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#31
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Speaking of Statistical Significance!
In article , Steve Willner
writes: Consider the standard version of the standard model, or any other universe with non-zero matter content... Thus proving how hard it is to discuss this stuff in words. In the earlier discussion, I thought it was clear from the context that we were discussing _only_ the effect of the cosmological constant, not anything about matter. OK. Now considering an empty universe with the dark energy being a cosmological constant and nothing else: The limiting case, when matter is too thin to matter (pun, as always, intended), is the de Sitter universe, which has exponential expansion. Exponential in what I've called "comoving coordinates." Divide by the scale factor to get what I called "metric coordinates," and the result is...? OK, I see the reason for the confusion. The usual usage is that "comoving" is the "physical" ("metric"?) distance divided by the scale factor, i.e. the other way around. Thus a distance which changes with time due only to the change in the scale factor will be a constant comoving distance. |
#32
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Speaking of Statistical Significance!
In article ,
"Phillip Helbig (undress to reply)" writes: The usual usage is that "comoving" is the "physical" ("metric"?) distance divided by the scale factor, You mean multiplied, right? "Physical" is probably a better word than "metric," but I'd expect either to be understood. Equations are easier than words. :-) Thus a distance which changes with time due only to the change in the scale factor will be a constant comoving distance. Yes. -- Help keep our newsgroup healthy; please don't feed the trolls. Steve Willner Phone 617-495-7123 Cambridge, MA 02138 USA |
#33
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Speaking of Statistical Significance!
In article , Steve Willner
writes: The usual usage is that "comoving" is the "physical" ("metric"?) distance divided by the scale factor, You mean multiplied, right? "Physical" is probably a better word than "metric," but I'd expect either to be understood. Suppose I have a physical distance, now, in meters. After the universe expands, it will be larger, in meters. Thus, I need to divide each quantity in meters by the corresponding scale factor, in meters, to get a quantity which doesn't change with the expansion of the universe, i.e. a comoving quantity. Equations are easier than words. :-) Indeed. Thus a distance which changes with time due only to the change in the scale factor will be a constant comoving distance. Yes. We of course agree here. |
#34
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Speaking of Statistical Significance!
On 6/30/2015 9:54 PM, Phillip Helbig (undress to reply) wrote:
In article , Steve Willner writes: The usual usage is that "comoving" is the "physical" ("metric"?) distance divided by the scale factor, You mean multiplied, right? "Physical" is probably a better word than "metric," but I'd expect either to be understood. Suppose I have a physical distance, now, in meters. After the universe expands, it will be larger, in meters. Thus, I need to divide each quantity in meters by the corresponding scale factor, in meters, to get a quantity which doesn't change with the expansion of the universe, i.e. a comoving quantity. But it would be unwise to call it a comoving distance, since you then use the same word for two different things. It was already used for the distance that was increasing.. (Perhaps better would be using something like "comoving seperation, or something similar). Equations are easier than words. :-) Indeed. If you use the same symbol for different things the same confusion will arise! (Like the Omega and Lambda game.) The situation is comparable to the use of "mass" in both rest mass and kinetic mass, but of course there wisdom has prevailed (after some time, I guess) and we now use mass only as a synonym for rest mass, while the velocity- dependent mass isn't called mass but energy. -- Jos |
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