tag:blogger.com,1999:blog-10614348.post1696390914699421859..comments2024-01-22T11:26:37.599-08:00Comments on TGD diary: What's new in TGD inspired view about phase transitions?Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-10614348.post-79324538448614527362016-01-19T20:31:02.844-08:002016-01-19T20:31:02.844-08:00In the following I try to relate our languages and...<br />In the following I try to relate our languages and concepts and at the same time try to relate the vision about quantum phase transitions to the notion of 4-D spin energy landscape. <br /><br />1. I am not sure why you mean with giving "weight" to the global symmetry. <br /><br />2. You mention degeneracy. Vacuum degeneracy of Kaehler action is certainly a key feature of TGD and distinguishes it from all classical field theories that I know. Deformation of the vacua or more probably, gluing of magnetic flux tubes (primordially cosmic strings) to these vacuum space-time sheets deforms them slightly and would give rise to TGD Universe analogous to 4-D spin glass.<br /><br />*You speak about competition of orders.<br /><br />In condensed matter physics one speaks of fractal spin energy landscape with free energy minima inside free energy minima which by the way obeys ultrametric topology: p-adic topologies are ultra metric!. Free energy is replaced with Kahler function now.<br /><br />In spin glass there is a competion between different minima of free energy. The presence of several degenerate minima leads to what is called frustration. In TGD framework all the vacuum extremals have the same vanishing action so that there is infinite degeneracy and infinite frustration (also created by the attempt to understand what this might imply physically!;-)).<br /><br />When one deforms vacua slightly, classical gravitational energy becomes in play and the actions are not anymore the same. Classical gravitation is crucial: this is a strong guideline! In TGD inspired quantum biology gravitation is indeed fundamental (gravitational Planck constant). Penrose was right I believe.<br /><br />*Not only phases compete: also phase transitions compete. <br /><br />Spin energy landscape becomes 4-D instead of 3-D. The quantum physical vision is that it gives rise to 4-D spin glass phase which involves infinite number of phases (the minima of free energy). By 4-D property not only phases but also phase transitions become relevant in ZEO. Not only phases are competing, also phase transitions are competing. <br /><br />What does this mean? Temporal patterns besides spatial patterns are present and are competing for survival. In biology the notion of function corresponds to temporal pattern. These functions/behaviors could correspond to phase transitions changing Planck constant.<br /><br />*You also talk about symmetry breaking of phase transitions. <br /><br />I talk about fractal hierarchy of symmetry breakings for which initial and final symmetry groups are isomorphic. This is the new element.<br /><br />How should this kind of symmetry breaking relate to the spin energy landscape picture. Could the phase transitions lead from a bottom of free energy well to bottom of another one? Could the increase of h_eff increasing criticality lead to the bottom of smaller well where the situation is more critical? <br /><br />Matpitka6@gmail.comhttp://tgdtheory.com/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-62871214310642967832016-01-19T07:31:13.595-08:002016-01-19T07:31:13.595-08:00This comment has been removed by the author.Sheeverhttps://www.blogger.com/profile/12931916936543585461noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-69857041887341097912016-01-19T07:30:45.433-08:002016-01-19T07:30:45.433-08:00Hi Matti,
The degeneracy and kahler action on the ...Hi Matti,<br />The degeneracy and kahler action on the vacuum manifold requires to result in giving "weight" to the global symmetry. This will give a treshold for the symmetry breaking and corresponds to the phase transition. The symmetry breaking is essentially a result of competition of orders and ends up in the relaxation of the field also in the sane time the lowest energy level or ground state occured.cosmologically speaking its observable as shock waves propagate in space.Sheeverhttps://www.blogger.com/profile/12931916936543585461noreply@blogger.com