tag:blogger.com,1999:blog-10614348.post985968919394592779..comments2024-01-22T11:26:37.599-08:00Comments on TGD diary: Transition from flat to hyperbolic geometry and q-deformationMatti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-10614348.post-36232922965159836202015-06-25T21:26:30.649-07:002015-06-25T21:26:30.649-07:00The main new observation of the posting came clear...<br />The main new observation of the posting came clear only one day after writing it as it often happens. The TGD inspired conjecture that finite measurement as a discretisation and described using quantum groups are aspects of one and same thing. The connection is very concrete and testable: the reduction of representations<br />of groups to representations of discrete subgroups should<br />give representations of corresponding quantum groups.<br /><br />*Discretization defined by a coset space of Lie group with discrete subgroup can be described in terms of gauge group action defined by the right action of group leaving the coset invariant. <br /><br />*Braid statistics makes sense by strong form of holography implying that 2-surfaces (string world sheets and partonic 2-surfaces are basic objects as far as scattering amplitudes are considered - space-time sheets.<br /><br />* R-matrix defining braiding and quantum group is representable as this gauge action. This is very beautiful result and in p-adic context quantum groups are unavoidable since phases and exponents of hyperbolic angles must be discretized. <br /><br />*Also the observation that e^p is p-adic number and e thus an algebraic number (p:th) root is essential and makes possible p-adic discretisation of hyperbolic "phases" and and also implies discretisation of Lorentz<br />boosts and thus cosmic redshifts if astrophysical objects from hyperbolic tesselations. A testable prediction.<br /><br />Matpitka@luukku.comhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-73740114572529013822015-06-25T18:03:18.525-07:002015-06-25T18:03:18.525-07:00Matti,
In the case of the 4D polytope called the ...Matti,<br /><br />In the case of the 4D polytope called the 24 cell it is more than a spherical top (that is topological ball) and is an exception in four space to all dimensions above and below it. This trend of thinking so too narrow to reach new understanding if we at least know the n-dimensional Euclidean geometry. This is nothing else that the generation problem where iterative looping (not sure it applies to the deepest idea of gravity) is an isolation. But even if this building of a real space is the case and case only as a hierarchy fractal it oscillates in duality tripling the partial fractal. Have we not understood this from Riemann when we cross an Euclidean boundary - or of Feynman as you also mentioned when we rotate his diagrams 90 degrees to describe particles? I would say that in a sense the hyperbolic and the elliptical are primordially equivalent in the description and that to build such an elaborate theory as they put forth is equally only half the picture. In the bigger picture such infinite lattices would then be remote and not hold up, even with the know consideration of complex hypernumbers. The age of such physics is over and in my opinnion your general take on things still stands among a handful of other future mainstream theories.L. Edgar Ottohttps://www.blogger.com/profile/00525169618204198073noreply@blogger.com