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Doppler-shift/hubbles-law implies big bang/universe age?

  1. Jun 8, 2008 #1
    I'm reading the relativistic mechanics chapter, of Hestenes' New Foundations for Classical Mechanics.

    After the derivation of relativistic doppler shift is some general discussion of applications. The last of which (4) discusses Hubbles law:

    "distant galaxies are receding from the Earth with velocities proportional to their distance from the Earth"

    The text then mentions that these velocities are "one of the main empirical supports for the Big Bang Theory".

    I don't quite see how a point in time measurement of velocities is enough to build a model of an always expanding/exploding universe.

    The big bang ideas aren't really discussed in detail in the text (this part of the book is about application of spinor/clifford algebras to relativity which is quite enough to get your head around by itself).

    If the galaxies we can see are currently (ie: were previously) moving outwards, I'd imagine that this could be a part of an oscillatory or more complex motion. Additionally, I could imagine that there would be universe with different motion characteristics outside of the range that we can perceive with our telescopes.

    My Dad always angrily proclaimed the big bang as absurd (religious bias), but like my grade school teachers who (somewhat religiously) taught this as fact without saying the reasons, he also didn't have any good reasons to call it absurd. I suppose that some of this doubt wore off on me, but until now I never thought much about it. The engineer in me ignored the whole topic because it can't be used to do or build anything.

    I don't really want to get too sidetracked on this issue, since my immediate goal is to understand enough of the relativity to work with e&m intelligently. However, I am curious at a high level, especially given the pervasive acceptance of the big bang theory, what rules out more complex motion?
    Last edited: Jun 8, 2008
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  3. Jun 9, 2008 #2


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    That's the important part. Redshifts are only ONE of many observations that support a big bang model.

    There are many other observations that point to a big bang model. Perhaps the most important is the cosmic microwave background radiation. Another observation is that very distant galaxies are substantially different than those closer to us. They appear to be at earlier stages of development. So if really distant galaxies are all older then distance appears to represent the passage of time.

    You'd need to look at a good text on cosmology to get the real picture but the big bang is quite firmly established in mainstream science.
  4. Jun 9, 2008 #3


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    What I can recommend is to check out the podcast "Astronomy Cast", specially episodes 5&6 titled "The Big Bang and the Cosmic Microwave Background" and "More Evidence for the Big Bang" respectively. They go over it quite well, in language anyone can understand.
  5. Jun 9, 2008 #4


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    Scientists have measured the redshifts of tens of thousands (millions?) of galaxies, from the very close (30 million light years) to the extrordinarily distant (10+ billion light years). That's not just one snapshot in time, that's a cross section of most of the history of the universe.
  6. Jun 9, 2008 #5
    Thanks for the comments and references. That gives me a better high level idea of the ideas behind this. After posting I also found and read the wiki page on the topic which had a lot of good info.

    I should have looked for that first, but it looks like my post was worth it just to find out about the Astronomy cast. There's a lot of of interesting looking episodes there (special and general relativity, Lagrange points, big bang, ...).
  7. Jun 11, 2008 #6
    I was listening to the GR Astronomy cast episode, in which red shift was also given as an example phenomena (I presume to a larger degree than regular SR velocity based doppler shift).

    There's no math or numbers in that Astronomy cast, so I was curious what the orders of magnitude differences there are between the SR velocity based red shift vs. GR mass based red shift, and how much apparent motion results from that adjustment for something as large as a galaxy?
  8. Jun 11, 2008 #7
    Based on a mass of 8E41 Kgs for the Milky Way galaxy the gravitational redshift is about Z=0.000001. The mass quoted here includes assumed dark matter of about 20 times the visible mass and is convenient because dark matter gives a spherical distribution to the overall mass making the calculations simpler. The largest known galaxy is Abell 2029 with a radius of 60 times the size of our galaxy and about 228 times the mass of our galaxy and that equates to a gravitational redshift of Z=0.0000045. I am not sure if the quoted mass estimate of Abell 2029 includes dark mass but if it is assumed that it is not included then multiplying the mass by 20 would give a dark matter included redshift of about Z=0.00009.

    Put into context, redshifts of galaxies of Z=7 to about Z=10 have been claimed. It should also be noted that in a model of the universe where all galaxies are the identical that the component of redshift due to gravitational dilation is constant and independent of distance.
  9. Jun 12, 2008 #8
    Thanks Kev! That's exactly the sort of comparisions I was hoping to see. So, even after invoking dark matter, the GR effect on the red shift is still small. Interesting.

    I still don't have enough concrete info that I'd, say, be able to convince my Dad about the validity of the big bang theory if I tried. There's so many indirectly measured things in astrophysics! Assuming I was able to explain the doppler idea to him (or have him accept that as a given) I'm have to hope that he wouldn't also ask me how do we measure the distances to the stars, or how we measure the masses (neither of those questions I'd know how to answer or have any idea about the errors involved in those measurements).
  10. Jun 12, 2008 #9


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    Distances to stars that are close enough to us are measured by geometric means, paralax, and are quite accurate. Some of those close stars have a known intrinsic, or actual, brightness (Cepheid variables) and can be used to determine distances to some nearby galaxies. Certain types of supernovae also have a known intrinsic brightness and are used to detemine the distances to galaxies further from us. Galaxies with known distance are used to calibrate the Hubble constant which gives us the distance to the furthest galaxies.

    Masses of stars are usually determined in binary or multiple systems by observing orbital speeds. The same method can be used for the mass of galaxies that are gravitationally bound. Other galaxies have mass estimates based on their brightness and distance. This is clearly less accurate than the former method.

    There are probably other methods but these are the most important and widely used methods.
  11. Jun 12, 2008 #10
    Interesting. Thank you for the nice explaination.

    Yes, I was thinking of the far star case. A while back I calculated the set of frame rotations that I think I'd be able to use to calculate the distance to satellite given two simultaneous very well separated angular ground based measurements. I'm pretty sure I could do such a calculation for star distance and position too.

    From your description and googling the cepheid variable you mentioned, it appears there's quite a heirarchy of distance determination techniques. Each one building on the next to try to figure out still further distances. If I was to tell my Dad that this and redshift was a basis of the universe is expanding everywhere concept he'd probably just say that compound error is a more likely explaination. I'd be hard put to argue against that without spending a long time becoming an astronomer, so that I could understand each of the measurement processes in this heirarchy, and how much error and what assumptions were associated with each step in the calculation;)
  12. Jun 12, 2008 #11


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    Yes, that's quite true. And to make matters worse some of the methods are occasionally called into question as new observations are made. Distance measurements have been corrected a number of times over the years and so the estimated size (and age) of the universe has changed as well.

    But keep in mind that the changes have never made the big bang impossible. In general the confidence in distance measurements has increased with time. I think the age (and consequently the size) of the universe is now considered to be 13.7 +/- ~0.1 GY which is a lot more precise than it was 30 years ago.

    So to argue that the big bang theory is nothing more than accumulated error in measurement would be shortsighted. Whether a person wants to believe is a whole different story...........
  13. Jun 12, 2008 #12
    the evidence against an oscillating motion is that we see back in time as we look deeper into space. So when we look at very high redshift galaxies we are seeing light that came from them very early in the history of the universe. If there was an epoch where the universe as a whole was contracting we would see some galaxies blue shifting rather red shifting. On the whole the the universe has always been expanding although in the fine detail there was a period when the expansion slowed down a bit followed by a period when the expansion rate started accelerating again. The acceleration is based on analysis of very distant super nova. There is some room for error because there might be some uncertainty as to which galaxy the super nova belongs to. Just because the super nova and its apparent host galaxy are on the same line of sight is not prooof by itself that the super nova is in that galaxy. There has also been some recent speculation that the distant super nova may have been in "voids" and experienced diferent gravitational time dilation compared to other super nova in areas that are more densely populated by other galaxies. The number of high-z super nova that have been sighted and analysed is a mere handful (the last time I looked) so more data may be needed.

    Anyway, when we look out to space we do not see a snap shot of "now" but a cross section of the history of the universe. In fact there are claims that scientists have seen as far back as the time when the universe was a plasma of ions and was opaque.

    My comments above do not rule out the possibilty that the universe collapsed to a point and then "bounced" back as we would not be able to see back past the initial singularity. Some people like to think the universe repeats itself, expanding, collapsing and then starting again. However, the revelation that the expansion rate of the universe is accelerating rules out that possibilty.
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