On 2/5/2014 9:47 PM, Jesse Mazer wrote:
On Wed, Feb 5, 2014 at 7:38 PM, meekerdb <[email protected] <mailto:[email protected]>> wrote:On 2/5/2014 9:31 AM, Jesse Mazer wrote:--question 1 dealt with the question of how YOU would define p-time simultaneity in a cosmological model where there's no way to slice the 4D spacetime into a series of 3D surfaces such that the density of matter is perfectly uniform on each slice (and that uniform can be characterized by the parameter Omega), unlike in the simple FLRW model where matter is assumed to be distributed in this perfectly uniform way.I don't see that perfect uniformity is necessary. We have calculated our epoch relative to the CMB as 13.8By. I assume any other scientific species in the universe could do the same and so say whether they were 'at the same time' as measured by expansion of the cosmos. I don't see how the existence of galaxies and galaxy clusters precludes this kind of measurement.Using the CMB may give an approximate answer, but would you argue it could distinguish between different simultaneity definitions that agree approximately when averaged over large scales, but disagree somewhat about the details of simultaneity in highly curved regions? For example, could the CMB be used to define a unique definition of simultaneity in the neighborhood of a black hole (where coordinate systems like Schwarzschild coordinates and Eddington-Finkelstein coordinates and Kruskal-Szekeres coordinates give very different definitions of simultaneity)? Edgar isn't just claiming some approximate pragmatic truth about simultaneity, he's claiming an absolute and exact truth about simultaneity in all circumstances, I was asking if he thinks this truth can be empirically determined to arbitrary precision even in principle, and if so what empirical observations would be used.
Of course it can't give great precision because the recombination event must have had significant duration. But aside from all the practical problems I don't see a problem in principle. From the CMB to a given 4-point in the universe there is a world line that is longest and that length can be used as a t-label for that point. It may be a rather convoluted world line near a BH, but I think it will still exist. That's what you would call the co-moving coordinate time. Of course there are other coordinate times that imply different 3-surfaces of simultaneity. Ned Wright discusses several in his UCLA tutorial. Edgar's error is not that you can't define simultaneity, it's that you can't define a *unique* simultaneity. Some ways have some physical motiviation, i.e. they make some calculation easier because they incorporate some physical symmetry. That's what the idealized FLRW model does. Even if you could measure the co-moving time I suggest above it would be useless because it would introduce all the "bumps" that you want to average over anyway. I'm just saying the bumps don't prevent its definition.
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