# B Age and size of the Universe?

1. Jul 17, 2017

### Chris Miller

Since time and distance are relative, it would seem that the universe's age (and shape, too) depends on the measurer's frame of reference? Like while for us the universe is 14 billion years old, to an observer in a black hole it might be only a few seconds old (and small). What frame of reference would enjoy oldest universe? And how old would it be?

2. Jul 17, 2017

### Staff: Mentor

That's not quite correct. The correct statement is that, for a hypothetical comoving observer at our location (i.e., one who has always seen the universe as homogeneous and isotropic), the universe is 14 billion years old. See below.

It's not a question of "frame of reference", it's a question of the state of motion of the observer. Observers who have always been comoving will see the maximum age for the universe at a given event. We, on Earth, are not comoving observers (we don't see the universe as homogeneous and isotropic--the simplest sign of this is the dipole anisotropy we see in the CMBR), so if you extrapolated our worldline all the way back to the Big Bang, it would give an age slightly less than the "comoving" age. Cosmologists quote the "age" of the universe as the comoving age since that's the longest possible one.

3. Jul 18, 2017

### Chris Miller

Very much appreciate your taking the time to explain this. Am assuming the minimum age approaches zero. And that the maximum "comoving" age must have been unimpacted by any gravitational forces. But is this even possible? It would seem the accepted "age" is hypothetical.

Would it be correct to consider every point (not matter) in the universe as comoving and isocentric with respect to the CMB? Or is this some sort of coordinate misuse?

4. Jul 18, 2017

### Staff: Mentor

Yes, you can have timelike worldlines from the Big Bang to right now that have elapsed proper times as small as you like. (In the limit, you can have lightlike worldlines, of zero length, from the Big Bang to right now.)

What gravitational forces? Gravity is not a force in GR. The maximum comoving age is certainly dependent on the overall geometry of spacetime in the universe, so it's not "unimpacted" by gravity--or more precisely by the presence of matter and energy--in that sense.

Only in the sense that there doesn't have to be any actual observer who has existed since the Big Bang and can directly observe that age on his clock. But we can calculate what the comoving age is from observations we can make directly, so there doesn't have to be any actual observer that observes it directly.

This doesn't make sense; points aren't "comoving". There is a (hypothetical) comoving observer whose worldline passes through each spatial point, and who sees the universe as homogeneous and isotropic, which means such an observer would see the CMB as isotropic.

5. Jul 18, 2017

### Staff: Mentor

Adding to the previous explanation and closing the loop, our speed with respect to "space" (the CMB) is about 627 km/sec, which is nowhere near high enough to show a difference between a universe age calculated from our frame and the oldest. The difference (from an online time dilation calculator) is less than a thousandth of a percent.

6. Jul 18, 2017

### Chris Miller

So to a photon the universe has zero age?

So if all spacetime is shaped to some degree by the presence of matter, then nowhere (e.g., in a black hole) is the universe actually as old as theorized. Really it seems like no two hypothetical comoving observers would measure exactly the same age.

So all such hypothetical comoving observers would see the universe as having exactly the same age... which raises for me questions regarding relative simultaneity that I've learned better than to try to express.

7. Jul 18, 2017

### jbriggs444

The point of view of a photon is undefined. There is no inertial reference frame in which a photon can be at rest.

To a particle moving arbitrarily fast, the universe has an arbitrarily small age. One need not invoke photons.

8. Jul 18, 2017

### Staff: Mentor

No, to a photon the concept of "age" is meaningless. "Age" only has meaning along timelike worldlines, and the worldline of a photon is not timelike (it's null).

No, that's not correct. The comoving age is the maximum age, and it already takes into account the matter and energy present in the universe.

You appear to be making the mistake of thinking that there is gravitational time dilation in the universe as a whole when matter is present. That is not the case. The concept of "gravitational time dilation" only makes sense in a static spacetime, and the spacetime of the universe as a whole is not static.

Only if you look at events on their worldline that all have the same coordinate time in FRW coordinates. But those coordinates are defined so that surfaces of constant coordinate time are also surfaces of constant comoving age.

Your concern is quite valid; the notion of simultaneity embodied in FRW coordinates is indeed a convention, not a physical necessity. The only thing that picks it out physically is the fact I just alluded to, that this notion of simultaneity is the one that makes events with the same comoving age happen "at the same time". But that still doesn't mean you have to describe the universe using FRW coordinates; you could pick other coordinates in which the notion of simultaneity was different, and in those coordinates, events on different comoving worldlines that happened at the same coordinate time would not have the same comoving age.

9. Jul 19, 2017

### Chris Miller

No, not as a whole. It's hard for me to think of the universe "as a whole" in regards to time/age. It just seems (from my schooling here) like this could only be FOR dependent. E.g., I wonder how an observer within dark matter would see the universe.

10. Jul 19, 2017

### Staff: Mentor

Assigning a single "age" to the universe as a whole does depend on your choice of simultaneity convention, yes. But saying that a particular observer, following a particular worldline, observes a certain "age" to have elapsed since the Big Bang does not. That's not a claim about the universe as a whole. It's just a claim about the elapsed time along that particular worldline.

11. Jul 19, 2017

### Chris Miller

Thanks for your patience and clarifications, Peter. I think I almost understand now. though I'm still not clear on how arbitrary our convention selection is.

12. Jul 19, 2017

### Staff: Mentor

It's arbitrary in the sense that we can in principle select any simultaneity convention we want (subject to some very general requirements, such as that any two events that are considered simultaneous must be spacelike separated). But in particular cases, there might be particular conventions that make things look simpler or more convenient. That is the case with the simultaneity convention that underlies FRW coordinates, i.e., saying that events are simultaneous if they have the same comoving age (comoving observers whose worldlines contain the events have the same elapsed time since the Big Bang at those events). That makes each spacelike surface of constant time homogeneous and isotropic (since that's how comoving observers see the universe), which makes things much simpler mathematically and conceptually. But it's still a convention; you can describe the universe using other coordinates. Your description will just look more complicated and be harder to work with mathematically. But it will still, in principle, give you all the same predictions for actual observations.

13. Jul 20, 2017

### Chris Miller

Again, thank you. You have a way of explaining the underlying mathematical decisions that I can almost grasp. I hope the following doesn't belie too much this professed (almost) understanding.

While mathematically possible and convenient, I just can't see the physical universe as homogeneous in any regard. If there were a clock at every point in it, I wonder what their average measured time elapsed would be (from the BB). I'm guessing, given all the dark matter, a lot less than 14 billion years.

14. Jul 20, 2017

### Chris Miller

Interesting. Thank you. So only missing 100,000 years or so.

15. Jul 20, 2017

### Staff: Mentor

Homogeneity is an approximation that describes the universe reasonably well on large scales (hundreds of millions of light-years and larger). It is not intended to be an exact description at all scales; obviously the universe is not homogeneous on the scale of individual stars or planets, or even on the scale of galaxies with dark matter "halos" around them.

16. Jul 20, 2017

### Staff: Mentor

This is not a good guess; you are drastically overestimating the time dilation factor due to clouds of ordinary matter.

Just as a rough estimate, the gravitational time dilation factor in the core of an average galaxy like the Milky Way is perhaps 1 part per million, so the difference in "universe age" for an observer in the galactic core vs. one well outside the galaxy would be about 1 millionth of the comoving age, or about 14,000 years.

Time dilation factors can get much larger near the horizon of a black hole, but there's no way for a free-falling observer to stay near the horizon of a black hole for a long time; there are no stable orbits anywhere close to the horizon.

17. Jul 21, 2017

### Chris Miller

Good points. Space is mostly space. Matter that can significantly dilate time, even dark matter, comprises a minuscule to negligible percent of the universe volume-wise, which is only decreasing with expansion. Although, this wasn't always the case, was it?

18. Jul 21, 2017

### Staff: Mentor

"Matter that can significantly dilate time" does not just mean "very dense matter". It means something more like "very dense matter that is static". The matter in the early universe was not static; it was expanding rapidly. The concept of "time dilation" is not well-defined in that situation.

19. Jul 21, 2017

### Staff: Mentor

Does that last part matter? Yes, the universe used to be denser. But that is part of the base case, not a deviation from it.

20. Jul 21, 2017

### Chris Miller

Not sure on the definition of static. Matter would've been expanding, but with no relativistic velocity (same as with distant galaxies separating > c). Mass would've remained constant. Not surprised time isn't well defined, though I'd imagine all clocks to be basically stopped given the mass involved.