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quick questions about Hubble's law and universe expansion
Quick questions about Hubble's constant and universe expansion.
1) Am I right to think that Hubble's law (HL) means that Hubble's constant is fixed over all of space at a given time (e.g. now), but not over all of time? I.e. when people say there is a constant rate of expansion, do they simply mean that v = H * d at any given moment, where H is a function of time? Where v is velocity of recession of object X from object Y, H is Hubble's constant, d is the distance between X and Y, and t is the time since the Big Bang, I get: v = H * d = f(t) * d = dd/dt = d * f(t) = d = A * e^(integral of f(t) dt) where A really is a constant, depending on how far X and Y are apart at a given time. Is this right? If so, what is know or speculated about f(t)? 2) Given Hubble's law, which idea is deduced from which, out of: a) d proportional to t b) H = 1/t ? 3) Am I right to think that if we accept Hubble's law, then the idea that expansion is accelerating means that H cannot equal 1/t ? So does acceleration of expansion mean that the figure of 14 billion years for the age of the universe must necessarily be revised? If so, how? Thanks! John |
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quick questions about Hubble's law and universe expansion
"John Nagelson" wrote in message ... Quick questions about Hubble's constant and universe expansion. 1) Am I right to think that Hubble's law (HL) means that Hubble's constant is fixed over all of space at a given time (e.g. now), but not over all of time? I.e. when people say there is a constant rate of expansion, do they simply mean that v = H * d at any given moment, where H is a function of time? Where v is velocity of recession of object X from object Y, H is Hubble's constant, d is the distance between X and Y, and t is the time since the Big Bang, I get: v = H * d = f(t) * d = dd/dt = d * f(t) = d = A * e^(integral of f(t) dt) where A really is a constant, depending on how far X and Y are apart at a given time. Is this right? If so, what is know or speculated about f(t)? 2) Given Hubble's law, which idea is deduced from which, out of: a) d proportional to t b) H = 1/t ? 3) Am I right to think that if we accept Hubble's law, then the idea that expansion is accelerating means that H cannot equal 1/t ? So does acceleration of expansion mean that the figure of 14 billion years for the age of the universe must necessarily be revised? If so, how? Thanks! John Does this mean there really are canals on Mars? http://michaelgr.files.wordpress.com...canals-003.jpg Or does it mean some astronomers are cranks? Thanks! Androcles |
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quick questions about Hubble's law and universe expansion
Dear John Nagelson:
On Mar 17, 10:51*am, John Nagelson wrote: Quick questions about Hubble's constant and universe expansion. 1) Am I right to think that Hubble's law (HL) means that Hubble's constant is fixed over all of space at a given time (e.g. now), but not over all of time? It seems that way for the ages displayed, yes. snip math unchecked, since you may not be aware of the basis .... Is this right? If so, what is know or speculated about f(t)? http://www.astro.ucla.edu/~wright/cosmo_01.htm 2) Given Hubble's law, which idea is deduced from which, out of: a) d proportional to t b) H = 1/t The dimensions fall out to that, yes. Correctly, however it is "velocity per unit distance". 3) Am I right to think that if we accept Hubble's law, then the idea that expansion is accelerating means that H cannot equal 1/t ? No more than it paves over the distinction you then set out to wonder at... So does acceleration of expansion mean that the figure of 14 billion years for the age of the universe must necessarily be revised? If so, how? No. It describes the distance to the objects, based on measured redshift. Or vice versa. So we "know" how "far" it is to the quench of the CMBR medium, and use GR to infer the "distance" to the Big Bang. Hubble's relation is just a useful first blush correlation. David A. Smith |
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quick questions about Hubble's law and universe expansion
On 3/17/10 12:51 PM, John Nagelson wrote:
Quick questions about Hubble's constant and universe expansion. See: http://www.astro.ucla.edu/~wright/CosmoCalc.html |
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quick questions about Hubble's law and universe expansion
"John Nagelson" wrote in message ... Hubble's constant and universe expansion. 1) Am I right to think that Hubble's law (HL) means that Hubble's constant is fixed over all of space at a given time (e.g. now), but not over all of time? I.e. when people say there is a constant rate of expansion, do they simply mean that v = H * d at any given moment, where H is a function of time? Where v is velocity of recession of object X from object Y, H is Hubble's constant, d is the distance between X and Y, and t is the time since the Big Bang, I get: v = H * d = f(t) * d = dd/dt = d * f(t) = d = A * e^(integral of f(t) dt) where A really is a constant, depending on how far X and Y are apart at a given time. Is this right? If so, what is know or speculated about f(t)? 2) Given Hubble's law, which idea is deduced from which, out of: a) d proportional to t b) H = 1/t ? 3) Am I right to think that if we accept Hubble's law, then the idea that expansion is accelerating means that H cannot equal 1/t ? So does acceleration of expansion mean that the figure of 14 billion years for the age of the universe must necessarily be revised? If so, how? John: hanson wrote: John, cosmology is a wonderful and wondrous thing. It's truly the greatest story ever told... So, enjoy it in all of its fashions, forms and presentations. Cosmic expansion, like SR/GR, are stories/theories that tell you that some y ought to be there at point x, but when you actually go to x, y is nowhere at all or somewhere else. Until some-one has actually been out there and comes back to tell, the field will just remain the source of stories that, when peppered and fudged with math manipulations are called "theories"... yet still just ... stories, tales & fables.... Enjoy all of 'em and most importantly make up you own story and sell it.... instead of humbly asking "Am I right to think that"... You are as "right" as is the next guy! My favorite story is the most fundamental tale in cosmology codified by the "1234-cosmic envelope" which says: ||||||| c = (GM/R)^1/2 = (GMH)^1/3 = (GM*b_r)^1/4 ||||||| wherein ( notice the cool exponent sequence) c= lightspeed, G= Newton, M= total mass in the a sphere of R, H= 1/Travel time from any center to R at the speed of c and br = the deceleration caused by G & M fixing the value of c, or visa versa. All these events, according to this view, do happen in a universe that is much larger then is our portion of M & R to which we have observational access to. In your question, what is perceived as "cosmic expansion" may simply be another time dependant interpretation of the background acceleration caused by the average mass density in the static, observable universe. More cosmic phantasms he http://tinyurl.com/yfo89uk. Enjoy! PS, have you noticed how cosmology has drifted away from pure, abstract pontification and is concentrating on picture taking, guessing & interpreting what may be there?... The song remains the same, though... ahaha.. ahahaha.... ahahahanson |
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quick questions about Hubble's law and universe expansion
In article ,
John Nagelson writes: 1) Am I right to think that Hubble's law (HL) means that Hubble's constant is fixed over all of space at a given time (e.g. now), but not over all of time? Hubble's constant varies with time in all Big-Bang-type models. The natural assumption is that all physical constants and the physical laws themselves are the same everywhere in space. This is called the "cosmological principle." There are observations ruling out certain kinds of violations of this principle, but smaller or subtler violations could exist without being detectable by existing observations. I.e. when people say there is a constant rate of expansion, do they simply mean that v = H * d at any given moment, That more or less captures the meaning, though the equation itself is an approximation valid only for small distances and only if you are willing to treat redshift as indicating velocity. That last may not be the best idea. The symbol H_0, i.e., H with subscript zero, is often used to mean "the value of Hubble's constant now." If you want to do calculations for large redshifts, you need to specify a cosmological model. Details are given, as others have suggested, in links from Ned Wright's cosmology calculator: http://www.astro.ucla.edu/~wright/CosmoCalc.html There are other calculators on the web, but Ned's has the best explanations of the ones I've looked at. 3) Am I right to think that if we accept Hubble's law, then the idea that expansion is accelerating means that H cannot equal 1/t ? If you think of the expansion as galaxies drifting at constant speed into a pre-existing space, then H would indeed go as 1/t, but that's not a typical (or useful) model. So does acceleration of expansion mean that the figure of 14 billion years for the age of the universe must necessarily be revised? This age comes from the "concordance model," which fits a wide variety of existing data. In particular, the model agrees with the WMAP results, the supernova magnitudes, and the local H_0 measurements with HST and other telescopes. The concordance model is the default on Ned's calculator and gives an age of 13.7 Gyr, but you can use the calculator to find ages for other models. For example, with the same matter density and H_0 but cosmological constant =0, the age would be 11.3 Gyr. This model is, of course, inconsistent with observations. -- Help keep our newsgroup healthy; please don't feed the trolls. Steve Willner Phone 617-495-7123 Cambridge, MA 02138 USA |
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