tag:blogger.com,1999:blog-10614348.post7776974190002707520..comments2024-01-22T11:26:37.599-08:00Comments on TGD diary: A simple quantum model for the formation of astrophysical structuresMatti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-10614348.post-76964486754497999392007-05-25T21:46:00.000-07:002007-05-25T21:46:00.000-07:00Dear Kea,I have gone through those extrasolar syst...Dear Kea,<BR/><BR/>I have gone through those extrasolar systems for which one or more planets are known. See <A HREF="http://www.helsinki.fi/~matpitka/tgdclass/tgdclass.html#astro" REL="nofollow">TGD and Astrophysics </A>. The fit works with 10 per cent accuracy for all of them. The systems for which the planet is very near to the star correspond to n=1 Bohr orbit (n=3 for Mercury).<BR/><BR/>The key point is velocity quantization v=v_0/n which is universal in the simple systems considered. This fixes the scale of orbits completely and gravitational Bohr radius GM/v_0 becomes the universal size scale for these systems. This prediction is not possible in GRT or Newtonian theory. <BR/><BR/>Last night I pondered the basic objection of General Relativist against the model, which is of course is the lack of the manifest General Goordinate and Lorentz invariances. In GRT context this objection would be fatal.<BR/><BR/>a) In TGD framework one can use Minkowski coordinates of the imbedding space as preferred space-time coordinates. The basic aspect of dark matter hierarchy is that it realizes quantum classical correspondence at space-time level by fixing a preferred M^4 coordinates as a rest system(preferred time coordinate) and quantization axis of angular momentum. Fixing quantization axis selects preferred coordinates.<BR/><BR/>b) One can identify in this system gravitational potential as the g_tt component of metric and define gravi-electric field E_gr uniquely as its gradient.<BR/><BR/>Consider now the quantization condition.<BR/><BR/><BR/>a) The left hand side of the quantization condition is velocity circulation<BR/><BR/>Int v*dl .<BR/><BR/>L is the length L of E^3 projection of the dark matter orbit satisfying geodesic equations of motion (possible problem, perihelion shift of Mercury making orbit slightly non-closed: finite length scale resolution?).<BR/><BR/>b) Right hand side would be the generalization of<BR/><BR/>n GM<BR/><BR/>by the replacement<BR/><BR/>GM --> Int e*r^2E_gr x dl<BR/><BR/>e is a unit vector in direction of quantization axis, and r is the radial M^4 coordinate in the preferred system. For Schwartschild metric this reduces to the expected form and reproduces also the contribution of cosmic string correctly.<BR/><BR/>Everything is Lorentz and General Coordinate Invariant.Matti Pitkänenhttps://www.blogger.com/profile/13512912323574611883noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-75470425786195034612007-05-25T16:36:00.000-07:002007-05-25T16:36:00.000-07:00Hi Matti. I am glad you have been thinking about t...Hi Matti. I am glad you have been thinking about this. But I suspect that people are not going to be convinced by solar system evidence currently available. What about hot jupiter systems? There is a lot of data available now, and I think a few systems with more than 1 planet.Keahttps://www.blogger.com/profile/05652514294703722285noreply@blogger.com