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marcus
#15
Sep29-03, 06:49 PM
Astronomy
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DrChinese, Mentat, Brad, thank for keeping this thread alive! I got distracted and didnt check here for several days. Mentat and Brad exactly right about metric distances increasing being different from stuff moving through space. Stuff can be sitting still and yet be getting farther apart---metric is dynamic (a solution to some equations that include matter density etc).

DrC your comments and questions are clearsighted (plainspoken too ) and I wish I had noticed what was going down at this thread, would have replied earlier.

Originally posted by DrChinese


I think we have something as follows:

a. There are a number of possible space-time metrics which satisfy GR.

yes

b. The discovery of actual high z values from the relatively early universe indicate that certain of these metrics are supported, and therefore others must be discarded as describing our universe.

c. In the high z scenarios we are able we witness, the additional "velocity" component - which gives rise to recession >c - is a function of the expansion of the spacetime metric.

yes and it is probably simpler than you imagine, Friedmann got simpler equations boiled down from Einstein by assuming a sort of uniform largescale sameness, and when the Friedmann equations are combined with the observed largescale spatial flatness the metric turns out to be incredibly simple---the spatial part of the metric is just an ordinary euclidean distance with a timedependent scalefactor a(t) multiplying it so that distances between regions increase in exact proportion as this function a(t) is increasing----and it is just an ordinary real function of one real variable right out of first year calculus. so there is hope for us. like, you can graph a(t)----Lineweaver does this at Figure 14. He calls it R(t)----there are these two mainstream notations for the same thing, a(t) and R(t). Both are loosely referred to as the "size" of the universe and usually normalized so that they equal one at the present time, also, since universe is quite possibly infinte saying "size" doesnt sound quite right so people sometimes say "average distance between galaxies" but the mathematical reality is that it is the scalefactor of the metric, normalized to equal one at the present time.

I hope this is accurate. If so I would ask as follows:

1. Presumably it would not be possible for any objects to move towards each other faster than the speed of light - only away from each other in this fashion.


interesting thought! but if cosmos ever starts to contract then a(t) will start to go back down to zero and things will rush towards us the same way they now rush away. Friedmann equation allows contracting U as one solution but we happen to be in an expanding case.Distances could be decreasing, they just happen to be increasing.


2. I would also assume that this would throw a wrench into our understanding of relativistic QM and our need to integrate QM and GR. But perhaps not.
3. The Hubble constant is not, as I understand it, a fundamental value itself but more an outgrowth of our understanding of cosmology.


the Hubble parameter is defined by a(t). You see that a(t) is the basic thing in cosmology. It is defined as the slope of a, then divided by a-----or the timederivative of a(t), divided by a(t)----in freshman calculus terms H(t) equals a'(t)/a(t)

so if a is growing then its derivative a'(t) is positive and you divide by a(t) to sort of normalize it or get a percentagewise increase rate handle on it, it just turns out to be a convenient
handle on a(t)'s growth that you can work with and relate to observational measurements etc.


4. For the life of me, it seems as if there is an ether after all!


yes of course! we still have much to learn about what space itself is! and many pratfalls by the "experts" still to come, if would not surprise me in the least if there turned out to be ether, and elusive loop soup perhaps, or a giant polymer. what color is it I wonder

I will continue to follow your links and try to get an understanding of what is being said. Thanks for your patience.
It is mutual. Your responses help me get understanding of the subject matter as well.