tag:blogger.com,1999:blog-10614348.post6598225392856646806..comments2024-01-22T11:26:37.599-08:00Comments on TGD diary: Does instability of Einstein's equations explain accelerated expansion?Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-10614348.post-44244328887238722242017-12-16T19:39:08.193-08:002017-12-16T19:39:08.193-08:00Good question.
Certainly Einstein's equation...Good question. <br /><br />Certainly Einstein's equations are highly non-linear. Infinite number of variables is certainly part of answer. Any metric with Minkowski signature will due if one takes the source term given by energy momentum tensor T as free input. If one expresses it in terms of other fields satisfying action principle, not all metrics are possible. This does not help much but makes things more complicated. Besides this one must make fermionic fields Grassmann algebra valued and the classical field equations make no sense anymore and one must use path integral approach. <br /><br />In TGD frame one does not have path integral: allowed space-time surfaces are like Bohr orbits, preferred extremals and there are very few of them. The situation is also very simple locally: just 4 coordinates of M^4xCP_2 appear as "field like" variables. Strong form of holography reducing the boundary data to 2-D data implies preferred extremal property. Preferred extremal property reduces to a huge generalization of already infinite-D conformal symmetries in H=M^4xCP_2 picture and to a reduction to algebraic equations for algebraic surfaces in M^8 picture. <br /><br />This allows simple interpretation of solutions in terms of external particles entering into interaction region defined by causal diamond (there is of course infinite hierarchy of CDs but fractal reductionism makes life still very simple). It is amusing that the phenomenological picture of particle physics translates to the structure of space-time surfaces very precisely.<br /><br />Matti Pitkänenhttps://www.blogger.com/profile/13512912323574611883noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-58722138398991273342017-12-16T13:22:43.719-08:002017-12-16T13:22:43.719-08:00What is so hard about determining whether Einstein...What is so hard about determining whether Einstein's equations have an instability? I must confess, I still do not understand tensors. A matrix is just a "2-tensor" ? The inverted pendulum is a classical example used in control theory to test stabilization methods.. why can't the same type of analysis be done?Stephen A. Crowleyhttps://www.blogger.com/profile/11587191916122583498noreply@blogger.com