Do all observers agree on the age of our Universe?

[Spinnor]

Do all observers agree on the age of our Universe? If not is there some measure they do agree on?

Thanks for any help!

 

[bcrowell]

No, they don't all agree.

But in an FRW cosmological model, there are preferred observers, who are essentially observers who detect no dipole asymmetry in the CMB. Such observers agree with one another on the amount of clock time since the Big Bang, and this is what we mean when we speak of the age of the universe in such a model.

In the real universe, a clock on the Earth's surface is not a bad approximation to such a clock. The solar system isn't moving at any large fraction of c relative to the CMB, and there is not a huge amount of gravitational time dilation between the Earth's surface and a point that is, say, outside the local group of galaxies.

 

[Matterwave]

The "preferred observers" in this sense are "preferred" just because they agree with one another, or because their measurement is somehow more "right"? If it is the latter, then does that mean in GR there is some "absolute" frame (e.g. the frame of the CMB)?

 

[bcrowell]

The "preferred observers" in this sense are "preferred" just because they agree with one another, or because their measurement is somehow more "right"?

It's not just because they agree with one another. You could make other sets of observers whose clocks would all agree, e.g., the set of all observers whose velocity relative to the CMB was 0.5c.

But just because they are preferred in some sense, that doesn't mean that they're the only observers who are "right."

If it is the latter, then does that mean in GR there is some "absolute" frame (e.g. the frame of the CMB)?

It's plural. There is not just one such frame for the whole cosmos. There is one such frame for every point in the cosmos. Global frames of reference don't exist in GR.

The existence of these preferred frames is also not a general characteristic of GR. It's just a characteristic of this particular solution of the GR field equations.

 

[Spinnor]

So to the second part of my question, is there some invariant, say some combination of the age of the universe and its volume that all observers would agree on?

Thanks for your reply!

 

[Spinnor]

(age of my universe/volume of my universe) =
(age of your universe/volume of your universe) even if you move very fast relative to me, who is basically at rest?

Edit, it is the same universe just seen through different eyes.

 

[bcrowell]

If the universe is flat or open, its volume isn't finite. Even if it happens to be closed, frames are local things in GR, so it doesn't necessarily make sense to discuss, e.g., the Lorentz contraction of a region of cosmologically distant space. You can't apply a Lorentz contraction to a cosmological solution.

There are certainly definable characteristics of cosmological models like FRW and ΛCDM. The models have adjustable parameters, and those parameters characterize the universe: http://en.wikipedia.org/wiki/Lambda-CDM_model#Parameters

 

[Matterwave]

I believe in a FRW metric, at least all observers would see the same Omega factor (some measure of the curvature or density of matter) right? At least, if one observer observes Omega to be >1, another observer cannot have Omega<1 or else they would disagree on the ultimate fate of the universe. I don't know if one observer can see Omega=1.5 and another see Omega=1.6 or something though.

 

[bcrowell]

I believe in a FRW metric, at least all observers would see the same Omega factor (some measure of the curvature or density of matter) right? At least, if one observer observes Omega to be >1, another observer cannot have Omega<1 or else they would disagree on the ultimate fate of the universe. I don't know if one observer can see Omega=1.5 and another see Omega=1.6 or something though.

Parameters like that are properties of the entire FRW solution. They're not things that individual observers measure in their own frames of reference.

 

[Naty1]

Crowell...Great explanations: Had I not been hanging out here for several years I wouldn't have understood...

Seems like the above posts covers it...but I'd also add that there are no "right" observers...each frame of reference is "right" for that frame, but none generally agree with others. Crowell says it this way:

There is not just one such frame for the whole cosmos. There is one such frame for every point in the cosmos. Global frames of reference don't exist in GR.

You can get an idea of this from our own GPS system (see wiki)...where time for satellites passes more slowly than time on the surface of the earth...staellite time is slower because of greater speed relative to Earth and less gravitational potential than on earth...
hence the atomic clocks passage of time between the satellites and Earth have to be constantly "adjusted"...that is, reconciled...

Time also passes differently between airplanes going west to east versus east to west relative to Earth for similar reasons...and each is different from "earth time" ...

"Preferred" observers, as Crowell describes more completely above, use an agreed upon convenient standard.

 

[Spinnor]

If we can talk about the size and age of our universe,

http://en.wikipedia.org/wiki/Observable_universe

then why can't someone who is moving fast also talk about the size and age of the universe? I'm told that different observers won't agree on the age of the universe so I'm guessing they won't agree on the size as well. Can we come up with order of magnitude estimates?

Thanks for your help!

 

[bcrowell]

If we can talk about the size and age of our universe,

http://en.wikipedia.org/wiki/Observable_universe

then why can't someone who is moving fast also talk about the size and age of the universe? I'm told that different observers won't agree on the age of the universe so I'm guessing they won't agree on the size as well. Can we come up with order of magnitude estimates?

The WP article is about the *observable* universe.

 

[Spinnor]

The WP article is about the *observable* universe.

That is O.K., what does a fast moving observer say about the age and size of his observable universe compared with our observable universe's age and size? Is there some simple close formula?

Thanks for your help!

 

[Spinnor]

Let me reform the question, if the Wiki article on the Observable Universe,

http://en.wikipedia.org/wiki/Observable_universe ,

was written by a civilization moving at 9/10 c relative to me I'm guessing the article would remain the same only the numbers would change? Is there a simple formula for those numbers?

 

[bcrowell]

The speed of light is the same for all observers. Therefore the radius of the observable universe is the same in all directions, and equals ct, where c is the speed of light and t is the age of the universe according to that observer.

There are dozens of numbers estimated in the WP article. If you wanted to attempt to recalculate them all for an observer not at rest with respect to the CMB, you'd have to start by figuring out how to define them all more rigorously. E.g., you'd have to decide whether to count a hydrogen atom's rest mass, or its total mass-energy.

 

[Spinnor]

The speed of light is the same for all observers. Therefore the radius of the observable universe is the same in all directions, and equals ct, where c is the speed of light and t is the age of the universe according to that observer.

...

So for a fast moving observer t is smaller so then ct is smaller?

 

[Calimero]

Therefore the radius of the observable universe is the same in all directions, and equals ct, where c is the speed of light and t is the age of the universe according to that observer.

No, that is common misconception. Radius of observable universe is around 46 Gly, or proper distance from us to the surface of last scattering.

 

[bcrowell]

No, that is common misconception. Radius of observable universe is around 46 Gly, or proper distance from us to the surface of last scattering.

Thanks for the correction.

[EDIT] I made two later edits to this post, both of which were wrong. I'll try again below.

 

[bcrowell]

After several false starts above, here's an attempt at a careful analysis of the observer-dependence of stuff like the volume of the observable universe.

Frames are local in GR, not global. One of the things we have to specify in order to define a frame of reference is a state of motion. To define the volume of the observable universe, there end up being three spots in the definition at which we might need to pick a state of motion. I've labeled these 1-2-3 below.

Observer O is in some state of motion [1] at event A. O's past light-cone intersects the surface of last scattering (or some other surface where some other physically well-defined thing happens) in a spacelike two-surface S. S does not depend on O's state of motion. At every event P on S, we define a state of motion [2] that is at rest relative to the Hubble flow, and we construct a world-line that starts out in this state of motion and extends forward in time inertially. One of these world-lines intersects O's world-line at A. Let the proper time interval along this world-line be t. We extend all the other world-lines from all the other P by the same interval of proper time t. The end-points of all these world-lines constitute a spacelike 2-surface B that we can define as the boundary of the observable universe according to O. Let R be the 3-surface contained inside B. In order to define R, we need to define some notion of simultaneity, which depends on one's state of motion [3]. If we like, we can pick this state of motion to be one at rest with respect to the Hubble flow. Given this choice, we can define the volume V of R (e.g., by chopping R up into pieces and measuring those pieces using rulers that are in this state of motion).

State of motion 1 had absolutely no effect on V, but states of motion 2 and 3 did. If O is not at rest relative to the Hubble flow at A, then 2 and 3 do not match O's state of motion at A. This probably means that O will object that V is not the answer in his frame but in someone else's. However, there is no clear way to satisfy O by modifying the above definition. We can't just say that 2 and 3 should be chosen to be the same as O's state of motion at A, because frames are local things, so matching them to O's motion at A isn't the same as matching them at points far from A. In a cosmological solution there is no well-defined notion of whether or not two cosmologically distant objects are at rest relative to one another.

 

[Spinnor]

After several false starts above, here's an attempt at a careful analysis of the observer-dependence of stuff like the volume of the observable universe.
...

Will study this further along with Ned Wright's cosmology tutorial tonight.

http://www.astro.ucla.edu/~wright/cosmolog.htm

Thank you for your effort! So much interesting stuff to learn.