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How do we know for certain that space is expanding?

Let's say that in the year 1950, we observe that galaxy 1 is 5 billion light years away from us and galaxy 2 is 10 billion light years away from us, putting both galaxies at a distance of 5 billion light years from each other. Then in 2013, we observe that they are now 7 billion light years away from each other so we conclude space is expanding.

We see that galaxies are move away from each other but how does that prove that space is expanding? Could this illusion of expanding space simply be due to something larger in mass pulling the farther galaxy 2 away from galaxy 1? This larger mass could be accelerating the velocity of galaxy 2 faster then it's accelerating the velocity of galaxy 1.

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On that last part, see Dark Flow and Great Attractor –  Izkata Mar 29 '13 at 17:58
    
Re the second paragraph, there is no need to posit the existence of gravitational forces. Simple cosmological models are homogeneous and isotropic, so by symmetry any such force would have to vanish. Actually GR doesn't even describe gravity as a force. You can have tidal effects, but those vanish as well because of isotropy and homogeneity. –  Ben Crowell Mar 30 '13 at 1:41
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The expansion of the universe is not based on the observation of one or two galaxies moving away from us. Basically all stars and galaxies we have observed seem to follow the pattern known as Hubble's law, i.e. the further away they are the faster they are moving from us. Sure, for the observation of a single galaxy, there could be some unknown local effect, but it's not very likely that there would be such an explanation for every single galaxy. There are also additional proof of an expanding universe.

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Hubble observed that the speed of all objects is proportional to their distance. What does that mean? –  SSpoke Mar 29 '13 at 13:54
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@SSpoke It means either everything is expanding uniformly as we believe, or else the Earth lies at the center of the universe, and that beyond the most distant galaxies there are invisible clumps of matter pulling everything away from us in a cosmic conspiracy to imitate the expansion of space as seen from our vantage point only. –  Chris White Mar 29 '13 at 15:14
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Actually, the proposal of this "expansion of universe" date back to almost a century when Friedmann tried to explain GR's prediction of an non-static universe. Then, Hubble's observation of distant stars proved it. Hubble's law gives the velocity of the expansion of universe. $v=Hd$ as told, where $H$ is his constant, which has been corrected from 72 to 69 km/s per Mpc by the Planck results. Though the value seems to be large in normal scales, it is very small. The universe, when taken as a whole (or atleast in scales of Mega parsecs) - this factor is negligible. As the distance $d$ increases, the velocity (with which it's moving away) increases. So, the farther apart the galaxy is from us, the faster it's moving. That's all...

Your assumption is very wrong. We don't say that two galaxies are moving away from each other, while we sit and observe. Instead, they're moving with respect to one-another. All celestial objects move away from you at similar velocities (based on how far or closer they are). There's no center for this expansion. The expansion is the same from wherever you look. Any location in the universe can be a center (which is difficult to assume). For instance, our Earth can be considered a center.

Hence, your second paragraph is contradicted by the wrong assumption...

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I guess what I'm trying to figure out is whether the galaxies are moving faster and faster in actual speed through space or are they only moving away from each other. If something is increasing their speed and only a force such as gravity can do that, that's why I had the idea that something is pulling on them much the same way gravity pulls on things. If space was only expanding the velocity of the galaxies should stay the same, only the distance should increase between them. –  SSpoke Mar 29 '13 at 15:48
    
@SSpoke: Ahh... I understand. The farther the galaxies are, their velocity increases with time. So, yes - the universe is accelerating, by the presence of some indirectly observed constant called the dark energy. This dark energy interacts with gravity, thereby accelerating the expansion of universe. In GR, it's called the cosmological constant. The acceleration is so negligible that it can be observed for farther galaxies relative to nearer ones ;-) –  Waffle's Crazy Peanut Mar 29 '13 at 15:59
    
I can understand how it's possible to observe two objects getting further away from each other but I don't think there is a possible way to actually figure out if the objects speed at which it is traveling through space is increasing. But we must assume that they are increasing in speed otherwise they would not move away from each other. Space could expand all it wants but if the objects are not speeding up they won't move away from each other, space will just expand around them. –  SSpoke Mar 29 '13 at 16:22
    
@SSpoke: If you're unable to understand how we measure that objects are continually getting farther away from us, have a look at Redshift. And, you're doing right. Yes... The increase in velocity of objects in every direction (we look out) simply implies the expansion of universe ;-) –  Waffle's Crazy Peanut Mar 29 '13 at 16:30
    
Dark energy expanding all around an object is a little easier to visualize. I guess as dark energy expands all around every single object in space it pushes everything apart. The key being that it is energy so it is able to exert a force on mass. Empty space without gravity cannot exert a force on mass so saying that space is expanding is nonsense. It is easier to assume space is infinite and the objects are simply all moving away from each other due to dark energy pushing them apart in space. –  SSpoke Mar 29 '13 at 16:41
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How do we know for certain that space is expanding? The answer is that we don't. Expansion of space is just one possible verbal description of cosmological models. General relativity doesn't provide any way of unambiguously describing the velocity of object A relative to distant object B. It's purely a pedagogical issue whether to describe it one way or another. Some people, e.g., Francis et al., think it's better pedagogically to describe space as expanding, while others such as Bunn and Hogg feel the opposite way. All we can say as a matter of empirically testable fact is that the distance between A and B is increasing over time. The fact that Francis disagrees with Bunn doesn't mean that there's a scientific controversy, only a pedagogical one.

Francis et al., "Expanding Space: the Root of all Evil?," http://arxiv.org/abs/0707.0380v1

E.F. Bunn and D.W. Hogg, "The kinematic origin of the cosmological redshift," American Journal of Physics, Vol. 77, No. 8, pp. 694, August 2009, http://arxiv.org/abs/0808.1081v2

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