How can scientists estimate the age of the universe when time itself is not absolute according to Einstein's Theory of Relativity?
The Earth's reference frame is approximately that of the Cosmic Microwave Background's reference frame.
You are absolutely correct: time is not absolute according to Einstein's Theory of Relativity. Time is relative!
Relativity is based upon frames of reference. Different observers in different frames will measure different values for identical quantities.
So, how do we get away with measuring the true age of the universe from Earth's frame of reference?
Well, we consider how our frame of reference relates to the true frame of reference.
If we wanted to measure the true age of the universe, we would want to be in the frame of reference that is directly relevant to the expansion of the universe. This frame of reference happens to be the Cosmic Microwave Background (CMB). So the age of the universe would need to be measured with respect to clocks that are at rest relative to the CMB.
It turns out that the Earth is hurdling through space relative to the CMB at a speed of roughly a few hundred kilometers per second. Now, this may seem fast, but it really isn't. It's on the order of
As we know, the relativistic correction that is needed for computing quantities like length and time is dependent on velocity, specifically the velocity as a fraction of the speed of light. The closer an object is to moving at the speed of light, the larger the relativistic contribution/correction.
Since Earth is only moving at
Another key property of the expanding universe is that it appears homogeneous and isotropic. When observed from Earth, the universe appears to be expanding and moving uniformly in every direction. Of course, it is not exactly isotropic for Earth's frame of reference. The CMB frame would be the only truly isotropic frame. But as we've already shown, Earth is a pretty good approximation.
A key word you used is estimate. This most certainly is an estimate of the true age. But we are fortunate that our frame of reference here on Earth is comparable on a relativistic scale to that of the CMB. So we are able to make measurements here on Earth that are very decent estimates of the actual value.