# Age of Universe & Relativity

1. Jun 18, 2006

### kuahji

I was just thinking... :tongue: perhaps this is a dumb question & the two are unrelated. But, they say the universe is roughly 14 billion years old. My question would be, relative to who?

2. Jun 18, 2006

### pervect

Staff Emeritus
That's 14 billion years in cosmological time - which is measured by a co-moving clock, i.e. a clock which is moving so that the cosmic microwave background radiation (not to mention the rest of the universe) appears to be the same in all directions (isotropic).

Note that as you go back in time, the cosmic microwave background radiation goes up in frequence, so that it is no longer microwaves, but can get into the visible range (and even shorter wavelengths).

There is still a special frame, though, in which the background radiation appears to be the same in all directions (isotropic). This is the same special frame in which the distribution of matter in the universe also appears to be isotropic. This special frame is the frame for the clocks for measuring "cosmological time".

3. Jun 30, 2006

### cincirob

Pervect, You are correct that the CMBR sould be CVBR (V for visible) at some point in the past. The temperture of the universe when the CMBR radiation was released was about 3000K (at least fromone source I have). That's somewhat lower than the surface of the sun, so the light would be pretty red at that point. Do you have any idea how long after that the temperture of the light dropped below vivible range?

4. Jun 30, 2006

### pervect

Staff Emeritus
If you pick a redshift factor, z, that you define as "below the visible" you can use Ned Wright's cosmology calculator to determine the age of the universe then. The results from the cosmology calculator are model-dependent, usually the Lambda-CDM model is used.

Recombination (3000K) occurred around z=1100, which was 372,000 years since the big bang in cosmological time according to the calculator.

Pick a temperature, calculate z via

z = temperature * 1100 / 3000

and put the resulting z number into Ned Wright's cosmology calculator for the time elapsed since the big bang

http://hyperphysics.phy-astr.gsu.edu/hbase/bbrc.html#c3

gives "red hot" at being around 800-900 degrees. So if we take t=600 degrees, then z=220

Ned Wright's calculator gives an age of the universe of 5 million years for z=220

5. Jul 9, 2007

### miscellanyous

I think this is an excellent question. I have spent some time thinking about it, but without much success. The original answer given by pervect is good, but I have one question and a comment.

Has anyone gone to the frame of reference where the CMB is isotropic and measured it from there? Or is this special frame of reference predicted to exist? I will settle for a reference on this question. Out of curiosity, how does this frame compare with the motion of the earth?

As I understand, there is a preferred frame of reference where the microwave background is isotropic and from this we conclude the expansion of the universe is also isotropic with respect to this frame. This privileged frame seems like trying to sneak Newton in the back door. Consider the privileged frame as belonging to one twin in the famous twins paradox of special relativity. When the twins are reunited, they will disagree on the how much time has elapsed and therefore disagree on the true age of the universe. So I am still unconvinced – it seems like special relativity must allow for a non-unique age for our universe.

But I do think this is a really fascinating question and I am hoping for some interesting responses!

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http://csmeenk.batcave.net" [Broken]

Last edited by a moderator: May 3, 2017
6. Jul 9, 2007

### marcus

the solar system is moving about 370 km/second with respect to CMB
in the direction of constellation Leo

so that means a frame which is at rest with respect to CMB would be moving 370 km/second past us in the opposite direction

you ask if the frame exists. yes. Astronomers use it all the time because they correct their data for the solar system's motion (removing the asymmetry caused by solar system motion)

they also have to correct for the earth's orbital motion around the sun but that is only 30 km/second----less than ten percent of the overall solar system motion.

COBE measured the 370 figure very accurately. there is a paper from around 1993-1995 from the COBE team that gives this figure, and the directional coordinates. You could look it up at arxiv.org.

I don't understand why you bring up Special relativity. General relativity trumps special. We are working in GR here.
Suppose one twin is at rest with respect to CMB, and the other twin farts around and goes this way and that. then the time on the first twin's watch is right---corresponds more close to universe time. and the time on the giddy twin who was gadding about is just wrong. it doesnt correspond to the age of the universe we mean when we talk about the age of the universe.

However I think everybody recognizes that for GEN REL REASONS there is still no PERFECT universal absolute time----only approximations to it. This is not because of one twin moving around (we can forget about him).

It is because one twin could be DEEPER IN A GRAVITY WELL than the other twin. So time would be going slower for him. One twin might be out in the very empty space between clusters of galaxies, and the other twin might be living in some massive galaxy in the heart of some massive cluster of galaxies.

Both of them could be at rest with respect to CMB, but their clocks would still not agree perfectly.

it is still convenient to talk as if there was a welldefined standard universe time measured by observers at rest, and ignore gravity differences in definition, so there is a bit of imprecision in how the standard time is defined----but who cares, there are much more important sources of uncertainty in the observation data themselves. the usual LCDM model, with its co-moving distance, and its standard time, gives an impressive fit and works remarkably well.

Last edited: Jul 9, 2007
7. Jul 10, 2007

### miscellanyous

Thanks for your response. I would not say G.R. trumps special relativity, rather, special relativity exists as a limiting case of G.R. I put my query in terms of special relativity because it is easier to understand and my example does not require the full analysis of G.R. (as far as I can tell).

The twins example is designed to show that there is no right or wrong time - the twins age differently with respect to one another. It doesn't make sense to say one twin's age is right and the other wrong. Such an explanation seems based on a privileged frame of reference - Newtonian ideas.

I thank you for the info about the effects of gravity on time. I was not aware of this. I take your point is that it would not affect the age of the universe significantly. I am not sure if the same can be said about my objections too.

----
http://csmeenk.batcave.net" [Broken]

Last edited by a moderator: May 3, 2017
8. Jul 10, 2007

### marcus

About the effect of gravity on time, clocks deep down in a potential well run slower.
So I could imagine extreme situations where it would make a substantial difference. But people ordinarily overlook this and think of some kind of universal standard time as measured by a clock that is either out in intergalactic empty space or at least not in TERRIBLY strong gravity. We are "terra-centric" and tend to imagine other observers in roughly similar circumstances to our own.

As for your objection, Special Rel does not strictly speaking apply in an expanding universe. Because we live in a particular solution of the Einst. Eqn of Gen Rel, there IS an approximate idea of rest and a preferred frame.

Observers who are at rest with respect to the expansion, or with respect to the Cosmic Microwave Background (which is the same condition of rest) DO see things differently from observers who are gadding about.

In the field of cosmology there is an idea of preferred frame.

So what they told you in Special Rel is wrong when applied too generally. It applies only to small local neighborhoods, or else it applies to a different universe where distances are not expanding and there was no big bang.

Fortunately small-scale distances as we normally measure them are not expanding and Special Rel works very well when applied in the appropriate circumstances.
the only thing one must not do is assume Special Rel is TRUE in some absolute way, universally applicable, and draw philosophical conclusions
which fly in the face of accepted Cosmology. this is what I urge you not to do.

Last edited: Jul 10, 2007
9. May 2, 2009

I am not a physicist, just a crazy amateur questioning things.

How do we know that the CMB speed is the "right" speed? In other words, what is is measured relative to, since all speed is relative?

Also, how do we know that the entire universe is not subject to significant, relativistic distortion based on gravity - especially since some physicists need to hypothesize dark matter to account for the observed gravitational effects. And of course, if there is unaccounted gravity, we do not have any way of knowing its effects on the past, right?

10. May 2, 2009

### marcus

What do you mean by "the CMB speed"?

And what do you mean by "what is is measured relative to?"

I assume the question is "what is it measured relative to?"

But what is "it" here?
=======================

I would say that the CMB has no speed. It is ancient light emitted by the primitive (evenly distributed) matter of the universe---a partially ionized gas that filled all space.

One makes the arbitrary choice of saying that that gas had no net motion, was not moving in a bulk sense. (Individual molecules in it had random thermal motion of course.)

So one assumes that the CMB emitted from it has no net motion, and one takes that as the landmark, or criterion of rest. Speed measured relative to CMB. You are at rest, in this sense, if you are at rest relative to CMB.

Then your coordinate system will agree with the standard Friedman model that cosmologists use.

It is just a convention, a professional convenience if you like. It's what they use, in practice. Optional, of course. You are free to use whatever alternative coordinates.

So I don't understand your question about "the CMB speed". In standard mainstream cosmo, the Background does not have a speed.

You don't sound crazy, so keep asking until someone understands your question.