tag:blogger.com,1999:blog-10614348.post6499469640876948142..comments2024-01-22T11:26:37.599-08:00Comments on TGD diary: About the new proposal of Hawking, Perry, and Strominger to solve the blackhole information loss problemMatti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-10614348.post-15921299801968739402016-01-12T20:32:52.389-08:002016-01-12T20:32:52.389-08:00
Authors talk about topology of solutions. Topolo...<br /><br />Authors talk about topology of solutions. Topology of space-time surfaces would be central also now. <br /><br />h_eff/h=n labelling given level of fractal hierarchy of sub-algebras would correspond to n-fold coverings of space-time sheet with sheets co-inciding at the boundaries of CD. The sheets differing by a gauge transformation generated by algebra with weights larger than n would be regarded as equivalent so that light-cone orbits of partonic 2-surface would define gauge equivalence classes as in gauge field theories. <br /><br />This condition conforms with the view about quantum criticality. Quantum criticality implies quantum fluctuations and loss of complete predictability. Now non-determinism would correspond to n different orbits connecting initial and final 3-surfaces. Long range fluctuations associated with criticality would correspond to increase of h_eff scaling up scale of quantum coherence. Phase transition increasing n_1 to n_2 would increase the number of sheets of the covering.<br /><br />One might perhaps interpret the situation also differently: replace 3-surfaces unions of space-like 3-surface at both ends of CD and of light-like partonic orbits to get closed 3-surfaces which are everywhere space-like or light-like (nowhere timeline). Quantum measurement in ZEO theory however favours the original interpretation.<br /><br />Matpitka6@gmail.comhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-73085622183124543522016-01-12T20:19:40.106-08:002016-01-12T20:19:40.106-08:00Pleasant surprise: I had the feeling that the art...<br />Pleasant surprise: I had the feeling that the article is readable by me. It was about "a global theory of boundary conditions" and Cayley space is the space of general boundary conditions. At least I had the experience of understanding what they are talking about! <br /><br />Consider first what boundary conditions mean in TGD.<br /><br />a) The boundary conditions at the ends of causal diamond (and at the light-like orbits of partonic 2-surfaces) define what preferred extremal property means and realize strong form of holography: 3-D system behaves almost like 2-D one so that only the data at partonic 2-surfaces and string world sheets (this implies "almost") matters. <br /><br />b) The conditions state that the Noether charges of sub-algebras of various generalised conformal algebras involved (in particular, symplectic algebra of light-cone boundary times CP_2) vanish. This algebra is isomorphic to the entire algebra so that one has fractal hierarchies of isomorphic sub-algebras. By including fermion sector one obtains super-symplectic algebra realised in terms of second quantized fermions.<br /><br />This is roughly the physical picture. The Cayley space of general boundary conditions is quite too large in TGD framework. One must restrict it to the above boundary conditions. <br /><br />a) The fractal hierarchy of sub-algebras of conformal algebras isomorphic to it - perhaps symplectic algebra is enough - would define a hierarchy of linear spaces of boundary conditions. This kind of algebra is identifiable as the tangent space of infinite-D "conformal group" (includes Kac Moody type groups and supersymplectic group) defining the non-linear structure. The generators O_m , m=k*n annhilate the physical states, n characterizes the subalgebra and would correponds to Planck constant h_eff/h=n. The number of physical degrees of freedom would be still infinite.<br /><br />b) Finite measurement resolution suggests stronger boundary conditions. If the conditions are strengthened so that not only elements with conformal weights coming as multiples k*n of n annihilate or produce zero energy states from physical states but also also the elements for which m>=n do this, the space of physical degrees of freedom becomes finite-D. For n=1 one obtains ordinary conformal gauge conditions.<br /><br />c) Lie-algebraically this means that the commutator algebra of sub algebra with the full Lie algebra annhilates the physical states and sub-group behaves effectively like normal subgroup so that the coset space of full conformal group with the subgroup is a finite-D group characterizing the physical degrees of freedom. One would perhaps obtain a dynamical gauge symmetry: finite-dimensional ADE type Lie groups assignable to the hierarchy of Jones inclusions would appear as dynamical gauge groups the situation at given hierarchy level. One might say that TGD is able to mimick any ADE type gauge theory dynamically: electrowek and and color symmetires are of course different thing. This mimicry would happen at the level of dark matter. <br /><br />Gauge conditions would effectively reduce the number of superconformal degrees of freedom to finite number. Hawking et al recent paper suggests weakening of conformal gauge conditions. Thinking five minutes this leads to the hierarchy of conformal algebras ( http://matpitka.blogspot.fi/2016/01/about-new-proposal-of-hawking-perry-and.htm ). <br /><br />Matpitka6@gmail.comhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-37991880845938447322016-01-12T16:25:35.865-08:002016-01-12T16:25:35.865-08:00Sorry, missing link in previous comment, here is t...Sorry, missing link in previous comment, here is the URL<br /><br />http://arxiv.org/abs/hep-th/0403048<br /><br />" Global Theory of Quantum Boundary Conditions and Topology Change"<br /><br />this is related to that orthogonal basis whose elucidation would would allow one to construct the proof of the Riemann hypothesis in an elegant way<br /><br />--StephenAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-10614348.post-15351652625068081962016-01-12T16:22:44.914-08:002016-01-12T16:22:44.914-08:00This paper is on the topic... can you comment from...This paper is on the topic... can you comment from TGD's perspective?<br /><br />"<br />The singularity of the Cayley transform implies that some energy levels, usually associated with edge states, acquire an infinity energy when by an adiabatic change the boundary cond<br />itions reaches the Cayley submanifold C−. In this sense topological transitions require an infinite a mount of quantum energy to occur, although the description of the topolog<br />ical transition in the space M is smooth. This fact has relevant implications in string the<br />ory for possible scenarios with joint descriptions of open and closed strings. In the partic<br />ular case of elliptic self–adjointboundary conditions, the space C −can be identified with a Lagrangian submanifold ofthe infinite dimensional Grassmannian. The corresponding C<br />ayley manifold C− is dual of the Maslov class of M . The phenomena are illustrated with some simple low dimensional examples"<br /><br />Cheers,<br />Stephen<br /><br />Anonymousnoreply@blogger.com