| Subject: Unique future dynamical state?
Date: Tue, 13 Jul 2004 14:49:57 +0300 From: Dimi Chakalov <dimi@chakalov.net> To: Dean Rickles <phldpr@leeds.ac.uk> CC: huw@mail.usyd.edu.au, time@staff.usyd.edu.au, Peter.Menzies@mq.edu.au, piet@ias.edu, David.Miller@arts.usyd.edu.au, sutherland@usyd.edu.au, rhealey@u.arizona.edu, savitt@unixg.ubc.ca, harvey.brown@philosophy.ox.ac.uk, oliver.pooley@philosophy.oxford.ac.uk, ccallender@ucsd.edu BCC: [snip] Dear Dean, I still cannot find the final version of your "Time and Structure in Canonical Gravity" (to appear in "Structural Foundations of Quantum Gravity", Edited by S. French, D. Rickles, and J. Saatsi, Oxford University Press, 2005), so let me quote form your draft version: "However, for an initial data set (g0,K0), on a hypersurface,
Einstein's equations fail to determine a unique future dynamical state:
there are many diffeomorphisms (X) such that (XXX) is a solution too. This
is simply the basic content of the general covariance (active diffeomorphism
invariance) of the theory.
"I shall call the overall structure formed from such correlations a *net*. (...) But there is a middle way between these two extremes: neither relations nor relata have ontological priority. (...) The best route, available to all three, is to adopt a structuralist account of the relations and relata, so that neither category has ontological priority: the two come as a package deal." I wonder if your *net* can determine a unique future dynamical state, hence resolving the problems from active diffeomorphism invariance. Perhaps you have noticed that I propose a hypothetical 'global mode of spacetime' for these *potential* states, invariant under Diff(M) action. I believe one can derive the putative global mode of spacetime even from non-relativistic QM; see Daniel T. Gillespie at http://God-does-not-play-dice.net/Kijowski.html#note See also the global mode of spacetime in the context of the dark energy, http://God-does-not-play-dice.net/Hongsheng.html Hence I believe we need the "mysterious time" of Bill Unruh, http://God-does-not-play-dice.net/Unruh.html#preprint I also wonder if you have received my email with request for a copy from the 1991 paper by Bill Unruh ("No time and quantum gravity", in R. Mann and P. Wesson, editors, Gravitation: A Banff Summer Institute, pages 260–275. World Scientific Publishing, Singapore, 1991), which you quoted as [Unr91]. Regards, Dimi
Note: There is yet another, a bit more technical application of the hypothetical global mode of spacetime: the Cauchy problem. Read about it here. As to the "mysterious time" of Bill Unruh and Karel Kuchar's Perennials, see a brief outline here.
|
