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Edited version From Hubble's measurement, the only thing that he can conclude, in my opinion, is that the galaxies move away from Earth with their speeds proportional to their distances from the Earth.

But without making observations from other points in the Universe i.e. other galaxies, how did Hubble (or we) conclude that every galaxy recedes away from every other? Was it just based on the hypothesis that there is no center of the universe and hence, whatever observed from Earth is nothing special and will be the same for any other observer in any other galaxy?

In short, doesn't the argument of expanding the Universe require both Hubble's measurement from earth + the fact that there is no preferred center?

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    $\begingroup$ If we can map the position of two galaxies A and B moving away from us, can we not also see that A and B are moving away from each other? $\endgroup$
    – Kenshin
    Apr 8 '17 at 12:43
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    $\begingroup$ There is no center of the universe. $\endgroup$
    – Kyle Kanos
    Apr 8 '17 at 12:45
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    $\begingroup$ @KyleKanos I think you're missing the point. Did Hubble need to invoke the assumption/fact that there was no centre of the universe, or was he able to directly observe that galaxies are moving away from each other too (not just from the Earth.) $\endgroup$
    – Kenshin
    Apr 8 '17 at 12:47
  • $\begingroup$ @kenshin: the phrase ...we are not in the center of the universe... suggests that OP believes that there is a center and that we are not located there, not that there is no center at all. It is important to clear up that at the onset, rather than let it dwell. $\endgroup$
    – Kyle Kanos
    Apr 8 '17 at 13:35
  • $\begingroup$ @KyleKanos I know there is no centre of the Universe. Well. If it confuses you then I would like to phrase it as follows. Did Hubble need to invoke the hypothesis that there is no centre of the universe, and therefore, whatever is observed from Earth must also be true from any other point in the Universe? Does it make sense? $\endgroup$
    – SRS
    Apr 8 '17 at 13:39
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There is a short answer involving Newtonian ideas and flat space, and a longer answer involving General Relativity.

On a historical note, let's also recall that both Lemaitre and Hubble deserve mention when thinking about the early work here; Lemaitre first clearly enunciated the idea we now call Hubble's law, and estimated a value for the constant we now call Hubble's constant. Hubble contributed greatly to the experimental methods and observations and making the idea take hold.

Now let's present the Newtonian argument. Suppose an observer at one place finds that galaxies are moving away from him with a velocity whose size is some sort of function of distance away, but we don't say what function yet. So we have $$ {\bf v} = v(r) \hat{\bf r} = \frac{v(r)}{r} {\bf r} $$ where $\bf r$ is the vector from the observer to the galaxy. In particular, for two galaxies A and B we get $$ {\bf v}_A = \frac{v(r_A)}{r_A} {\bf r}_A, \;\;\;\;\;\; {\bf v}_B = \frac{v(r_B)}{r_B} {\bf r}_B $$ It follows that the relative velocity of galaxy B with respect to galaxy A is $$ {\bf v}_B = \frac{v(r_B)}{r_B} {\bf r}_B - \frac{v(r_A)}{r_A} {\bf r}_A, $$ For most functions $v(r)$ this has no simple expression. But suppose the function is $$ v(r) = k r $$ for some constant $k$. In that case we find $$ {\bf v}_B = k {\bf r}_B - k{\bf r}_A = k ({\bf r}_B - {\bf r}_A) = k {\bf r}_{AB} $$ and this applies for all galaxies B. The vector ${\bf r}_{AB}$ here is the vector from A to B. Therefore we have found that an observer on galaxy A finds that he too observes the same effect: other galaxies are moving directly away from him, and with a speed proportional to their distance away.

In this way observations from a single location can be used to infer what would be observed from other locations, and in the case of a linear relationship between $v$ and $r$ the whole situation has this uniformity with respect to position. Other relationships would not be so simple. In the case of a bomb exploding, for example, if some material moves away quickly and some more slowly, then typically the front material begins to slow as it encounters air resistance and the relationship between speed and distance away at any one time is not any simple function. The Hubble expansion is not like a bomb exploding, and indeed, as we have seen by the above derivation, there is no unique centre. All positions can equally well serve as the centre, which is the same as saying there is not really any centre. Many other examples of this sort of expansion can be found in thermal physics: think of a loaf of bread expanding in the oven, for example, or more generally practically any uniform solid undergoing a thermal expansion.

That is the "short" answer.

The longer answer is that similar ideas apply in a full treatment employing General Relativity. The main difference is that you can no longer obtain relative velocities just by subtracting one galaxy's velocity from another. Instead the typical way to proceed is to propose a model in which there is a global expansion of a homogeneous fluid, and then show that this is consistent with observations. The "fluid" here is the whole universe; "particles" in the fluid are galaxies or galaxy clusters.

Finally, note that the proportionality constant $k$ is a constant in the sense that it is the same for the whole universe at any given time, but it can in principle change with time, and the expansion would still have the same uniform quality, but now it would proceed more rapidly at some times than at others. This is why the proportionality factor is called the Hubble parameter rather than the Hubble constant, when we want to consider the long-term evolution of the universe.

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  • $\begingroup$ This is a nice explanation. Do we find this kind of reasoning in any book? @AndrewSteane $\endgroup$
    – SRS
    Sep 23 '20 at 5:03
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You don't actually need the idea that there is no preferred center. Take a look at this diagram, where each arrow refers to a galaxy:

enter image description here

Let's say you are at the center of the diagram, and at $t=0$ five galaxies are piled up at the origin. After some time, all the galaxies have moved to the tip of their respective arrows. From your perspective at the origin, all the other galaxies are receding.

Now imagine you're on the galaxy that's moving directly towards the right (galaxy A). Note you also observe all the other galaxies are receding. At $t=0$, the distance between you and the other four galaxies is zero, but the distance between you and the other galaxies (as illustrated by the red arrows) increase with time. It doesn't matter which way the other galaxies are moving, the distance between you and all the others increases with time.

Edit: found the proof, see slide 21/49 of these notes. If we observe the Hubble law, so do all other observers.

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  • $\begingroup$ Instead of moving every galaxy in your drawing you could have you center point move in a direction perpendicular to the plane of your screen. Of course this geometry is no longer Euclidean. You are implicitly assuming that our universe is euclidean. Is this assumption more or less costly than the one preffering no center ? $\endgroup$ Sep 22 '20 at 9:02
  • $\begingroup$ @InfiniteLooper pretty sure the idea that the Universe is flat is empirically testable (and has been observed, which is a major reason behind cosmic inflation theory). $\endgroup$
    – Allure
    Sep 22 '20 at 11:13
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Thinking that Hubble law $$ v=H_{0}\,D $$ applies only from our own Milky Way galaxy, makes our galaxy somewhat unique, which brakes standard cosmological view postulating spatial isotropy and homogeneity in a universe. Albeit, there are small inhomogeneities in CMB as can be seen

enter image description here

Due to these inhomogeneities in a primordial universe, galaxies were borned, thanks to that. However, CMB radiation root mean square variations are only $18~\mu K$, so this anisotropy is very very tiny. In the sense that at a global structure view universe still can be considered a homogenic one as can be seen from a computer simulated cosmic web, a large-scale cosmos structure, of 50 million light-years across

enter image description here

HISTORICAL PERSPECTIVE

Before 1920 astronomers and people thought that there are no other galaxies in universe apart our own. Hubble discovered it's law in 1929. So it's only 9 years has passed after people start to believe that there are other galaxies in universe at all. And it's partly thanks to Hubble, who raised a debate on this issue on 1925. So as for me, this question doesn't make much sense cause in any case Hubble had to push-through a lot of "common-sense" of that time.

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