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Basic Hubbles Law Concepts.

  1. Jan 12, 2013 #1
    Okay so if I'm correct, Hubbles red-shift relationship was first established via expecting a doppler shift - a change in the observed wavelength (perspective of reciever at the time of reception) with respect to that emitted (perspective of the emitter), caused solely due to the respective motion between the two bodies.

    However the cosmological red-shift was then dedcuded via the fact that a correlation between the distant of the galaxy and the recession velocity was sufficiently significant.

    My questions are:

    - Is it correct that if the red-shift was solely down to the doppler shift, such a correlation would not be expected following the cosmological principle - all red-shifts observed, if data is collected on a wide enough scale would cancel due to the isotropy and homogenity tof the universe?

    -However, I also thought that Ho was determined via taylor expansion, and so assuming sufficiently small distances/redshifts , such that all terms can be neglected expect the first one giving arise to the linear relationship.

    But these two seem to contradict one another?

    Thanks very much anyone who can shed some light on this.
  2. jcsd
  3. Jan 12, 2013 #2


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    It is true that the observed redshift was interpreted as a recessional velocity, which is totally valid. It's valid to say, "that galaxy is moving away from us." In fact, "all galaxies beyond a certain distance appear to be moving away from us." So, in this sense, it is a shift in the wavelength of light due to relative motion, just like the Doppler shift. What is different about this redshift is that the cause of this recession is cosmic expansion, and as a result, the Special Relativistic Doppler shift relation between redshift and recessional velocity is not obeyed. Instead, there is a different relation between redshift and recessional velocity: it is not subject to Special Relativity and can even exceed c. We have an FAQ about this: https://www.physicsforums.com/showthread.php?t=508610 [Broken]

    This "correlation" that you're talking about is Hubble's Law, and it was discovered right from the get go. Edwin Hubble discovered that all galaxies appear to be moving away from us, and that the recessional velocity appears to increase linearly with the distance to the galaxy. The discovery of the "correlation" wasn't something that came later. It also wasn't long before people realized that Hubble's Law was consistent with a uniform expansion in which every point in the universe moves away from every other point.

    See my first paragraph above. Many prefer to think of cosmological redshift as occurring because of an expansion OF space itself that carries the source and observer apart, rather than due to any motion through space of those objects. It's an interpretation that is consistent with the observations. In fact, we can think of two components of the relative motion of a distant galaxy: the component that is due to being carried along with the uniform expansion, which is referred to as the "Hubble flow", and a second random component, which is due to the motion of that galaxy through space, relative to us. This second component is known as the peculiar velocity. Redshifts cannot "cancel out", but I think that what you are asking is the following: if the universe were not expanding, and the only observed Doppler shifts were due to peculiar motions of galaxies, then would we statistically expect to see just as many galaxies to be blueshifted as redshifted? The answer to that question is yes. There would be no "net" or "bulk" flow in that scenario.

    I think you mean that Hubble's law is determined by Taylor expansion, not the constant H0, that appears in it. And the answer is no, Hubble's Law is not determined by Taylor expansion. Hubble's Law is v = H0d, where d is the proper distance to an object, and v is the rate of change of that proper distance with cosmic time. This linear relation is always true in the case of a uniform expansion. What is determined by Taylor expansion is the Newtonian (non-relativistic) Doppler shift formula for redshift in terms of recessional velocity: v= cz. This linear relation is not true, it's just an approximation that holds for low values of z. As you alluded to, the true relationship between redshift and velocity contains higher order terms. It is a result of cosmic expansion, and therefore depends on the details of the dynamics of the universal expansion, which depends on your cosmological model.

    It is true that Hubble assumed v = cz in interpreting redshifts as velocities, and arriving at Hubble's law. I would have to refresh my memory by running some numbers, but I think the redshifts out to which v = cz is a valid approximation still correspond to cosmological distance scales, much larger than the distances at which the Hubble flow begins to dominate over peculiar motions. That's why his assumption worked (meaning that he was able to draw the right conclusion: Hubble's Law). That's also my explanation for why there is no "contradiction" of the type you were worried about.

    EDIT: This doesn't seem like homework, so I'm moving it to the Cosmology discussion forum.
    Last edited by a moderator: May 6, 2017
  4. Jan 12, 2013 #3
    Thanks for the reply, currrently reading through it. Just a quick question on this - what I actually meant was that if the universe is isotropic and homogenous then all galaxies would have equal gravitational attractions in all directions and therefore no relative motion would exist, as there is no source of graviational fluctuation?
  5. Jan 13, 2013 #4
    That's a different question. If the Universe were perfectly isotropic and homogenous and not expanding or contracting then I would think that no relative motion would exist. It is very isotropic and homogenous but not perfectly so, which is what all that careful measurement of Big Bang radiation is about. The is a lot of work with cosmological models to get them to fit the small amounts of isotropy that are observed.

    If the Universe is not expanding or contracting and not perfectly homogenous then matter tends to gather together into a point. The expansion prevents this.
  6. Jan 13, 2013 #5
    Thanks for the reply, so you have specified the universe is not expanding for this to hold - is this necessary? My thoughts were that if the universe is expanding and isotropic and homogeneous - net gravitational attractions would still be equal in all directions and so no actual motion of the galaxies with respect to one another would occur, although there would in this case be apparent motion as a pose to the case if the universe is not expanding when there would not be.But either way, any red-shift would solely be a consequence of the universe expansion. However I think this assume that the expansion is also perfectly in line with the cosmological principle.
  7. Jan 13, 2013 #6


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    To elaborate on what ImaLooser said, the question of whether the universe is "homogeneous" depends on what spatial scale you consider. The universe is homogeneous on the largest spatial scales, meaning that if you took a giant "ice cream scoop" of matter from one place in the universe, and compared it to another sample taken from another place using that same scoop, these two samples would look roughly the same (in terms of mean density and overall amount of matter within the scoop). This is true provided your ice cream scoop is big enough: larger than the scale of galaxy clusters.

    However, if your ice cream scoop were too small, you'd find that the two scoops might differ quite drastically in matter distribution. This is because the universe is fairly inhomogenous on small scales. You look and you see a galaxy cluster "over here", and a giant void with no galaxies "over there." Clearly, there are dramatic variations in the density of matter on these scales.

    In the very early universe, all the matter was in the form of a very smooth (i.e. mostly homogeneous) gas with some mean density. However, the gas was not perfectly homogenous. There were tiny fluctuations in the density. Maybe the gas was slightly over-dense "here", and slightly under-dense "there." These variations were the key to why there is structure in the universe today, because they grew under their own gravity to form gravitationally-bound structures (stars, galaxies, and clusters of galaxies). If there had been no such variations, then all the matter in the universe would still be in the form of a smooth, featureless gas today, and we wouldn't exist. Anyway, the peaks in the density distribution of matter are the places where there are now clusters of galaxies: the largest gravitationally-bound structures in the universe. On scales smaller than this, things are quite inhomogeneous, and the velocity of objects relative to each other is a result of local conditions e.g. since there is inhomogeneity, maybe locally there is some large central mass concentration whose gravity is affecting everything else, like the Great Attractor, or the central cD galaxy in a cluster. Galaxies in a cluster are bound to each other, meaning none will escape, but they buzz around the centre of the cluster like bees in a bee hive, interacting gravitationally in complex ways. So, for an astronomer in one of those galaxies, the other ones in his local universe would probably have a statistically pretty random distribution of Doppler shifts, since he is looking on a spatial scale where things are gravitationally-bound, and so the peculiar motions of those galaxies dominate over the Hubble flow. This is true in our Local Group: the Andromeda galaxy is blueshifted. This is what I was talking about when I referred to peculiar motions, and it is probably the case in both the static and non-static universe scenarios.

    I would be willing to believe that, ignoring expansion, peculiar motions would be minimal between extremely large matter structures in the universe (e.g. galaxy superclusters and the great "walls" and "voids" in the sponge-like large-scale structure) due to the large scale homogeneity.
    Last edited: Jan 13, 2013
  8. Jan 24, 2013 #7
    @ Cepheid #2: We have an FAQ about this: https://www.physicsforums.com/showthread.php?t=508610 [Broken]

    I read the above referenced thread referred to in your post here (#2). Not to be picayune, but the following phrase in that thread is not an accurate statement:

    The expansion of the universe was originally discovered by Hubble...

    I think it would be more accurate to state there that:

    The expansion of the universe was predicted by the models developed by de Sitter and LaMaitre, and the data reported by Slipher, Hubble and others indicating a systematic red shift in the spectra of light received from galaxies proportional to their distance from us was accepted as confirming the expansion predicted by these models.

    Anyway, for what its worth.
    Last edited by a moderator: May 6, 2017
  9. Jan 26, 2013 #8

    I don't understand the answers provided relating to these issues:

    A simple reply is that these two proposals/observations are 'backwards'... in other words, the opposite is actually true.

    You are in good company however: Even Einstein at first thought the universe was STATIC!!! Even after HE developed general relativity. It was Hubble's observations that distant galaxies were receding from us in all directions that caused Einstein to rethink his "biggest blunder"....that the universe was actually expanding.

    A homogeneous and isotropic universe expands. That's the basis of the FLRW metric...the distance measure. Isoptropic and homogeneous assumptions mean that there is a uniform gravitational curvature that leads to redshift.

    A SIMPLIFIED way to BEGIN thinking about this classically is to maybe consider that once you start rolling down a hill of steady incline you don't stop....gravity in general keeps you moving along. If friction is high enough,sure you might stop. In the universe, that 'friction' might have been analogous to the attractive force of gravity. But Einsteins initial instinct was wrong: such gravitational attraction is NOT sufficient for a static universe, nor to stop cosmological expansion. As far is is currently known expansion will continue for all time.

    Cephid's second post explains very well how our cosmological model is NOT precise.....the primordial expansion 'gas' was not perfectly smooth...nor is our universe today....but over large enough scales and with the use of fine tuned observation measures in our model, we think the FLRW cosmological model does give accurate predictions.

    The explanations here are pretty good...even without studying all the math:

    Friedmann–Lemaître–Robertson–Walker metric
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