Relativity says that time dilation occurs as velocity approaches c. The faster a particle moves, the slower Time flows for it. In the extreme case of photons, time does not flow at all, and photons “experience” no Time at all. Since there are no two particles in the Universe that have identical motion histories, no two particles need to agree on the amount of time that has elapsed after any particular event; for the purposes of this question, this would be the Big Bang.

So: if no two particles need to agree on elapsed time, how is it meaningful to state that the Universe is 13.5 billion years old? Is it valid to say, “13.5 billion years have elapsed on Earth, because, by virtue of being gravitationally co-located for billions of years, we have largely smoothed out an earlier chaotic phase of motion, and therefore the Age largely holds (on Earth/Solar System/local Universe).”

But this would be a weak statement, other areas of the Universe may have a radically different measure for the age of the Universe (and yet be right).

The age of the universe does depend on the frame in which its measured, and the usual convention for this sort of calculation is to use the comoving frame, the (unique) one in which the cosmic background radiation is isotropic. The speed of the earth relative to that frame is (currently) about v = 625 km/s, giving a time dilation factor γ = (1 - v[sup]2[/sup]/c[sup]2[/sup])[sup]-1/2[/sup] = 1.000002.

There is no single locally-preferred reference frame, but when you look at the Universe as a whole, at any given location, there is a reference frame that can be considered preferred. The catch is that this special frame is different in each location, and they can only be defined in a global (that is, encompassing a significant portion of the entire Universe) context, not just locally. In any given location, in that location’s own locally-relevant frame (called the comoving frame), the age of the Universe is well-defined.

I feel like you stopped short of answering the question: Would hypothetical alien scientists in different parts of the universe measure different answers from each other? And, follow-up: How does our answer compare with the other answers?

The only possible answer to this question is circular: They would measure the same age if they make the measurements at the same time, and wouldn’t if they made the measurements at different times, where “at the same time” means “at the same age of the Universe”. There really isn’t any other good definition of “at the same time” that one could substitute.

And just to add to this ( please correct me if I am wrong) there is no universally unique concept of ‘now’. So you cannot say what would an alien on the other side of the observable universe measure the age of the universe to be now, because is there is no uniquely defined ‘now’ for the whole universe.
I am not qualified to explain why that is so I will leave that to someone else.
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I wouldn’t get caught up in the difference between local and global, the very nature of the question “what is the age of the Universe at some event p?” leads you to consider the entire history of all future-directed timelike curves terminating at p which means the question is not a local one.

The conformal timelike symmetry of cosmological spacetime naturally defines equivalence classes of observers whose clocks define uniquely a cosmological time for all events. This is really the best you can hope for in relativity when asking whether different events have the same ‘now’.

I think that this means that if we were in that unique frame of reference, the Universe would be (very roughly) 26,000 years older than it is in our frame of reference. I’m probably quite wide of the mark, however.

You are wide of the mark, though the mistake is not particularly egregious.

The age of the Universe in the Earth’s peculiar frame is not

t/sqrt(1-v[sup]2[/sup])

where t is the Universe’s age in the CMBR frame and v is the Earth’s peculiar speed as a fraction of the speed of light,

it is instead the integral with respect to τ over [0,t] of

t/sqrt[1-(v/a(τ))[sup]2[/sup]]

where a(τ) is the scale factor of the Universe.

This results in a difference that is larger than 26,000 years, though this ‘peculiar age’ is nothing more than the time experienced since the big bang of an entirely hypothetical observer.

Thankful for all the erudite responses, but all this leaves me no wiser than before. Ignorance stubbornly prevails. I guess the answer is just too complicated for a layperson to intuitively understand.

Perhaps the the answer for you is in the question where you say:

The point is that yes indeed, there are other areas, but the smoothed out nature of the universe means they are not radically different. You might be able to find pathological circumstances (right next to a primordial black hole maybe) but in, general, we assume that the universe is everywhere pretty much the same as what we observe locally, and that is smooth.

Thank you for the clear, straightforward answer. Not that I don’t respect the more complex answers above but a layman who hasn’t studied science for quite some time will need a simple answer. Your explanation looks unambiguous and almost evident (maybe also because it is in line with what I have learned so far).