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neophyte question about hubble's law
In article , Thomas Smid
writes: On 17 Sep, 02:32, dfarr --at-- comcast --dot-- net wrote: The 'Hubble's law' Wikipedia article states '...that the velocity at which various galaxies are receding from the Earth are proportional to their distance from us.' This is at least historically incorrect (so Wikipedia shouldn't be writing that): what Hubble discovered was the linear redshift/ distance relationship; To be pedantic, he discovered a linear relationship between redshift and apparent magnitude. One can interpret apparent magnitude as distance and redshift as velocity, at least at the low redshifts Hubble was working at. Then one has a relationship between velocity and distance. The linear relationship between velocity and distance applies at all distances and for all velocities (even those greater than the speed of light) and the constant of proportionality is the Hubble constant, so some call this Hubble's Law. However, at large redshifts one can't simply calculate the velocity from the redshift, and the distance involved is not a "directly observable" distance. |
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neophyte question about hubble's law
Phillip Helbig---remove CLOTHES to reply wrote:
To be pedantic, he discovered a linear relationship between redshift and apparent magnitude. One can interpret apparent magnitude as distance and redshift as velocity, at least at the low redshifts Hubble was working at. Then one has a relationship between velocity and distance. The linear relationship between velocity and distance applies at all distances and for all velocities (even those greater than the speed of light) and the constant of proportionality is the Hubble constant, so some call this Hubble's Law. However, at large redshifts one can't simply calculate the velocity from the redshift, and the distance involved is not a "directly observable" distance. What formula is used to compute velocity from redshift? Hans |
#13
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neophyte question about hubble's law
On 20 Oct, 12:53, Phillip Helbig---remove CLOTHES to reply
wrote: To be pedantic, he discovered a linear relationship between redshift and apparent magnitude. The Big-Bang model of the universe rests solely on the interpretation of the redshift as being due to recessional velocities, so you can hardly call this issue pedantic. The point is that Hubble's work has nothing to do with this interpretational step. The latter is an ad-hoc assumption made by others, so with the formulation as in the Wikipedia article (and many other publications), Hubble's name and work has effectively been hijacked to promote this ad-hoc interpretation of the galactic redshifts. One can interpret apparent magnitude as distance and redshift as velocity, Whether one 'can' or not is not the point here. The question here is whether one *has to*. Only if one could answer this unambiguously with yes, would this justify the interpretation of the redshifts as recessional velocities. [Mod. note: in science, one rarely 'has to' interpret anything as anything, as Descartes pointed out some time ago -- mjh] Thomas |
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neophyte question about hubble's law
If you actually read Hubble's work for yourself
(here's a copy of his 1929 paper, for example) http://spiff.rit.edu/classes/phys240.../hub_1929.html you'll see that he discusses a relationship between distance and radial velocity. Note the title of the paper, for example: "A RELATION BETWEEN DISTANCE AND RADIAL VELOCITY AMONG EXTRA-GALACTIC NEBULAE" Hubble used several methods involving stars (including Cepheids and luminous blue stars) to estimate distances to other galaxies. He converted the shift in apparent wavelength of their spectra into radial velocities. It is true that he offered two explanations for the shift in wavelengths, one of which is motion (radial velocity) and the other some sort of scattering. I recommend that people who argue about the work of old-timey astronomers actually read those old-timey papers themselves, rather than reading an interpretation of those papers on someone's website. |
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neophyte question about hubble's law
In article , Hans Aberg
writes: Phillip Helbig---remove CLOTHES to reply wrote: To be pedantic, he discovered a linear relationship between redshift and apparent magnitude. One can interpret apparent magnitude as distance and redshift as velocity, at least at the low redshifts Hubble was working at. Then one has a relationship between velocity and distance. The linear relationship between velocity and distance applies at all distances and for all velocities (even those greater than the speed of light) and the constant of proportionality is the Hubble constant, so some call this Hubble's Law. However, at large redshifts one can't simply calculate the velocity from the redshift, and the distance involved is not a "directly observable" distance. What formula is used to compute velocity from redshift? For small redshifts, the Doppler formula. Since you're a mathematician, I'm sure you understand that all things are linear to first order. :-) For larger redshifts, the easy part is v = H*D. This is why has the dimensions of inverse time, or km/s/Mpc. The hard part is calculating D from the redshift. What you want is the proper distance. This, in the general case, is rather tricky and involves elliptic integrals. See, for example, http://www.astro.multivax.de:8000/he...fo/angsiz.html The paper is mainly concerned with a general numerical method for calculating certain distances in the case of a locally inhomogeneous universe, but for questions like this there is an appendix which explains the relationships between redshifts and various distances. |
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neophyte question about hubble's law
In article , Thomas Smid
writes: On 20 Oct, 12:53, Phillip Helbig---remove CLOTHES to reply wrote: To be pedantic, he discovered a linear relationship between redshift and apparent magnitude. The Big-Bang model of the universe rests solely on the interpretation of the redshift as being due to recessional velocities, so you can hardly call this issue pedantic. But Hubble's discovery came first, the big-bang model as a model for the real universe came later. |
#17
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neophyte question about hubble's law
In article , Stupendous_Man
writes: If you actually read Hubble's work for yourself (here's a copy of his 1929 paper, for example) http://spiff.rit.edu/classes/phys240.../hub_1929.html you'll see that he discusses a relationship between distance and radial velocity. Note the title of the paper, for example: "A RELATION BETWEEN DISTANCE AND RADIAL VELOCITY AMONG EXTRA-GALACTIC NEBULAE" OK, but it is still an interpretation, even if it is Hubble's. I was merely pointing out that if on the one hand one is discussing whether to interpret the redshift as velocity, one should or could also discuss---and I did use the word pedantic---whether to interpret the magnitude as distance. The latter is actually non-trivial, since it relies on a "standard candle". Only within the last 10--15 years have reliable standard candles been found and used to accurately measure the Hubble constant. As Mach said: "Every statement in physics has to state relations between observable quantities." What is observed are magnitude and redshift, ^^^^^^^^^^ distance and velocity are derived. (One could be even more pedantic and talk about what is actually recorded by the photographic emulsion, which in practice actually has to be taken into account.) |
#18
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neophyte question about hubble's law
"Thomas Smid" schreef in bericht
... On 20 Oct, 12:53, Phillip Helbig---remove CLOTHES to reply wrote: One can interpret apparent magnitude as distance and redshift as velocity, Whether one 'can' or not is not the point here. The question here is whether one *has to*. Only if one could answer this unambiguously with yes, would this justify the interpretation of the redshifts as recessional velocities. I have no problem with the statement one can interpret redshift as velocity. IMO the issue is how. The current point of view is that for values of z 1 one has to use the equation v = c*z (Also called the nonrelativistic equation for the Doppler shift) I have a problem with that equation. Suppose a galaxy at a far distance in the past is receding from us with a speed of 0.01c resulting in a value of z of 0.01. Light from that galaxy in an expanding universe is travelling towards us at a speed c and is stretched. Suppose we receive it now. Is it not possible in principle that we measure a value of z=0.02 implying a speed of v=0.02*c ? My point is what we measure is not the true speed of the source at the point of emission. This speed is much lower because the waves are stretched. Even if we measure a z=2 it does not mean that the source in the past was travelling at a speed higher than c. The overall implication is that maybe there is no reason to use the relativistic equation for the Doppler shift. A second implication in principle is that the true speed, of a galaxy with z=2 measured now here, could be zero over there. A third implication is that the size of the Observable Universe is much smaller than 47 Gyr. See the posting by Hans Aberg. Nicolaas Vroom http://users.pandora.be/nicvroom/neophyte.htm |
#19
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neophyte question about hubble's law
Phillip Helbig---remove CLOTHES to reply wrote:
What formula is used to compute velocity from redshift? For small redshifts, the Doppler formula. Since you're a mathematician, I'm sure you understand that all things are linear to first order. :-) For larger redshifts, the easy part is v = H*D. This is why has the dimensions of inverse time, or km/s/Mpc. The hard part is calculating D from the redshift. What you want is the proper distance. This, in the general case, is rather tricky and involves elliptic integrals. See, for example, http://www.astro.multivax.de:8000/he...fo/angsiz.html The paper is mainly concerned with a general numerical method for calculating certain distances in the case of a locally inhomogeneous universe, but for questions like this there is an appendix which explains the relationships between redshifts and various distances. But it is this redshift-velocity interpretation that results in speeds exceeding c? And my guess there is no experimental verification of such a formula at high speeds. Suppose a particle at speed close to c emits a photon, what is the measured wavelength shift? Hans |
#20
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neophyte question about hubble's law
In article , Hans Aberg
writes: But it is this redshift-velocity interpretation that results in speeds exceeding c? Yes, but that's not a problem. See @BOOK {EHarrison81a, AUTHOR = "Edward R. Harrison", TITLE = "Cosmology, the Science of the Universe", PUBLISHER = "Cambridge University Press", YEAR = "1981", ADDRESS = "Cambridge" } and @ARTICLE {EHarrison93a, AUTHOR = "Edward R. Harrison", TITLE = "The Redshift-Distance and Velocity-Distance Laws", JOURNAL = APJ, YEAR = "1993", VOLUME = "403", NUMBER = "1", PAGES = "28", MONTH = jan } And my guess there is no experimental verification of such a formula at high speeds. Suppose a particle at speed close to c emits a photon, what is the measured wavelength shift? I'm sure this happens all the time in particle accelerators which produce synchrotron radiation. |
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