B Does the age of the Universe differ for observers in expanding space?

[mister i]

The age of the universe is said to be about 13.8 billion years. But, since time depends on the observer, would it be the same for a possible inhabitant of a planet in a galaxy about 10,000 million light years away that is separating from us at 60% of the speed of light?

 

[PeterDonis]

The age of the universe is said to be about 13.8 billion years.

More precisely, the age of the universe according to comoving observers, i.e., observers who always see the universe as homogeneous and isotropic, is about 13.8 billion years.

would it be the same for a possible inhabitant of a planet in a galaxy about 10,000 million light years away that is separating from us at 60% of the speed of light?

If both galaxies are comoving (which galaxies are on average), yes. The "separation speed" you refer to has nothing to do with the "rate of time flow"; it is a coordinate speed and has no direct physical meaning.

What can affect the "rate of time flow", although in practice the effect is small, is the fact that particular observers might not be comoving. For example, we here on the Earth are not comoving; we observe a dipole anisotropy in the CMBR that tells us that, relative to a hypothetical comoving observer co-located with Earth, we are moving at about 600 km/s. That means our "rate of time flow" is not the same as that of a comoving observer. However, 600 km/s is still very small compared to the speed of light (about 0.2%), and the difference in the "age of the universe" for us on Earth as compared to a comoving observer is proportional to the square of that, or about 4 parts per million, which is way smaller than the measurement error in the 13.8 billion year figure. So 13.8 billion years still works just fine as our best estimate of the age of the universe according to us here on Earth.

 

[Ibix]

A feature of our cosmological models is that they are the same everywhere. So if we say the universe is a certain age, so must observers in any other galaxy. This is one area where "neither galaxy is moving, but the space between them is expanding" is the simplest description.

 

[mister i]

"neither galaxy is moving, but the space between them is expanding" is the simplest description.

And what happens regarding the light (which is indeed moving), from our point of observation it travels in this expanding space at 300,000 km/s or do we have to add the part of the spatial expansion?

 

[jbriggs444]

And what happens regarding the light (which is indeed moving), from our point of observation it travels in this expanding space at 300,000 km/s or do we have to add the part of the spatial expansion?

One can think, by analogy, of an ant crawling down the length of an expanding rubber band.

 

[Ibix]

And what happens regarding the light (which is indeed moving), from our point of observation it travels in this expanding space at 300,000 km/s or do we have to add the part of the spatial expansion?

Locally, you will always measure it to be doing $c$. In the "expanding space" interpretation, the distance light still has to go to reach us is decreasing at less than $c$ because the space between us and it is expanding. Sufficiently distant light will never reach us because the total remaining distance is increasing faster than even light can decrease the distance.

 

[cianfa72]

What can affect the "rate of time flow", although in practice the effect is small, is the fact that particular observers might not be comoving. For example, we here on the Earth are not comoving; we observe a dipole anisotropy in the CMBR that tells us that, relative to a hypothetical comoving observer co-located with Earth, we are moving at about 600 km/s.

Sorry, I was reading this thread. With an hypothetical comoving observer co-located with Earth do you mean a comoving observer that at a given point/event along its geodesic worldline is spatially co-located with the Earth ?

If the above makes sense then such a comoving observer will be spatially co-located with the Earth just at that "event/point" along its worldline (i.e. Earth and the co-moving observer meets only at that event).

 

[phinds]

do you mean a comoving observer ...

No. A comoving observer, as you would know if you just looked it up, is:

A comoving observer is the only observer who will perceive the universe, including the cosmic microwave background radiation, to be isotropic. Non-comoving observers will see regions of the sky systematically blue-shifted or red-shifted.

So comoving observers can be billions of light years apart. What matters is how they are moving (NOT moving, actually) relative to the CMB.

 

[PeterDonis]

With an hypothetical comoving observer co-located with Earth do you mean a comoving observer that at a given point/event along its geodesic worldline is spatially co-located with the Earth ?

Yes.

such a comoving observer will be spatially co-located with the Earth just at that "event/point" along its worldline.

Yes.

 

[PeterDonis]

No.

Read more carefully, and see my response in post #9 just now.

 

[cianfa72]

The "separation speed" you refer to has nothing to do with the "rate of time flow"; it is a coordinate speed and has no direct physical meaning.

Ok, but in FRWL spacetime in standard coordinates assuming on average galaxies as comoving "observers" then their spatial coordinates are fixed. Therefore such "separation speed" is nothing but the derivative w.r.t. the cosmological time of the proper distance between galaxies evaluated on spacelike hypersurfaces of constant cosmological time.

 

[PeterDonis]

in FRWL spacetime in standard coordinates assuming on average galaxies as comoving "observers" then their spatial coordinates are fixed.

In the idealized model, yes. But in actual fact we know that most galaxies are not exactly comoving. That includes our own galaxy. The closest things we have in actual fact to something physical that is comoving to the best of our knowledge are the centers of mass of galaxy clusters.

Therefore such "separation speed" is noting but the derivative w.r.t. the cosmological time of the proper distance between galaxies evaluated on spacelike hypersurfaces of constant cosmological time.

Yes, that is a valid interpretation. (Note, though, that this "proper distance", and the "separation speed" that goes along with it, is not something we actually measure. We have to calculate it, and the calculation is model dependent.)

However, it is still the case that this "speed" does not imply any "time dilation" of comoving observers relative to each other. So the OP's statement that "time depends on the observer", with the implication that a galaxy whose separation speed away from us is 60% of the speed of light should be time dilated relative to us (assuming both to be comoving), is not correct. That was the key point of my response.

 

[cianfa72]

However, it is still the case that this "speed" does not imply any "time dilation" of comoving observers relative to each other.

Yes, the proper time $\tau$ of comoving observers is the FRWL cosmological time $t$ so there is not any "time dilation" between them.

I believe such comoving observers can check there is not any time dilation relative to each other by exchanging radar signals.

 

[PeterDonis]

the proper time $\tau$ of comoving observers is the FRWL cosmological time $t$ so there is not any "time dilation" between them.

More precisely, this is the case if we choose the simultaneity convention of FRW coordinates. "Time dilation" always depends on a choice of coordinates.

I believe such comoving observers can check there is not any time dilation relative to each other by exchanging radar signals.

No, they can't, because the proper distance between them is increasing. Exchanging radar signals to check time dilation only works between observers if the proper distance between them is constant.

 

[cianfa72]

More precisely, this is the case if we choose the simultaneity convention of FRW coordinates. "Time dilation" always depends on a choice of coordinates.

You mean that picking as simultaneity convention that implied from FRW coordinates, then the proper time of comoving observers "evaluated" at the same coordinate time $t$ is the same for both comoving observers.

 

[PeterDonis]

You mean that picking as simultaneity convention that implied from FRW coordinates, then the proper time of comoving observers "evaluated" at the same coordinate time $t$ is the same for both comoving observers.

The proper time since the Big Bang, yes.

 

[feynman101]

Yup, it depends on your inertial frame of reference. The age of the universe is calculated by assuming that we are at the centre of the universe and everything is moving away. Therefore we are at the centre of the universe. The current figure that you cited is now out of date due to observations from the James Webb telescope. The perimeter of the universe that we observe as the cosmic background radiation is when the big bang coalesced into matter. Due to time dilation the edge of the universe is very young because it has been expanding at the speed of c.

 

[Ibix]

The age of the universe is calculated by assuming that we are at the centre of the universe and everything is moving away.

No it isn't. The age of the universe is the time measured on clocks that see the CMB as isotropic.

Therefore we are at the centre of the universe.

There is no such place.

The current figure that you cited is now out of date due to observations from the James Webb telescope.

Do you have a reference (a proper journal, not a pop sci article) for that?

The perimeter of the universe that we observe as the cosmic background radiation is when the big bang coalesced into matter. Due to time dilation the edge of the universe is very young because it has been expanding at the speed of c.

This sounds like a misunderstanding of standard cosmological models. The correct statement is that the CMB was emitted around 14bn years ago when the universe cooled enough to become transparent. We still see this simply because it happened everywhere so light from distant parts of this event has been travelling for 14bn years.

 

[cianfa72]

We still see this simply because it happened everywhere so light from distant parts of this event has been travelling for 14bn years.

And travelling since Big Bang, now its spectrum is at microwaves (CMB) and it is homogeneous and isotropic for comoving observers.

 

[Drakkith]

Yup, it depends on your inertial frame of reference. The age of the universe is calculated by assuming that we are at the centre of the universe and everything is moving away. Therefore we are at the centre of the universe. The current figure that you cited is now out of date due to observations from the James Webb telescope.

Observations by the JWST absolutely did no such thing. In fact, they do the opposite. They give even more evidence (and more accurate evidence) in support of the current cosmological model as a whole. That is, the big bang theory, specifically the LCDM model, with an expanding universe that is approximately 13.7 billion years old without any known 'center'. One of the things that the JWST observations HAVE shown us that wasn't predicted/known was to show that galaxy formation happened earlier than expected, which isn't exactly surprising since we didn't know very much about early galaxy formation to begin with. Its observations have also helped up better understand the expansion rate of the universe, atmosphere's of nearby exoplanets, planetary formation in protoplanetary disks, and much more.

Due to time dilation the edge of the universe is very young because it has been expanding at the speed of c.

Not true. Roughly the same amount of time has passed for the edges of our observable universe as has passed here on Earth.