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Im trying to understand what Hubble's law

$$v = H_0 d$$

means. The thing is I keep getting two different explanations.

  1. Galaxies are moving at a constant speed, the ones further away are so because they move faster.
  2. Galaxies move faster away the further they are from each other, because there is more matter between them that expands.

Which of these two is correct?

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  • $\begingroup$ "galaxies move faster away the further they are from each other, because there is more matter between them that expands." This is mostly correct. It is the space itself that expand not the matter. $\endgroup$
    – shai horowitz
    Feb 27, 2021 at 0:49

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The space is expanding between non gravitationally bound systems, such as galaxies. The greater the space between them, the greater the amount of expansion. It is believed there are galaxies so far away that we will never see their light as the space between us and them expands faster than their light travels toward us. However this does not mean all galaxies are moving away from each other. In fact the Andromeda galaxy and our Milky Way galaxy are nearing each other and are expected to collide in 4 to 5 billion years.

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  • $\begingroup$ I'd like to point out that for a galaxy with superluminal recession velocity, it does not follow that we won't ever receive light from them. In a non-inflationary universe, light from such galaxies will eventually reach earth because $\dot{v}_{rec} < 0$. Even though an emitted photon is initially moving away from earth, it is slowing down in that direction, will eventually have $v_{tot} = v_{rec}+v_{pec} = 0$, and then will begin traveling towards earth, reaching our telescopes with $v_{tot} = v_{pec} = c$. $\endgroup$
    – bapowell
    Mar 10, 2021 at 21:11
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I find it helpful to separate the observations from the model and interpretation. The observation was that there was a curious linear trend between distance from Earth and velocity. This was simply an observation made on galaxies that we could see. Such a trend would not be expected in random data. Indeed, it would suggest that we might actually be the center of the universe, as everyone expands out from us.

Of course, that is not the popular interpretation. We don't like to assume we are that special. Instead, it was identified that modern relativistic theories permitted space to expand. If space itself was expanding, then a linear relationship like we see from Earth would be seen from everywhere. This is the preferred interpretation: $v=H_0d$ is seen as evidence that space itself is expanding (and taking matter along for a ride).

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  • $\begingroup$ @safesphere I'd not seen the Milne model, so that's an interesting one for me, thanks you. As for the lack of direct experimental evidence, I did word my last paragraph carefully. It certainly is not proof, but it is seen as evidence. Perhaps I am being presumptuous in claiming that expanding space is the preferred model, but as far as I am aware it is the current favorite. $\endgroup$
    – Cort Ammon
    Feb 27, 2021 at 16:39

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