# How is the Age of the Universe Determined?

How can the age of the universe be determined when there is no absolute measure of time or distance in the universe. Every other place in the universe has another rate of the passing of time. Since time expands with the expansion of space, trying to use expanded time to measure time is circular and self refuting.

PeterDonis
Mentor
How can the age of the universe be determined when there is no absolute measure of time or distance in the universe.

Because "the age of the universe" is not an absolute measure of time. It is the elapsed time on the clocks of idealized "comoving" observers (observers who always see the universe as homogeneous and isotropic) since the Big Bang. Observers in different states of motion would measure a different age.

time expands with the expansion of space

What does this even mean?

I think you might want to spend some time working through Ned Wright's cosmology FAQ and tutorial:

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

Because "the age of the universe" is not an absolute measure of time. It is the elapsed time on the clocks of idealized "comoving" observers (observers who always see the universe as homogeneous and isotropic) since the Big Bang. Observers in different states of motion would measure a different age.

What does this even mean?

I think you might want to spend some time working through Ned Wright's cosmology FAQ and tutorial:

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

So if the other observer calculates a different age of the universe, which is the correct age?

PeterDonis
Mentor
f the other observer calculates a different age of the universe, which is the correct age?

What do you mean by "the correct age"?

What do you mean by "the correct age"?
Which age is the actual age of the universe?

Bandersnatch
Which age is the actual age of the universe?
Depends on who's measuring.

diogenesNY
Depends on who's measuring.
: )

PeterDonis
Mentor
Which age is the actual age of the universe?

What do you mean by "the actual age"?

In case you haven't caught on yet, there is no such thing as "the correct age" or "the actual age". All there is is the age as measured by a particular observer. Different observers can measure different ages. That's all there is to it.

phinds
Gold Member
2021 Award
Peter, correct me if I'm wrong but I believe that it is also true that everywhere in the universe it is possible to determine an age that is associated with a co-moving (to the CMB) observer and that all such measurements/calculations no matter where taken/done will give the same answer since they compensate for the movement of actual observers. Further, that age is about 13.8 billion years by our latest calculations from the European Space Agency's Plank Mission.

PeterDonis
Mentor
I believe that it is also true that everywhere in the universe it is possible to determine an age that is associated with a co-moving (to the CMB) observer and that all such measurements/calculations no matter where taken/done will give the same answer since they compensate for the movement of actual observers.

Yes, this is correct. You don't have to be a comoving observer to calculate the age a comoving observer would measure, as long as you know your own motion relative to a comoving observer at your spatial location. We estimate that by looking at the dipole anisotropy that we observe in the CMB and calculating our motion relative to a comoving observer (who would see the CMB as having no dipole anisotropy) from that. (Note that virtually all published data for the CMB temperature distribution already subtracts out the dipole.)

Chronos
Gold Member
A variety of other measurements have also been conducted and are consistent with CMB measures - e.g., relative abundance of long lived isotopes, the age of ancient stars. Gravitational simulations of large scale structures and galaxy formation, and temperature of remote dust and gas clouds in the universe.

Drakkith
Staff Emeritus
So if the other observer calculates a different age of the universe, which is the correct age?

As other have said, both are correct. The basic idea is that most structures in the universe (planets, stars, galaxies, etc) occupy frames of reference that move relatively slowly with respect to a convenient reference frame where the CMB is extremely uniform. This makes it convenient to measure the universe's age with respect to a co-moving observer, which is just an observer anywhere in the universe who is in our "convenient" frame of reference where the CMB is uniform. We'll call this convenient frame the CMB frame. (Note that this convenient frame is not an "absolute" frame nor a "preferred" frame. It's just a convenient one)

Observers moving with respect to our CMB frame experience time dilation with respect to that frame. This means that the age of the universe as measured by these frames would be different from what the observer in the CMB frame measures. An observer moving very, very quickly with respect to the CMB frame would measure the universe as being much older than 13 billion years. You could say that the age of the universe measured from the CMB frame is the "minimum age" any observer would measure. (I think so at least)

As always, someone correct me if I'm wrong.

Jorrie
Gold Member
An observer moving very, very quickly with respect to the CMB frame would measure the universe as being much older than 13 billion years
Should it not be the other way round, i.e. that such observers, using their own clocks, would measure the universe to be younger than13 billion years?
Knowing their velocity relative to the comoving frame, they can transform their measurement to the comoving frame and get the standard 13.8 billion years for the universe.

Drakkith
Staff Emeritus
Should it not be the other way round, i.e. that such observers, using their own clocks, would measure the universe to be younger than13 billion years?

Now that you mention it, I'm not sure. I can remove that part of my post if necessary.

PeterDonis
Mentor
Now that you mention it, I'm not sure.

AFAIK Jorrie is correct; the proper time elapsed for comoving observers is maximal, in the sense that any other timelike worldline connecting the Big Bang and a given event on a comoving worldline will have less elapsed proper time between the two events than the comoving worldline does.

Chronos
Gold Member
Isotope abundance is not affected by observer reference frames, AFAIK.

Drakkith
Staff Emeritus
AFAIK Jorrie is correct

Roger.

mfb
Mentor
Observers moving quickly relative to the CMB do not get a single well-defined age of the universe, because different directions will appear to have a different age. They can extrapolate their motion back to figure out how long they could have been moving since the big bang, then they'll get a shorter time.

phinds
Gold Member
2021 Award
Observers moving quickly relative to the CMB do not get a single well-defined age of the universe, because different directions will appear to have a different age. They can extrapolate their motion back to figure out how long they could have been moving since the big bang, then they'll get a shorter time.
I don't get how different directions make any difference. Different speeds, yes. Since the CMB is everywhere, what does it even mean to have a DIRECTION relative to the CMB ?

PeterDonis
Mentor
what does it even mean to have a DIRECTION relative to the CMB ?

It means you don't see the CMB as isotropic; you see a higher temperature in the direction you are moving, and a lower temperature in the opposite direction. We actually observe this here on Earth; the usual term is "dipole anisotropy" in the CMB. But practically all published data on the CMB corrects for this by subtracting out the dipole in order to display what the CMB would look like to a "comoving" observer at our location.

mfb
phinds
Gold Member
2021 Award
It means you don't see the CMB as isotropic; you see a higher temperature in the direction you are moving, and a lower temperature in the opposite direction. We actually observe this here on Earth; the usual term is "dipole anisotropy" in the CMB. But practically all published data on the CMB corrects for this by subtracting out the dipole in order to display what the CMB would look like to a "comoving" observer at our location.
Yes, I understand that perfectly well. What I DON't understand is how direction matter to how you perceive the age. Let me be more clear.

Let's say you have a galaxy traveling in what we will call North relative to the CMB, at a given speed. Now we have a different galaxy traveling East at exactly the same speed relative to the CMB. Each sees the CMB as an ellipsoid with different temperatures in opposite directions relative to them and each computes an age with and without compensation for the anisotropy. How is it that they would get different results?

PeterDonis
Mentor
What I DON't understand is how direction matter to how you perceive the age.

It depends on how you are trying to evaluate the age. A comoving observer can use the redshift of the CMB (which he sees to be the same in all directions) to evaluate how much time has elapsed since the CMB was emitted; and for him, this will give the same answer as the elapsed proper time along his worldline from then to now.

But a non-comoving observer sees the CMB to have a different redshift in different directions, so if he tries to use the observed redshift to calculate an "age", he won't get a single well-defined answer. And if he corrects for the anisotropy so that he can get a single well-defined answer, what he calculates won't be the "age" along his own worldline; it will be the "age" along a comoving worldline.

For the non-comoving observer to calculate the "age" along his own worldline, he has to add an extra step after the above calculation: he has to extrapolate his own motion, relative to comoving observers, back to whatever spacelike hypersurface he wants (such as the one when the CMB was emitted), and adjust the comoving "age" he calculated above for his own motion. That will always give an answer that is smaller than the comoving "age"; but how much smaller will depend on the details of the non-comoving observer's motion, and will be different for different non-comoving observers.

mfb
Mentor
Yes, I understand that perfectly well. What I DON't understand is how direction matter to how you perceive the age.
Relativity of simultaneity. If we look 5 billion years in two opposing directions, we see the universe at the same age in both directions. If our fast-moving spacecraft does the same (with "forwards" and "backwards"), it will see the different ages in different directions.

PeterDonis
Mentor
Relativity of simultaneity.

This isn't quite as simple as it looks, because the fast-moving spacecraft can't construct an inertial frame that covers the entire universe (any more than a comoving observer can). So any simultaneity convention he adopts will have an arbitrariness to it that is not present in the usual SR case (where inertial frames pick out a particular simultaneity convention). But I agree that it will seem "natural" for him to adopt a simultaneity convention that is different from the "comoving" one.

mfb
Mentor
That's the point. It is unclear how such an observer would do it, but it would differ from the natural choice a comoving observer has.

Jorrie
Gold Member
That's the point. It is unclear how such an observer would do it, but it would differ from the natural choice a comoving observer has.
Is the point then not that although unclear how such observers would do it, two non-comoving observers with different directions, but with the same back-front anisotrophies, would get the same "incorrect" age for the universe? This is how I understood phinds' query.

phinds
Gold Member
2021 Award
I'm still not getting how two galaxies (or spaceships) moving at right angles to each other but at the same speed would see any quantitative differences in their computations for the age of the universe.

phinds
Gold Member
2021 Award
Is the point then not that although unclear how such observers would do it, two non-comoving observers with different directions, but with the same back-front anisotrophies, would get the same "incorrect" age for the universe? This is how I understood phinds' query.
Yes, that is what I am saying, AND they would also get the SAME computed age of a comoving observer. That's what I've been saying all along and it seems that I'm being contradicted and I don't see why.

mfb
Mentor
I'm still not getting how two galaxies (or spaceships) moving at right angles to each other but at the same speed would see any quantitative differences in their computations for the age of the universe.
No one said that. They would see different apparent ages if they compare the universe in front of them with the universe behind them, no matter how they do that (apart from transforming to a comoving observer frame). Both observers would do so for their respective directions.

phinds
Gold Member
2021 Award
No one said that. They would see different apparent ages if they compare the universe in front of them with the universe behind them, no matter how they do that (apart from transforming to a comoving observer frame). Both observers would do so for their respective directions.
OK. I misinterpreted the "different directions" statement as being applicable to two different objects when it was really being applied only to different directions of the same object.

It means you don't see the CMB as isotropic; you see a higher temperature in the direction you are moving, and a lower temperature in the opposite direction. We actually observe this here on Earth; the usual term is "dipole anisotropy" in the CMB. But practically all published data on the CMB corrects for this by subtracting out the dipole in order to display what the CMB would look like to a "comoving" observer at our location.
So it appears the CMB would be relative to our frame of reference. What effect would another frame of reference have, say near a black hole?

phinds
Gold Member
2021 Award
So it appears the CMB would be relative to our frame of reference.
I think perhaps you still misunderstand what a frame of reference is. Or, perhaps that sentence doesn't quite reflect what you want to ask.

What effect would another frame of reference have, say near a black hole?
same comment.

To say "the CMB would be relative to our frame of reference" as a stand-alone statement just doesn't make sense. You can define a frame of reference in which the Earth is at rest, or at most is rotating, and you can define a frame of reference near a black hole and the computations on getting the age of the universe for a co-moving observer would be more complicated for the frame of reference near the black hole because you would have to account not only for the speed of the black hole relative to the CMB, you would also have to account for the fact that your space-time path is in a deep gravity well.

PeterDonis
Mentor
So it appears the CMB would be relative to our frame of reference

I'm not sure what you mean by this, but it doesn't look correct to me.

Chalnoth