# Age of the universe

1. Jan 4, 2007

### heliocentricprose

I've read that the universe is 13.7 billion years old.
Also, I've read that time passes "slower" when an object is close to a large mass as opposed to an object close to a smaller mass.
Take two galaxies. One galaxy is half the mass of the other. At this moment, has 13.7 billion years passed for both galaxies? Is the heavier galaxy using up its supply of hydrogen slower than the lighter one?

2. Jan 4, 2007

### chroot

Staff Emeritus
The figure of 13.7 billion years is given for an observer co-moving with the cosmic microwave background radiation. It will be different for every other observer. For example, an observer near a black hole may have seen the entire universe to date evolve in a matter of seconds according to his own watch.

- Warren

3. Jan 4, 2007

### heliocentricprose

In that case, how old are the particles making up the earth from their own perspective?

4. Jan 4, 2007

### chroot

Staff Emeritus
We certainly don't know the history of the earth's atoms well enough to assign such a number!

The Milky Way Galaxy does not have a particularly large velocity with respect to the CMBR, so time dilation with respect to it is really pretty negligible effect.

- Warren

5. Jan 4, 2007

6. Jan 4, 2007

### chroot

Staff Emeritus
I should also point out that, in absence of forces, every particle in the unverse would be going along with the Hubble expansion, and every particle would experience the same 13.7 billion years since the big bang. In truth, gravity complicates things a bit, and pulls particles off those trajectories. The resulting movement, with respect to the Hubble flow (CMBR rest frame), causes small time dilation effects that make each particle's elapsed time a little different from 13.7 billion years -- just not substantially different. The only exception are particles near very large curvatures in spacetime, like those near black holes.

- Warren

7. Jan 4, 2007

### quantum123

Very interesting, I mean the black hole part. I have never thought of it this way.

8. Jan 5, 2007

### Chris Hillman

Debunking a misconception in "Creation Science" [sic]

Hi, heliocentricprose,

Actually, for an observer "hovering" near a massive object, both the mass of the object and the "distance" to the object are relevant.

As you may know, the so-called "Young Earth theory" [sic], a topic in the so-called "Creation Science" [sic] movement, attempts to reconcile Ussher's age based upon scripture (see http://en.wikipedia.org/wiki/Bishop_Usher), 6010 years plus a few months, with the age based upon science, about 4.5 billion years, which is a considerable discrepancy. One of the sillier arguments I have seen is the claim that gravitational time dilation explains this away!

Recall that "gravitational time dilation" is a potentially misleading shorthand for the fact that if an observer, A, located on surface of the Earth, emits time signals at the rate of one per second by his ideal clock, and if these signals are received by a second observer, B, located very far away from any massive objects, then B will find that the signals arrive at intervals longer than one second by his ideal clock.

To see what's wrong with the "Creation Science" claim, note that in the Schwarzschild vacuum (the simplest model in gtr which can be used in this situation), we have
$$\frac{dt}{ds} = \frac{1}{\sqrt{1-2 m/r}} \approx 1 + m/r$$
where $m/r \approx 6.958 \times 10^{-10}$ for the Earth. This says that in our scenario, B will measure time signals from A to be running slow at a rate of less than one part per billion (in American terminology). So this certainly does not reconcile Bishop Ussher's alleged "scriptural age" with the scientific age!

(By the way, for a neutron star, the ratio m/r can be much larger, about 0.3.)

The analogous objection about mainstream cosmology is even easier to debunk: the textbook analysis of standard cosmological models such as the FRW models does take account of all relativistic effects in computing the elapsed time measured by an ideal clock carried by an observer more comoving with an idealized galaxy (see for example D'Inverno, Introducing Einstein's Relativity for a very readable discussion of these models).

In your scenario, you need to be more specific about where in each galaxy your two observers are located. E.g. if they are both hovering outside stars, the "gravitational time dilation" (wrt distant observers) will probably be dominated by this massive nearby object, but will be tiny. The details would depend upon the m/r ratio as above.

Last edited: Jan 5, 2007
9. Jan 5, 2007

### Myst

Excuse me if it's a stupid question, but how can we compute the age of the Universe ?
Is it explainable easily ? With which experimental data ?

10. Jan 5, 2007

### chroot

Staff Emeritus
Myst,

The principle means of finding the age of the universe is to measure the rate of its expansion, and extrapolate backwards. The most precise measurements to date have been made by the WMAP spacecraft. Here's a simple, easy-to-understand page on the topic:

http://map.gsfc.nasa.gov/m_uni/uni_101age.html

- Warren

11. Jan 5, 2007

### pervect

Staff Emeritus

There should be a very small difference in the time elapsed since the big bang for the two galaxies.

To try and get an estmate of how much, first we need an estimate of the potential at the center of the galaxy

a back of the envelope calculation based on a potential energy of -G * M_galaxy / r_galaxy gives a time dilation factor of about 1.0000001 if we assume that M_galaxy is 6e11 M_sun, and that r_galaxy is about 250,000 light years (for the dark matter halo), i.e about .1 part per million

Of course we will need some constant multiplier for -GM/r. I would guess that the above result could be off by an order of magnitude, but probably (hopefully) not more than two orders of magnitude.

One might be able to get some better data out of http://arxiv.org/abs/astro-ph/0612327 for the potential.

Note that cosmology, when it assigns a constant time since the big bang, assumes that there aren't any lumps of matter (which includes galaxies). On the average this isn't a bad approximation, as one can see by the small magnitude of the time dilation factors being discussed.

12. Jan 6, 2007

### Chris Hillman

Yes, if you are Steven Weinberg. See his popular book The First Three Minutes.

13. Jan 6, 2007

### Chris Hillman

Essential qualification

Oops! I should have said, at the surface of a neutron star, the ratio can be much larger. Sorry for any confusion I might have caused.