# Redshift due to expanding space, why not due to galaxies slowing down their escape?

#### Kamil Szot

We observe farther galaxies with higher redshifts.

How can we be sure that this is due space itself expanding?

How do we know that this is not just Doppler shift of galaxies running away from us at higher speeds long time ago, that got lowered (decelerated by gravity of matter in the universe) later on leading to lower redshift for closer galaxies?

Do you know of any papers investigating and/or dismissing such idea?

I know that observed redshifts are uniform irregardless of direction. Does that necessarily imply, if these are Doppler redshifts, that we must be at epicenter? Couldn't being at some point away from epicenter of large enough explosion lead to no asymmetry or to asymmetry that would be unnoticeable for us? What if epicenter of explosion was not a point? What if galaxies were like steel balls mixed with gun powder so energy that pushed that gave them kick away in the beginning was between them? Wouldn't that look uniform from the point of view of most debris that are far enough from the edge?

#### Chalnoth

Re: Redshift due to expanding space, why not due to galaxies slowing down their escap

We observe farther galaxies with higher redshifts.

How can we be sure that this is due space itself expanding?

How do we know that this is not just Doppler shift of galaxies running away from us at higher speeds long time ago, that got lowered (decelerated by gravity of matter in the universe) later on leading to lower redshift for closer galaxies?

Do you know of any papers investigating and/or dismissing such idea?
The basic issue is that it doesn't matter. The essence of General Relativity boils down to the Einstein Field equations, which can be written as:

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

On the left hand side of this equation, we have space-time. This is called the Einstein tensor ($G_{\mu\nu}$, and is a representation of the curvature of space time or, in this case, how space expands with time.

On the right hand side of this equation, we have what is called the stress-energy tensor. This is the matter component that makes up the universe, and includes things like normal matter, dark matter, and dark energy.

What we can do is sit down and write a stress-energy tensor for a bunch of galaxies moving apart from one another, and then, when we look at the left hand side of the equation, we get expanding space-time! So it's not really a question of whether it's doppler effect or expanding space-time: it's both!

Does that necessarily imply, if these are Doppler redshifts, that we must be at epicenter?
Nope. Let's pick a coordinate system with us sitting at the origin, and ask how things look. If we go some distance away, say a distance $d$, things are moving away from us, on average, at some velocity $v$. At a distance of $2d$, things are moving away from us at twice that velocity, $2v$.

So, what happens if we then change our coordinate system, so that we're sitting on a galaxy that is a distance $d$ away from us? Well, since they are moving away from us at a velocity $v$, we will appear to be moving away from them at a velocity $v$ as well!

And what about the galaxy that was twice as far away? Well, if we just take the one-dimensional case, that galaxy will appear to be only a distance of $d$ away, and moving at a velocity $v$. A galaxy that, to us, is a distance $3d$ and moving at a velocity $3v$ would appear, to this other galaxy, to be at a distance $2d$ moving at a velocity $2v$.

In other words, the expansion looks the same no matter where in the universe you happen to be.

#### Kamil Szot

Re: Redshift due to expanding space, why not due to galaxies slowing down their escap

The basic issue is that it doesn't matter. The essence of General Relativity boils down to the Einstein Field equations, which can be written as:

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

On the left hand side of this equation, we have space-time. This is called the Einstein tensor ($G_{\mu\nu}$, and is a representation of the curvature of space time or, in this case, how space expands with time.

On the right hand side of this equation, we have what is called the stress-energy tensor. This is the matter component that makes up the universe, and includes things like normal matter, dark matter, and dark energy.

What we can do is sit down and write a stress-energy tensor for a bunch of galaxies moving apart from one another, and then, when we look at the left hand side of the equation, we get expanding space-time!
So expansion of space-time is not necessarily the cause of expansion of universe, but just side effect of galaxies running away from one another?

How can such small things as galaxies cause expansion of vast voids between them? Isn't space-time in intergalactic void basically flat?

Why do we think that galaxies escape faster now than they were long time ago? Wouldn't there smaller redshift be observed for older (farther) galaxies?

So it's not really a question of whether it's doppler effect or expanding space-time: it's both!
Is it both in sense that they are same or mixed?

#### Ich

Re: Redshift due to expanding space, why not due to galaxies slowing down their escap

So expansion of space-time is not necessarily the cause of expansion of universe, but just side effect of galaxies running away from one another?

How can such small things as galaxies cause expansion of vast voids between them?
It's not cause and effect. It's different descriptions for the same thing.

Is it both in sense that they are same or mixed?
Expanding space redshift can always be decomposed into doppler shift and gravitational redshift as long as you can mathematically define a static coordinate system with some accuracy. So they are the same in that sense.
In a massively evolving universe, it is not always clear what "static" means. The decomposition becomes more and more arbitrary, and you're better off using "cosmological redshift" instead. Its definition doesn't rely on staticity, but on homogeneity and isotropy, which we believe are valid on large scales.

#### Kamil Szot

Re: Redshift due to expanding space, why not due to galaxies slowing down their escap

It's not cause and effect. It's different descriptions for the same thing.
Does presence of mass cause space-time curvature?

Is expansion of universe change of space-time curvature?

Chalnoth said that when you put in the observed movements of galaxies and masses to Einstein Field equations you can calculate tensor that indicates expansion of space.

Why do you think there is no cause and effect and they are both same thing?

Is mass and curvature also same thing? Or you don't agree with what Chalnoth said?

Let me get this straight. We observe galaxies of known masses and distance from us. We treat their redshift as Doppler shift. We put this data into Einsten Field equation and we see on the left side tensor that translates to space-time expanding at accelerating rate?

#### Chalnoth

Re: Redshift due to expanding space, why not due to galaxies slowing down their escap

Ich was agreeing with me.

#### Ich

Re: Redshift due to expanding space, why not due to galaxies slowing down their escap

Does presence of mass cause space-time curvature?
Yes.
Is expansion of universe change of space-time curvature?
No. Expansion of the universe the increase of distance between a class of "particles", e.g. galaxy clusters. If you think of these particles as "test particles" (i.e. massles), there is no change in spacetime curvature, but there is expansion. If the particles are massive, expansion always implies change of spacetime curvature.
Chalnoth said that when you put in the observed movements of galaxies and masses to Einstein Field equations you can calculate tensor that indicates expansion of space.
There's nothing in the tensor at any specific position that indicates expansion. But the way this tensor changes with position shows a certain symmetry, which leads to a certain maximally symmetric coordinate chart (FRW). It is these coordinates that define the meaning of "expanding space".
Why do you think there is no cause and effect and they are both same thing?
Distances get larger because things are moving away from each other.
Things are moving away from each other because distances get larger.
You may pick the one you like most, or simply say: well, motion is increasing distances. It's more the specific pattern of motion that makes the description as expanding space useful, not a fundamental difference between both concepts.
Is mass and curvature also same thing? Or you don't agree with what Chalnoth said?
I agree with what Chalnoth said, at least as far as I described above.
I do not say that mass and curvature are the same thing. I don't say they are different, too, maybe in a few hundred years this will be the prevailing philosophy. In a specific case (cosmological constant), physicists already use both concepts interchangeably.
Let me get this straight. We observe galaxies of known masses and distance from us. We treat their redshift as Doppler shift. We put this data into Einsten Field equation and we see on the left side tensor that translates to space-time expanding at accelerating rate?
We treat their redshift as cosmological redshift, which implies a certain model we use for the universe. We then see that the model works. But only if we choose a certain set of parameters, which correspond to accelerating expansion.
As I said, cosmological redshift is nothing else than Doppler shift on small scales.

#### Chalnoth

Re: Redshift due to expanding space, why not due to galaxies slowing down their escap

Perhaps a better way of saying that mass and space-time curvature are the same thing is instead that they are interdependent. It's rather similar to the relationship between an electric charge and an electromagnetic field. Neglecting radiation, you can't have one without the other. This means that if you know, perfectly, the electromagnetic field, you can also state the precise distribution of charges. Similarly, if you know the precise distribution of charges, you know the electromagnetic field (with the exception of radiation).

Gravity is the same way. If you know perfectly the gravitational field (i.e., the space-time curvature), then the energy/momentum/stress/pressure configuration is also exactly defined. Similarly, if you know perfectly the energy/momentum/stress/pressure configuration, you then know the space-time curvature perfectly (with the exception of gravitational radiation).

Radiation is special because it is a behavior of the field that is independent of any "source": it propagates freely. But in the case of expansion we aren't talking about gravitational radiation. So a statement about how the space-time curvature is behaving is also a statement about how the matter is behaving, and vice versa.

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