# B Expansion of space

1. Oct 19, 2017

### Richard lanning

How does knowing that galaxies are all moving away from each other and the farthest ones are moving more quickly prove that space is itself expanding and not just that the galaxies are moving through it?

2. Oct 19, 2017

### kimbyd

Galaxies are, on average, moving further away from one another at a rate proportional to their distance. That statement is what is meant by, "Space is expanding." The two descriptions are one and the same.

Edit:
One way to think of it is by looking at the Einstein Field Equations which describe General Relativity. They can be written as:

$$G_{\mu\nu} = {8\pi G \over c^4}T_{\mu\nu}$$

I'm sure this looks like a bunch of incomprehensible characters, but the basic premise is simple: on the left is what is known as the "Einstein tensor" which describes space-time. When people say, "space is expanding," they are talking about the behavior of the Einstein tensor.

On the right hand side is what is known as the "stress-energy tensor". This object describes the matter content of the universe. When people say, "galaxies are moving away from one another," they're describing the behavior of the stress-energy tensor.

The two terms are equal, so they're just different ways of looking at the exact same thing.

3. Oct 19, 2017

### Richard lanning

Thank you for the reply...another question if I may...If we happened to be at the "center" of the big bang or the "center of the universe" whatever that means, would we not see the same movement of the galaxies and their speeds that we see now??

4. Oct 19, 2017

### Orodruin

Staff Emeritus
It does not mean anything, there is no such thing. The expansion would look the same wherever you are. In fact, it is one of the underlying assumptions behind the standard model of cosmology.

5. Oct 19, 2017

### Richard lanning

6. Oct 19, 2017

### Staff: Mentor

The redshift/distance relation we see is incompatible with the idea of things moving through space.

7. Oct 19, 2017

### Orodruin

Staff Emeritus
Depends on how far away you go. If you do not go too far away, it can be interpreted exactly as things moving through space, which was Hubble's original interpretation.

8. Oct 19, 2017

### rede96

From a relativity point of view isn't the statement 'things moving through space' just as wrong as saying 'things static in space'? All we can talk about is how things move relative to some frame of reference.

As regards expansion I always got confused over questions like 'Is 'space' expanding' and never really got a satisfactory answer as opinions seem to differ.

For me is a much better way of thinking of expansion is from our point of view, in simple terms, everything is moving away from us and the further away something is the faster it is moving away. But that same can be said from any frame of reference we chose in the universe.

9. Oct 19, 2017

### Orodruin

Staff Emeritus
In cosmology, there is a preferred reference frame. The geometry of space-time does give a particular frame preference in much the same way that there would be preferred directions on the surface of an ellipsoid. When one talks about "moving in space" it typically refers to motion relative to that frame (called the "comoving frame"). This is also the CMB rest frame so you can actually measure your motion relative to it. Most of the dipole contribution to the CMB temperature comes from our motion relative to the CMB rest frame.

10. Oct 19, 2017

### kimbyd

I think it's very misleading to call this a "preferred reference frame". There is a convenient reference frame. You can do all the math in a different frame and get the same result. It's just that the math is easier if we choose a reference frame that matches the symmetry provided by the expansion.

11. Oct 19, 2017

### Staff: Mentor

Well, but we do go far away.
Space is expanding, and the (educated) opinions don't differ there.
Don't do it. This leads to various misconceptions.

12. Oct 19, 2017

### Orodruin

Staff Emeritus
Fine. I will sign off on that. Clearly you can use any coordinates you like. Let's call it a "singled out" or "natural" frame.

13. Oct 19, 2017

### Orodruin

Staff Emeritus
We do, but Hubble didn't, which is something I think is important to understand in order to get the connection between modern cosmology and the historical context. In other words, the first thing people usually hear is about "things moving apart" and then later we tell them that things are not moving (relative to the comoving frame), but space is expanding. Locally, it is the same thing, just different simultaneity conventions.

14. Oct 19, 2017

### kimbyd

"Distances between objects are increasing on average" is in some ways less misleading than "space is expanding".

They both describe the same thing, but "space is expanding" can lead to some misconceptions about the nature of space-time.

15. Oct 19, 2017

### Orodruin

Staff Emeritus
Both are to some extent misleading and convention dependent. Distances increasing comes with its own set of problems.

So does ”distances increase on average” so I don’t really see a clear preference for one or the other from this point of view. I have been here long enough to see both multiple times.

16. Oct 20, 2017

### Ken Ucarp

So if I'm understanding you, the left side is an abstraction which manifests itself concretely by measurements of the physical universe that fit the right side. And the right side could have been otherwise, but just so happens to be as noted. I'm also guessing that there are some solutions to this whereby the left side would be 0, i.e. no expansion. It's just that that's not what is observed.

17. Oct 20, 2017

### Orodruin

Staff Emeritus
If the left-hand side is zero, then so is the right-hand side. This corresponds to a Universe empty of content and indeed such solutions exist. The simplest one is just the Minkowski space of special relativity.

18. Oct 20, 2017

### Staff: Mentor

The left side of the Einstein Field Equation does not mean "no expansion"; it means "no stress-energy", i.e., as @Orodruin said, no content. Such solutions are usually called "vacuum" solutions, to emphasize the fact that there is no matter, radiation, etc. present.

For a spacetime to describe "no expansion", it needs to have a property which is called being "stationary". There is no simple way to express this criterion in terms of what you would see on the left side or the right side of the Einstein Field Equation; at least, I'm not aware of one. This property is neither equivalent to nor disjoint from the property of the left side of the EFE being zero: there are solutions which have both properties (vacuum and stationary), solutions which have only one (vacuum or stationary, but not both), and there are solutions which have neither property. The solution that describes our actual universe is of the latter sort (neither vacuum nor stationary).

19. Oct 20, 2017

### Orodruin

Staff Emeritus
Could you specify what you mean by "no expansion" here? As we discussed a few days ago, Minkowski space (or rather, the interior of the future light cone of any event in it) can be described by a FLRW-type metric with a linearly growing scale factor, yet it is certainly a stationary space-time.

20. Oct 20, 2017

### Staff: Mentor

I mean that the spacetime is stationary, in the technical sense of having a timelike Killing vector field. Yes, I know Minkowski spacetime, strictly speaking, doesn't fit this, because it has a timelike KVF but also can be described as "expanding" using an FLRW-type metric. For a "B" level thread I think it's better to put that aside as an edge case than to try to elucidate it.