How old is the Universe? That seems like an easy question to answer. It’s 13.7 billion years, or close to.
Where do we measure that time from? That’s another easy one: “now”.
Relativity tells us there is no universal now, all we can identify is the spacetime event that is “here and now”. So, what do we mean when we say that we measure back from now? Any reference frame that is in motion relative to ours will identify a different here and now. Every part of the Universe is in motion relative to every other part, and the faster that relative motion, the greater will be the discrepancy between the measurement of here and now with respect to each part.
We are assured that the more distant (from us) parts of the Universe are moving away from us at speeds faster than c. What can we say about the measurement of here and now in those areas? All these areas are parts of the Universe. If we can’t identify a “present” for them, how can we say how their “present” relates to the start of the Universe from their perspective? OK, the Big Bang may not be the start of everything, but that’s not the issue here.
We could assume that any measurement taken from any part of the Universe would show that the Big Bang occurred at 13.7 billion years before that local “present”, but what does that actually mean? Is our measurement of the age of the Universe just a feature of our particular location in spacetime?
Co-moving coordinates and cosmological time may be considered as “answers” to this, but they are only arbitrary coordinates, set to “work” in the 4+1 dimensional universe which we observe.
