If I take a spaceship and park it near the event horizon of a black hole and then measure the age of the universe by observing SNe Ia, then travel back out to normal space (no gravitational forces, at rest with respect to CMB), will the dates agree? That is, if the measured age of the universe is 13.8 billion years near the event horizon, and it takes me 100 million years (proper time) to travel back out to normal space, will my new measurement of SNe Ia agree with a date of 13.8 + 0.1 = 13.9 billion years? If that is true, can we say that time is absolute (i.e. all observers will agree on the age of the universe when using SNe Ia when coordinate systems are normalized)?
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$\begingroup$ The age of the Universe that you measure this way is just an averaged over some class of intrinsic observers quantity with dimensions of time. No, time is not absolute, as is well-known from relativity theories. $\endgroup$– Prof. LegolasovNov 2, 2016 at 13:51
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$\begingroup$ You are suggesting that the age of the universe depends on your reference frame. $\endgroup$– user32023Nov 2, 2016 at 13:56
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$\begingroup$ I am suggesting that it depends on my history, i.e. on the worldline along which I measure this age. There is no such thing as The age of the Universe, since the Universe is extended. Instead, each observer measures the passage of time as he ages with the Universe from the Big Bang. The age of the Universe is just an expected average over a particular class of observers. Note that I am not claiming to have answered your question completely, that's why this is just a comment. $\endgroup$– Prof. LegolasovNov 2, 2016 at 14:00
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$\begingroup$ Just to clarify: when you measure the age, you approximate General Relativity by a particular solution (FLRW?). In terms of a particular solution it is indeed sensible to define how much time has passed since the beginning of time. However, this can only be considered an approximate quantity and it can not tell us something fundamental like whether time is absolute or not. You have to consider the whole theory for that, and GR is pretty unambiguous on this: no, time is not absolute. $\endgroup$– Prof. LegolasovNov 2, 2016 at 14:08
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2$\begingroup$ @AGML's answer is spot on. But I think, perhaps you are conflating some of the language surrounding the issue. When people say, 'age of the universe' they are generally referring to a specific frame of reference: comoving with the Hubble-flow. So you're basically asking, "Will everyone agree on the time Alice measures?" --- sure, because we can all convert to her reference frame. Each reference frame can still measure something different. $\endgroup$– DilithiumMatrixNov 2, 2016 at 18:36
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Well, no. We can construct a much simpler example to see this: fix a point in Minkowski spacetime, and consider two observers following worldlines from that point with a relative velocity. They can even both be inertial. At fixed Minkowski time the two observers measure different proper time.
The FLRW universe, however, is sort of special in that there is a sort of preferred reference frame: that in which the coordinates follow the expansion. This frame is "preferred" in the sense that geodesics which have some relative velocity compared to the expansion asymptote towards it. But you're still allowed to view the solution from an arbitrary coordinate system (for example by considering non-geodesic observers), so you can come up with any "age of the Universe" you like.
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$\begingroup$ I'm having trouble with this answer. So if I measure the age of the universe in normal space by plugging the various parameters into FLRW and work backwards to find that it's 13.8 billion years. Then I fly into a black hole and just before I hit the event horizon, I perform the same measurement and get,... what? Anything I want? The universe can be 1 or 100 billion years old? $\endgroup$– user32023Nov 3, 2016 at 21:09
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1$\begingroup$ You'll get a different answer depending on the details of your worldline, yes. This is true of all time intervals, including the interval between now and the Big Bang singularity. You couldn't just "plug all the various parameters" into FLRW, because the relations you are thinking of assume quantities are measured in comoving coordinates, and you are not comoving. You're standing at the Big Bang and you have a clock. If you drift with the expansion until now your clock reads 13.8 billion years. If you move in some other way it reads a different time. $\endgroup$– AGMLNov 3, 2016 at 21:15
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$\begingroup$ Another way of thinking about this: you measure the age of the Universe outside the hole (13.8 billion years). You then hover outside a black hole for a while, fly back to Earth, and look at your watch. For you, the trip took (say) 1 year, so to you the Universe is now 13.8 billion + 1 years old. To your friends on Earth, it took you 1 billion years, so to them the Universe is 14.8 billion years old. If, outside the hole, you measure supernovae and make the FLRW calculations, you will get 14.8 billion years. $\endgroup$– AGMLNov 3, 2016 at 21:25
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$\begingroup$ One final point. For any age of the Universe you like, there exists a class of observers for whom the Universe is that age. However, we Earthlings are stuck with ages greater than 13.8 billion years, since there is nothing we can do to go back in time. To get a shorter age we would need to have been moving quickly relative to the expansion all along. (Thinking about it now, 13.8 billion years is possibly the maximum age, since proper time is maximized along geodesics). $\endgroup$– AGMLNov 3, 2016 at 21:30
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$\begingroup$ Let's work on special relativity first. If I put Edwin Hubble's telescope in a spaceship, then leave in any direction and accelerate to 0.9c, then take his telescope out and measure the red-shift of all the stars in a sphere around me, what value will I get for the Hubble constant? $\endgroup$– user32023Nov 3, 2016 at 22:16