How do you define at rest in the Universe?

[Xtyn]

How do you define "at rest" in the Universe?

I was reading in a Scientific American an article called: "Misconceptions about the Big Bang" By Charles H. Lineweaver and Tamara M. Davis.

In it I found this:
Individual galaxies move around at random within clusters, but the clusters of galaxies are essentially at rest. The term "at rest" can be defined rigorously. The microwave background radiation fills the universe and defines a universal reference frame, analogous to the rubber of the balloon, with respect to which motion can be measured.

How can you measure motion in respect to microwave background radiation?

Also, I was drawing something and I want to know if it is correct.

The "0" 's are bodies, "-" is a photon.
Each row is a year.
Because of space expansion, the bodies are increasing their distance (relative to one another) at the speed of light.
The bodies are at first 3 light-years apart.

......0-...0
......0...-...0
........0...-...0
.......0...-..0
......0...-.0
......0...-0
......0.....0

Although the bodies were 3 light-years apart, the photon arrived in 6 years from the first to the second body and it shows the first body as it was 6 years ago. When the photon arrives, the bodies are now 9 light-years apart.
So, the photon traveled 6 light-years.

Is this correct?

Can those bodies be "at rest"? If not, my calculations are wrong, because if they move through space, time gets dilated.

 

[sylas]

How can you measure motion in respect to microwave background radiation?

You measure motion by looking for Doppler shifts in the background radiation; a bit like what is done with a radar gun; except without needing to send out the signal and have it reflected.

The background radiation is an almost perfect blackbody spectrum, corresponding to a temperature of 2.725 degrees absolute.

You are at rest when it is the same temperature coming from every part of the sky. If you are moving with respect to the background, then it will appear blueshifted (hotter) in the direction to which you are moving, and redshifted (colder) behind. We are currently moving at about 380 km/s in the approximate direction of the constellation of Virgo, with respect to the cosmic background radiation.

Although the bodies were 3 light-years apart, the photon arrived in 6 years from the first to the second body and it shows the first body as it was 6 years ago. When the photon arrives, the bodies are now 9 light-years apart.
So, the photon traveled 6 light-years.

Is this correct?

Not really. For pictures of the path of a photon in an expanding universe, have a look at this diagram, taken Ned Wright's cosmology tutorial, part 2. Straight lines are co-moving galaxies, all expanding away from each other. Red lines are two photons, traveling in opposite directions. The vertical axis is time, from the bang at the bottom when everything is jammed up together. The little triangles are "light cones", showing the direction for photons emitted from one of the galaxies, both to the left and to the right.

Cheers -- sylas

 

[Xtyn]

You measure motion by looking for Doppler shifts in the background radiation; a bit like what is done with a radar gun; except without needing to send out the signal and have it reflected.

The background radiation is an almost perfect blackbody spectrum, corresponding to a temperature of 2.725 degrees absolute.

You are at rest when it is the same temperature coming from every part of the sky. If you are moving with respect to the background, then it will appear blueshifted (hotter) in the direction to which you are moving, and redshifted (colder) behind. We are currently moving at about 380 km/s in the approximate direction of the constellation of Virgo, with respect to the cosmic background radiation.

Thank you. I feel pretty stupid that it didn't cross my mind, it was obvious and I knew about the Doppler shift.

Now I'm curious how astronomers know that the redshift we see from distant galaxies is cosmological redshift and not Doppler redshift.

Not really. For pictures of the path of a photon in an expanding universe, have a look at this diagram, taken Ned Wright's cosmology tutorial, part 2. Straight lines are co-moving galaxies, all expanding away from each other. Red lines are two photons, traveling in opposite directions. The vertical axis is time, from the bang at the bottom when everything is jammed up together. The little triangles are "light cones", showing the direction for photons emitted from one of the galaxies, both to the left and to the right.

Cheers -- sylas

I don't really understand where I was wrong but I'll read the document.

 

[russ_watters]

Now I'm curious how astronomers know that the redshift we see from distant galaxies is cosmological redshift and not Doppler redshift.

They are functionally the same thing, so there is nothing to distinguish. Scientists may, if they wish, correct an observed redshift with respect to the CMB doppler shift, but I don't think it is really necessary as the observed redshift in very distant galaxies is far larger than the CMB redshift. In other words, I don't think there is a measurable difference between the cosmological redshifts of distant galaxies at the same distance.

 

[Chronos]

Doppler redshift is due to proper motion. That is a vanishingly small component of the observed redshift of distant galaxies. The milky way, for example, travels around 600 kps with respect to the CMB. It is probable most galaxies in the universe meander about their local spacetime within a order of magnitude of this velocity, with respect to the CMB. The redshift of CMB photons is z ~ 1090. The most distant galaxy observed to date is around z ~ 10. Doppler redshift cannot account for objects receeding much faster than z = 1 for reasons noted by Einstein.

 

[Xtyn]

Doppler redshift is due to proper motion. That is a vanishingly small component of the observed redshift of distant galaxies. The milky way, for example, travels around 600 kps with respect to the CMB. It is probable most galaxies in the universe meander about their local spacetime within a order of magnitude of this velocity, with respect to the CMB. The redshift of CMB photons is z ~ 1090. The most distant galaxy observed to date is around z ~ 10. Doppler redshift cannot account for objects receeding much faster than z = 1 for reasons noted by Einstein.

Yes, it seems you are right (after I've read some scientific articles about it).
Thank you.

 

[Ich]

What a pity, I missed this thread. I'll jump in with my usual agenda.

[...]So, the photon traveled 6 light-years.

Is this correct?

Essentially yes, but only if all your statements are meant to be defined in the reference frame you drew (the one where both galaxies have exactly the opposite velocity), and if you ignore gravity. It's a bit more complicated in real cosmology with curved spacetime and such.

Can those bodies be "at rest"?

At rest wrt each other? Definitely not. There is time dilation also, that's why your example works only in some special coordinates, like the one I told you.

Doppler redshift is due to proper motion.

Redshift is redshift, as russ watters pointed out, there is nothing to distinguish from an operational point of view. Wheter or not, and if yes, to what account, you call the measured redshift "doppler", depends on the coordinates you use. Standard cosmological coordinates attribute a certain peculiar motion to every object and call that portion of redshift "doppler".

 

[Xtyn]

What a pity, I missed this thread. I'll jump in with my usual agenda.

Essentially yes, but only if all your statements are meant to be defined in the reference frame you drew (the one where both galaxies have exactly the opposite velocity), and if you ignore gravity. It's a bit more complicated in real cosmology with curved spacetime and such.

OK

At rest wrt each other? Definitely not. There is time dilation also, that's why your example works only in some special coordinates, like the one I told you.

I meant "at rest" in respect to the CMB which represents space itself.

Is there time dilation in space expansion if the bodies have the same mass (negligible mass) and remain "at rest" in respect to the CMB?

 

[marcus]

I meant "at rest" in respect to the CMB which represents space itself.

That is a good criterion for being "at rest" and it is widely used by astronomers. Before the CMB was detected the same thing was called "at rest with respect to the Hubble flow" or also "comoving" although it is not motion in the ordinary sense of approaching some destination.

Before the CMB was detected and our solar system's motion relative to it was measured (380 km/s in the Leo direction) you could approximately measure the same motion because the relation of distance to recession speed was not quite the same in all directions. Distant galaxies in the Leo direction from us were not receeding quite fast enough.

And recession was faster than the Hubble rate indicated in the opposite-to-Leo direction. So you could get a better fit if you corrected for the solar system's motion (with respect to the Hubble flow.)

The old terminology is a bit misleading because nothing is "flowing". It is just the dynamic change in geometry that makes largescale distances increase.

So yeah, that is a long way of saying that you are in good company with the bulk of the astro community and you are using a useful criterion of rest.

Is there time dilation in space expansion if the bodies have the same mass (negligible mass) and remain "at rest" in respect to the CMB?

No. No such effect. You simply have the expansion redshift associated with the signals coming from A to B.

1+z = a_now/a_then

The parameter a is the scalefactor which appears in the metric and keeps track of expansion of distance. The ratio is that of distance now divided by distance then. The distance between A and B now when the light is received, over the distance then when the light was emitted.

So 1+z is the ratio by which the universe has expanded while the light is in transit.

That sums up the whole effect. Of course if we could watch them going about their business they would seem redder and be moving slower, because the whole movie is stretched out by the factor 1+z.

But my point is that this expansion redshift is the whole effect. There is no gravitational dilation and there is no motion dilation beyond this.

You can if you want give up the "CMB rest" perspective and go thru contortions and interpret the expansion redshift as the cumulative effect of an infinite number of coordinate changes along a path from A to B, made by an infinite sequence of observers. The expansion rate of the universe is always changing so it is a big bother to get this calculation right. It seems like a wasteful way to approach it. Most folks don't bother going thru such contortions, just to interpret expansion redshift in some mathematically equivalent way but without CMB rest. I believe Ich's "usual agenda" as he calls it is to tell everybody about this mathematically equivalent way . You can get him to explain it. Or read a paper by E. Bunn and D. Hogg. I'll get the link.
Here is the link: http://arxiv.org/abs/0808.1081
Both Bunn and Hogg are first rate, but I think what they are doing in this paper is more just a curiosity without significant effect on the rest of astronomy.

 

[Ich]

I believe Ich's "usual agenda" as he calls it is to tell everybody about this mathematically equivalent way .

Nutgeb found a paper that is close to my viewpoint - http://arxiv.org/abs/0809.4573" by J.A.Peacock.
Similar to Peacock (I think), I don't want to agitate against that picture. But I'm on a lonely crusade against the evil notion of "expansion is not motion", as I've seen so many personal tragedies of once reasonable physicists who fell prey to that aggessive meme. I'll continue to raise the banner of derived observables against excesses of scholastic interpretation, but not in this thread, and not now, 'cause I'm going to go to bed.
Edit: Just listen to Chalnoth: "https://www.physicsforums.com/showthread.php?p=2317373#post2317373"".