.790-08:002014-02-13T12:20:23.790-08:00When the text says "a Kähler–Einstein metric ...When the text says "a Kähler–Einstein metric on a complex manifold is a Riemannian metric that is both a Kähler metric and an Einstein metric" does this mean the same cone can have both Kähler metrics in one end and Einstein-metrics in the other end of the cone/manifold/surface, or is this case always flat, and the i is required to get the curvature? Ullahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-12923825788619004942014-02-13T12:07:26.489-08:002014-02-13T12:07:26.489-08:00http://en.wikipedia.org/wiki/K%C3%A4hler%E2%80%93E...http://en.wikipedia.org/wiki/K%C3%A4hler%E2%80%93Einstein_metric<br /><br />here are three possibilities, and they are all prooved? http://mathworld.wolfram.com/news/2003-04-15/poincare/<br /><br />Is this like the em-field with a torus? It has a quaternion structure too. This is also linked to Fano manifolds, hence atoms.<br /><br />I also have problems understanding the term "preferred". Is that your own term? Calabi only talked of extremals? From what did it come and how is the criticality done exactly? (without big math :)). If the criticality depends on i (Kähler geometry, linked with p-adics?) it forms a circle (octonion) as Baez writes about? Or knot.<br /><br />When is Kähler geometry used and when Kähler-Einstein geometry? Is it only when we link in another space (i) that we get Kähler geometry? What is a wormhole or Dirac fermion made of as instance? <br /><br />This is not my field of expertise, so I hope you get the meaning of my questions.Ullahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-91345335150924913712014-02-13T08:44:25.259-08:002014-02-13T08:44:25.259-08:00Hi,
I assume that you have idea about what comple...<br />Hi,<br /><br />I assume that you have idea about what complex numbers are and what is imaginary unit. It is a number whose square is -1: i^2=-1. i cannot be a real number, hence "imaginary".<br /><br />Kahler geometry requires a geometric representation of i. Here some knowledge of tensor analysis and basics of geometry would required. i is represented as geometric operation in tangent space (again something new) of Kahler manifold. In complex plane it is just reflection with respect to x-axis: (x,y) ---(x,-y), which can be visualised. This something concrete, not imaginary anymore.<br /><br />Kahler Einstein geometry requires also that Einstein tensor which by Einsteins equations would be proportional to energy momentum tensor is proportional to metric. Very conscisely: G= k*g. Standard sphere is Kahler Einstein geometry and also symmetric space: all points are equivalent geometrically as is easy to understand. Also CP_2 is such a geometry.It has also quaternion structure but this is another story.<br /> <br />Matti Pitkanenhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-22971254172001860632014-02-13T08:44:24.322-08:002014-02-13T08:44:24.322-08:00Hi,
I assume that you have idea about what comple...<br />Hi,<br /><br />I assume that you have idea about what complex numbers are and what is imaginary unit. It is a number whose square is -1: i^2=-1. i cannot be a real number, hence "imaginary".<br /><br />Kahler geometry requires a geometric representation of i. Here some knowledge of tensor analysis and basics of geometry would required. i is represented as geometric operation in tangent space (again something new) of Kahler manifold. In complex plane it is just reflection with respect to x-axis: (x,y) ---(x,-y), which can be visualised. This something concrete, not imaginary anymore.<br /><br />Kahler Einstein geometry requires also that Einstein tensor which by Einsteins equations would be proportional to energy momentum tensor is proportional to metric. Very conscisely: G= k*g. Standard sphere is Kahler Einstein geometry and also symmetric space: all points are equivalent geometrically as is easy to understand. Also CP_2 is such a geometry.It has also quaternion structure but this is another story.<br /> <br />Matti Pitkanenhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-36642313790218248752014-02-12T12:58:16.232-08:002014-02-12T12:58:16.232-08:00Perleman and Poincare conjencture , Ricci flow. ht...Perleman and Poincare conjencture , Ricci flow. http://arxiv.org/pdf/0803.0150.pdf<br /><br />Can you explain the difference between Kähler geometry and Kähler-Einstein geometry in a simple way?Ullahttps://www.blogger.com/profile/16634036177244152897noreply@blogger.com