Eaglespike said:
Thank you Chalnoth and phinds. However, the age would presumably depend on
the frame so have you any idea what the difference would be for
an observer at the limits of our visible universe and an observer nearby?
It seems to me that when they give the 13.2 billion figure they are assuming
that they can step outside the universe and watch it evolve.
Any comments would be appreciated!
Basically, we can set an overall reference frame by using the temperature of the CMB. An observer anywhere in our universe, no matter their reference frame, can look at the CMB and measure its temperature (provided they have the right instrument).
We can define a global reference frame by the following two criteria:
1. An observer in the global reference frame sees a CMB which is has the same average temperature in every direction (that is, it has no dipole). This means that the observer is at rest with respect to the CMB.
2. At a given time t, the every observer sees the same temperature of the CMB. That is to say, we can define a global "now" by saying that all observers "now" see the same temperature of the CMB that we see (2.725K). These observers will see the total time passed since the big bang as being the same, so we can use the same time coordinate.
This is perhaps a bit technical. But the upshot is that the fact that our universe is, on average, the same in every location and in every direction means that there is a convenient choice of reference frame. With this convenient choice, we can talk about things like the age of the universe in a sensible way, in a way that observers on far-away galaxies will agree with.