Universe Age and Size: A Matter of Perspective?

[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?

 

[PeterDonis]

for us the universe is 14 billion years old

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.

What frame of reference would enjoy oldest universe?

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.

 

[Chris Miller]

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.

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?

 

[PeterDonis]

Am assuming the minimum age approaches zero.

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.)

the maximum "comoving" age must be unimpacted by any gravitational forces.

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.

It would seem the accepted "age" is hypothetical.

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.

Would it be correct to consider every point (not matter) in the universe as comoving and isocentric with respect to the CMB?

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.

 

[russ_watters]

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?

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.

 

[Chris Miller]

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.)

So to a photon the universe has zero age?

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.

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.

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.

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.

 

[jbriggs444]

So to a photon the universe has zero age?

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.

 

[PeterDonis]

So to a photon the universe has zero age?

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).

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.

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.

So all such hypothetical comoving observers would see the universe as having exactly the same age

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.

which raises for me questions regarding relative simultaneity that I've learned better than to try to express.

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.

 

[Chris Miller]

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.

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.

 

[PeterDonis]

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.

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.

 

[Chris Miller]

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.

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.

 

[PeterDonis]

I'm still not clear on how arbitrary our convention selection is.

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.

 

[Chris Miller]

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.

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.

 

[Chris Miller]

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.

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

 

[PeterDonis]

I just can't see the physical universe as homogeneous in any regard.

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.

 

[PeterDonis]

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.

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.

 

[Chris Miller]

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.

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?

 

[PeterDonis]

this wasn't always the case, was it?

"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.

 

[russ_watters]

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?

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.

 

[Chris Miller]

"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.

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.

 

[PeterDonis]

Not sure on the definition of static.

Heuristically, it means "not changing with time". The universe is expanding, so it's changing with time. That's about as good a definition as can be given in a "B" level thread.

The more technical definition is that a static spacetime has a timelike Killing vector field. FRW spacetime (the spacetime that describes the universe as a whole) does not. You can look up those terms to find out more, but discussion of them here would have to be in a new thread at the "I" level (at least).

 

[PeterDonis]

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.

All of these statements are wrong; you are misapplying intuitions that work in a static spacetime to a spacetime that is not static.

 

[Ibix]

The point about gravitational time dilation is that it's something that happens between two clocks that are in different gravitational environments. Clocks don't run fast or slow - they only run fast or slow compared to another clock. And it's only really definable when the matter distribution isn't changing (or close enough that we can pretend).

So, in short, you don't get gravitational time dilation until matter starts to clump and form galaxies and black holes. Then you can have a clock close to a black hole and one far away from it and you can compare their rates. When the universe is dense everywhere, as Russ pointed out, everywhere is more or less the same, and there are no clumps of matter that are fairly stable over time. No point is much different from any other and it's all constantly changing so time dilation (not time!) is not definable.

 

[Chris Miller]

So, in short, you don't get gravitational time dilation until matter starts to clump and form galaxies and black holes. Then you can have a clock close to a black hole and one far away from it and you can compare their rates. When the universe is dense everywhere, as Russ pointed out, everywhere is more or less the same, and there are no clumps of matter that are fairly stable over time. No point is much different from any other and it's all constantly changing so time dilation (not time!) is not definable.

I get that time dilation is relative. That locally, all clocks appear to run the same. But are you saying there are no clocks in the universe on whose faces even the second hand has only barely moved since the BB?

 

[Ibix]

I get that time dilation is relative. That locally, all clocks appear to run the same. But are you saying there are no clocks in the universe on whose faces even the second hand has only barely moved since the BB?

In principle, one traveling at extremely high speed with respect to comoving observers. But that has nothing to do with the effects of mass, which is what you seemed to be talking about.

 

[Chris Miller]

In principle, one traveling at extremely high speed with respect to comoving observers. But that has nothing to do with the effects of mass, which is what you seemed to be talking about.

By "comoving observers" here, do you mean the CMB? But yes, I was referring to the effects of mass and its gravitational impact on time. So a clock that'd been very near a massive black hole or greater from the beginning.

 

[PeterDonis]

By "comoving observers" here, do you mean the CMB?

No, he means observers that always see the universe (including the CMB) as homogeneous and isotropic.

I was referring to the effects of mass and its gravitational impact on time. So a clock that'd been very near a massive black hole or greater from the beginning.

There were no black holes at the beginning of the universe. Also, there is no way for an observer (or a clock) to stay very near a black hole indefinitely; there are no stable orbits that close.

 

[Chris Miller]

No, he means observers that always see the universe (including the CMB) as homogeneous and isotropic.

Thanks for clarifying this for me.

There were no black holes at the beginning of the universe. Also, there is no way for an observer (or a clock) to stay very near a black hole indefinitely; there are no stable orbits that close.

Yes, of course. Black holes are downright fluffy compared to the primordial universe. I was referring to a hypothetical clock that could function in a black hole.

 

[Ibix]

Yes, of course. Black holes are downright fluffy compared to the primordial universe. I was referring to a hypothetical clock that could function in a black hole.

If it goes into a black hole it ends up in the singularity in a matter of seconds (if memory serves) and it doesn't read anything.

 

[Chris Miller]

If it goes into a black hole it ends up in the singularity in a matter of seconds (if memory serves) and it doesn't read anything.

Seconds? Not sure how to interpret "doesn't read anything" wrt time. Just googled, and found, "In the centre of a black hole is a gravitational singularity, a one-dimensional point which contains a huge mass in an infinitely small space, where density and gravity become infinite and space-time curves infinitely, and where the laws of physics as we know them cease to operate." But which strikes me as hyperbolic, too loose with infinities. The mass of the universe isn't infinite. But I can easily accept that we don't know.

 

[PeterDonis]

I was referring to a hypothetical clock that could function in a black hole.

There is no such thing in the sense you mean. If the clock is inside the hole's horizon, as Ibix says, it will be destroyed in the singularity, and anyway there is no way for an observer outside the hole to compare the clock's reading with the reading of any clock outside the hole. If the clock is outside the hole's horizon, it can't stay in a stable orbit close enough to the hole for the time dilation factor to be very significant.

 

[PeterDonis]

Seconds?

According to the clock falling into the hole, the time it takes to fall from the horizon to the singularity is approximately $2M$ in geometric units, where $M$ is the mass of the hole. If you convert this to SI units, you will find that for a black hole of one solar mass, it takes 10 microseconds ($10^{-5}$ seconds) to fall from the horizon to the singularity. The time scales linearly with the mass of the hole (as the formula I just gave makes clear), so you can calculate for yourself what the time would be for other masses.

However, none of this really matters for the question you are asking, because, as I said in my previous post, once a clock is below the horizon, there is no way to compare its reading with that of a clock outside the horizon. So the concept of "time dilation" has no meaning for a clock inside a black hole's horizon anyway.

 

[Ibix]

...and there are no black holes in the early universe anyway.

 

[Chris Miller]

...and there are no black holes in the early universe anyway.

"a black hole is a gravitational singularity, a one-dimensional point which contains a huge mass in an infinitely small space, where density and gravity become infinite and space-time curves infinitely, and where the laws of physics as we know them cease to operate." Sounds like the original universe to me.

 

[jbriggs444]

"a black hole is a gravitational singularity, a one-dimensional point which contains a huge mass in an infinitely small space, where density and gravity become infinite and space-time curves infinitely, and where the laws of physics as we know them cease to operate." Sounds like the original universe to me.

But you have quoted out of context, destroying the meaning of the passage you cite.