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What i really want to ask how much has the Milky Way moved, relative to where it was "at the big bang" or the soonest time that makes sense (since i doubt "at the big bang" makes much sense in this question). I suppose the galaxies have non-zero impulse, otherwise we wouldn't see things like galaxy collisions. So, relative to where our galaxy or whatever was there (dust cloud?) "in the beginning", how much did we move?

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    $\begingroup$ The way you asked this question suggests you have a fairly standard misconception of the big bang, that it was an explosion in space. A much better view is that it was an explosion of space. Every point in the universe can be viewed as the center of the universe. Another way to look at this: There is no well-defined center of the universe. Your question implicitly assumes there is a center of the universe and that the Milky Way has moved with respect to it since the big bang. That's not a good way to look at big bang cosmology. $\endgroup$ – David Hammen Sep 5 '14 at 15:19
  • $\begingroup$ Like everybody is pointing out, the real question is "How much has it moved relative to what?". General relativity does not set a preferred reference frame against which everything else moves any more than special relativity or classical mechanics do. The reference frame of the big bang (i.e. the CMB, as John Rennie points out) is a broken symmetry of the universe. In that sense your question makes sense. We have to ask, what in the early universe, breaks the symmetry of GR? As far as I can tell, that question is equivalent to "What caused there to be matter in the universe?". $\endgroup$ – CuriousOne Sep 5 '14 at 19:19
  • $\begingroup$ @DavidHammen I don't see how i am assuming in my question that the big bang itself happened at some specific point. I am only saying that what now is the Milky Way (or any galaxy) was at some point somewhere. I suppose not all galaxies move away from us at the same rate, thus they have velocity that is not explained by cosmic expansion. I don't see how the patch of space that the galaxy occupied a few billion years ago can't be a suitable reference frame (although it might be bigger now due to expansion). $\endgroup$ – kutschkem Sep 6 '14 at 10:02
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The cosmic microwave background gives us a convenient rest frame in that it represents the average distribution of matter in the universe. So if the CMB looks isotropic, i.e. there is no Doppler shift in different directions then this is a plausible definition of stationary. A velocity relative to the CMB would then indicate a peculiar velocity.

The Milky Way is moving at about 550km/sec relative to the CMB, and it probably hasn't interacted strongly with any large galaxies because it seems to be reasonably unperturbed (it's devoured many small galaxies!) so relative to the CMB the distance we've moved is just 500km/sec times 13.7 billion years. I make this about $2 \times 10^{23}$m, which is about 25 million light years or about ten times the distance to the Andromeda galaxy.

But please be aware of what we're calculating here. This is a somewhat arbitrary distance using an arbitrary reference frame. You shouldn't attach too much physical significance to it. Still it's quite interesting to note that we're expected to collide with the Andromeda galaxy in about 4 billion years, so our calculated figure seems a plausible distance to have travelled relative to the averaged positions of all the other galaxies.

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