# Is the age of the universe relative to an observer's location in that universe?

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According to Wiki the age of the universe is 13 billion years old, and I was taught that background radiation made the universe uniform in all directions.

Doesn't this define a sphere of space in the universe with Earth at the center? This sphere would have a radius of 13 billion light years.

We (on Earth) could not see anything outside this sphere. As light did not exist more than 13 billion years ago. So for us this defines some kind of edge for the universe.

But what happens when an alien in another galaxy 5 billion light years away from Earth also looks towards the stars. Don't they see a uniform background radiation and measure the same age of the universe?

That alien would also have a sphere of 13 billion years.

So we have two spheres, one for Earth and one for our alien friend.

These two spheres would overlap each other by 5 billion years. Which means, if we look in the opposite direction from that alien's galaxy. We can see an additional 5 billion years further than they can.

If we measure the total width of the two overlapping spheres we get a distance of 18 billion light years.

I now grasp my hair in confusion. Is this possible that two visible spheres could overlap to create a distance longer than the oldest ray of light? And from there I fall into more questions. Can two people measure the same universe age from different spots in the universe.

That's why I think my idea is is wrong, but how could it be wrong and why?

You are labouring under the misapprehension that how far we can see directly gives the age of the universe. Whilst it is true that the oldest light we can see was emitted some 13.7 billion years ago, the stuff that emitted that light is now roughly 46 billion light years away, thanks to expansion of the universe.

The universe itself probably extends significantly beyond this and may be infinite. That does not conflict with the big bang model or relativity. If the universe is infinite then it has always been infinite. Places that are separated by more than the oldest light ray as you put it, are not in causal contact and, depending on the cosmological parameters, may never be.

In a homogeneous, isotropic universe (and don't forget we can only make assumptions about regions beyond our observable universe), all observers would agree on the age of the universe and that the universe was once very much smaller and all would see (on average) the same sort of universe in all directions.

To ensure that places that are outside of causal contact now are homogeneous requires that they were in causal contact in the past. This is the nature of the "horizon problem"".

I took the picture below from the "slideplayer" website, I am unsure who the originator is, but it serves its purpose here and I think encapsulates your question. It appears in this diagram that A and B can never have "communicated" and can never have originated from the same place. The solution provided by inflation is to have a massive exponential expansion of space in the first fraction of a second. In short, the distances between points in space (or galaxies if you like, although there were no galaxies at the epoch of inflation) are suddenly increase by many, many orders of magnitude. This give the appearance of faster-than-light motion, although the cosmic speed limit only applies to local measurements and not to the expansion of space itself. The end result is a universe that appears homogeneous well beyond the limits of a radius of the age of the universe in light years.

Well, the “first” hypothesis was that the universe is infinite and the number of space objects is infinite. Then, the Big Bang theory came along and we found out that our universe is roughly 13 billion years old and the radius of the observed universe is 13 billion light years, and we postulated that the Universe is probably connected: there's no edge and if you could stop time and move in one direction you would probably arrive at the same point just like you would do on the surface of the Earth. Now we know that it was not a very precise idea: the radius of the observed universe turned out to be a bit larger: around 14 billion years, and it happens that the most distant galaxies move away from us faster than light, so this radius (14 billion years) is only the radius of the currently visible universe (we see how it looked 14 billion years ago when the universe was much smaller). Now this radius has reached 45 billion light years but we can only see the past (or 14 billion years). So wee see the past, not the present size. The fact that the galaxies that are very far away from each other move away from each other faster than light is attributed to the expansion of the space itself and doesn't violate the General Theory of Relativity (we may say it makes it somewhat imprecise, just like relativity made Newton's theory slightly imprecise). Our space is sometimes illustrated as an elastic rubber band on which the farther away two points are, the faster they will move apart, when you extend the rubber band. And our space is expanding in somewhat similar fashion. We don't see the invisible part of the universe (the whole universe may be 150-600 billion light years in diameter -- this size will never be visible and it's much more than the distance of 45 billion light years to which the most distant visible galaxies must have moved by now but we still observe them as if they were 13-14 billion light years away). Also we don't know if our universe is infinite or finite. You can imagine a finite one as a “connected universe” that is if we could stop time and go in one direction eventually arriving in our starting point. If, however, it is not the case and our universe is open and not connected, we may call it infinite. The both theories are fine. Unfortunately we don't know which one is correct! If the Universe is not connected, there might be abnormalities like “edges”, I mean, there may be a point in Universe where galaxies end and there are no more galaxies further beyond or something much weirder than that. This is unfortunately beyond our visible Universe and we have no way of knowing.

Another thing is that your question revolves around the concept of space. Well, it's roughly three-dimensional in real life, if we don't consider very small (as in quantum mechanics) or cosmologically large distances. Yet, we know that our space might warp, so things are not that simple. Right now we don't know much about the actual configuration of our metric space.

As I see, many folks have difficulty in imagining the connected Universe. Well, let's simplify everything greatly. Let's say our Universe is just like Earth, and let's imagine Earth grows in size, so towns that are far away from each other move away from each other the fastest. Then you can take the length of the equator and call it the diameter (or just use it instead of the diameter) of our “test” universe. Half the distance of the equator will be the radius (or just use it instead of the radius) of our “test” universe, and it will be the same everywhere, and everything will be expanding as we initially postulated. It explains the paradox with aliens and two circles you mentioned. Note that towns are not growing in size because, as is the case with galaxies, we presume here that our towns are held by "gravitation" from expanding. Also note that we use the surface of the Earth in this example, which is two-dimensional, and the universe is three-dimensional (probably, or, let's say, approximately to avoid imprecision). Hope, this primitive spherical illustration is of some help.

Here is an explanatory and helpful quote from the article Metric Expansion of Space from Wikipedia:

The universe could be infinite in extent or it could be finite; but the evidence that leads to the inflationary model of the early universe also implies that the "total universe" is much larger than the observable universe, and so any edges or exotic geometries or topologies would not be directly observable as light has not reached scales on which such aspects of the universe, if they exist, are still allowed. For all intents and purposes, it is safe to assume that the universe is infinite in spatial extent, without edge or strange connectedness.[15] Regardless of the overall shape of the universe, the question of what the universe is expanding into is one which does not require an answer according to the theories which describe the expansion; the way we define space in our universe in no way requires additional exterior space into which it can expand since an expansion of an infinite expanse can happen without changing the infinite extent of the expanse. All that is certain is that the manifold of space in which we live simply has the property that the distances between objects are getting larger as time goes on. This only implies the simple observational consequences associated with the metric expansion explored below. No "outside" or embedding in hyperspace is required for an expansion to occur. The visualizations often seen of the universe growing as a bubble into nothingness are misleading in that respect. There is no reason to believe there is anything "outside" of the expanding universe into which the universe expands. Even if the overall spatial extent is infinite and thus the universe cannot get any "larger", we still say that space is expanding because, locally, the characteristic distance between objects is increasing. As an infinite space grows, it remains infinite

You may want to read the full article. I think it's not bad and roughly in line with modern science. It'll give you way more information than my simplified explanations. You may also want to get acquainted with the four-dimensional Euclidean geometry - I think it might make some things easier to grasp when talking about our metric space. So, I recommend the article Metric Expansion of Space in Wikipedia as a good starter - I hope it's not very challenging.

PS: Please note that my explanations are substantial simplifications. Various topologies of the Universe or metric space (various combinations in terms of finiteness, infinity, connectedness, and curvature) might be theoretically possible. Let me add one more advanced notion here: Wheeler suggested that the topology of space-time might be fluctuating (space-time foam), thus bringing quantum mechanics into here. Well, I guess, we still have a very limited knowledge when it comes to our actual metric space.

## Does measuring the age of the universe result in objective observation?

Let me know if there are any errors or holes in my logic, facts, or assumptions.

I was thinking in regards to time being relative to the observer and the resulting impossibility of an objective measure of time: In determining the age of the universe, our current estimation is about 13.2 billion years. Now, this would be an estimate or measure based on our earthly frame of reference, the universe being 13.2 billion years old as observed by earthlings.

But since any point in the universe can be considered its center, then the 13.2by estimation would result as observed from any other frame of reference in the universe. Therefore, the measure of the age of the earth, as measured in units of time, according to the CMBR is objective and not relative to any frame of reference since every frame of reference is the same.

Also, wouldn't this apply to the estimation of the "diameter" of the universe in light years?

## Is Everything In The Universe The Same Age?

A view of many galaxies at varying distances from the Hubble ultra deep field. Image credit: NASA . [+] ESA G. Illingworth, D. Magee, and P. Oesch, University of California, Santa Cruz R. Bouwens, Leiden University and the HUDF09 Team.

It’s been 13.8 billion years since the Big Bang, something we’ve been able to date from a variety of lines-of-evidence. But that’s the amount of time that has passed for us since the Big Bang since time is relative, what does that mean for observers in other parts of the Universe? Our Earth exists in our galaxy, and everything that we perceive within it is that same 13.8 billion years old. Well, almost.

A view of the Milky Way galaxy from Earth. Image credit: Wikimedia Commons user ForestWander, from . [+] http://www.forestwander.com/.

You see, the planets, stars and other points-of-light we see in our night sky aren’t the exact same age as we are. Because the speed of light is finite, if we look at a star that’s say, 100 light years away, we’re seeing it as it was 100 years ago, not as it is today. When you compare that to 13.8 billion years, however — even if you take a star all the way across our galaxy at 100,000 light years away — that difference is insignificant. The difference between 13,800,000,000 and 13,799,900,000 years isn’t worth very much at all. But if we start looking at other galaxies — at very distant galaxies, that story begins to change.

A two-dimensional "slice" of our Universe, showing its clustering properties. Image credit: Sloan . [+] Digital Sky Survey (SDSS-III).

Every “point” in the image above is a galaxy unto itself. The green filament you see is a feature known as the Sloan Great Wall, and is located approximately a billion light years from Earth. The galaxies we’re seeing in that structure are only approximately 12.8 billion years old, and the farthest galaxies seen in the image above are even younger than that.

In fact, as we look farther and farther away, we’ve found galaxies that go as far back as when the Universe was less than one billion years old, and was just a few percent of its current age.

Looking back a variety of distances corresponds to a variety of times since the Big Bang. Image . [+] credit: NASA, ESA, and A. Feild (STScI), via http://www.spacetelescope.org/images/heic0805c/.

If our telescopes (and our light-gathering power) were good enough, we’d be able to see individual stars with very few heavy elements in them, as well over 99% of the atoms at that time were still the pristine hydrogen and helium formed from the Big Bang. There would be almost no carbon, oxygen, silicon, phosphorus, iron and more that requires stars to make.

Because of that, there would be practically no rocky planets, no organic molecules and no chance of life in these locations. When we see these galaxies in their early, pristine state, we are literally looking back in time.

An illustration of galaxy CR7, whose light arrives at our eye from 13 billion years ago and which . [+] contains only stars formed from pristine hydrogen and helium, before any other heavy elements were present. Image credit: M. Kornmesser / ESO.

But that’s a very important point here! We are not looking at these galaxies as they exist today, but rather it is our perspective: we are the ones looking back in time!

To someone on a distant star, in a distant galaxy or tens of billions of light years across the Universe, we would be the ones who appeared to be in the past. To someone 100 light years away, there would never have been signs of a nuclear bomb on Earth we would never have invented the computer no television broadcasts would ever have been transmitted even amplifying vacuum tubes wouldn’t have been invented yet. To someone in a galaxy a billion light years away, our Sun would appear younger and dimmer, the Earth would have housed only single-celled life, with no discernible plants or animals, and our planets’ continents would be mostly barren, covered only in ice and dirt.

Artist's conception of the exoplanet Kepler-186f, which may exhibit Earth-like (or early, life-poor . [+] Earth-like) properties. Image credit: NASA Ames/SETI Institute/JPL-Caltech.

And most frighteningly, to someone viewing what would become us from the most distant, visible galaxies, our Earth and Sun would not only not exist yet, but most probably neither would the Milky Way. Rather, we’d be a series of small gas clouds and proto-galaxies, yet to merge into the spiral structure that would come to form our home. Only the oldest, most ancient globular clusters — now found in the halo of our galaxy — would exist, and they would be rich with hot, young, blue stars, all of which have been long gone for billions of years.

To any of these observers, whether on another star, in another galaxy or all the way across the Universe, they would see a very similar Universe to us:

• A Universe that’s 13.8 billion years old today.
• A Universe where, in every direction that they look, they appear to be seeing farther back into the past.
• A Universe in which the cosmic microwave background has cooled to 2.725 K today.
• A Universe in which the great cosmic web appears indistinguishable from the cosmic web we see.
• And a Universe where, if they looked back at us, they would see us exactly as long ago as we see them.

The large-scale structure in the Universe as mapped by the previous best galaxy survey before SDSS. . [+] Image credit: 2dF Galaxy Redshift Survey.

With all of this in mind, doesn’t it seem like there’s some sort of absolute time, after all?

While it might appear that way, it turns out this isn’t quite the case! What turns out to be true is that the Big Bang occurred everywhere in space 13.8 billion years ago, and this is true when viewed from all the galaxies out there. But what if there were galaxies out there that weren’t moving at hundreds or thousands of kilometers-per-second relative to the rest frame of the cosmic microwave background, but were moving at hundreds of thousands of km/s, or very close to the speed of light?

One of the fastest known galaxies in the Universe, speeding through its cluster (and being stripped . [+] of its gas) at a few percent the speed of light: thousands of km/s. Image credit: NASA, ESA, Jean-Paul Kneib (Laboratoire d’Astrophysique de Marseille) et al.

Just as time passes differently for something moving close to the speed of light on Earth — a particle, a train or a person — if we had a planet, star or galaxy that was moving close to the speed of light, and had been for a long time, it would be significantly younger than the rest of the Universe!

Imagine the following scenario: back when the Universe was just a billion years old, a galaxy was — thanks to repeated gravitational interactions — accelerated to 99% the speed of light. For the 12.8 billion years that have passed for us since that time, only 1.8 billion years have passed for that lucky (or unlucky) galaxy. Compared to galaxies like our own, it will appear smaller, younger, bluer and “stunted” in its growth.

How galaxies appear different at different points in the Universe's history: smaller and bluer at . [+] earlier times. Image credit: NASA, ESA, P. van Dokkum (Yale University), S. Patel (Leiden University), and the 3D-HST Team.

So the Universe should appear the same for almost all observers anywhere, with the same amount of time having passed and the Universe having the same large-scale properties pretty much everywhere. But for a few select observers — the ones who’ve spent some significant time moving close to the speed of light relative to the CMB’s rest frame — the Universe will be quite bizarre. As soon as they slow down relative to the CMB and come to rest, they’ll find themselves as young ones in a strangely old Universe.

The fact that it’s been 13.8 billion years since the Big Bang is a fact that’s applicable to anyone and everyone within our observable Universe, but if you were (or are) close to the speed of light, you might be awfully reluctant to believe it!

## Origin of the universe

Creationist scientists demonstrate that the first law of thermodynamics and second law of thermodynamics argue against an eternal universe and they also demonstrate that these laws point to the universe being supernaturally created. [5] [6] [7]

### Equivocation

Equivocation is the use of word with multiple meanings, and then using a different meaning in the conclusion than in the premise.

For example: "The coach said we should eat light, so take your heavy coat off."

Atheists, using the fallacy of equivocation, attempt to obscure this matter (see: Atheism equivocation and the origin of the universe).

According to the Big Bang theory, the universe erupted into existence from a highly compact singularity [9] [10] approximately 13.7 billion years ago, and has been expanding ever since. This is the current scientific consensus and is agreed upon by the vast majority of the scientific community. [11]

Ancient Christian Biblical accounts disagree with contemporary science, and adherents to such are known as young Earth Creationists. Bishop James Ussher calculated the universe was created on October 23, 4004 BC. While this is not the only biblical chronology which has been developed, almost all chronologies give a creation date near 4000 BC [Citation Needed] .

This gives rise to the "starlight problem" for some Christians, although there is nothing inherently illogical about the creation of light in situ to inform humanity of the existence of objects farther away than 6000 light-years. Believers in relativity have constructed a number of models which explain the age of the universe as being affected by the time-warping effects of gravity as predicted by Einstein's General Theory of Relativity, so that the age of the universe as measured by a hypothetical observer at the edge of the universe might be 14 billion years, but as measured by an observer on Earth is only 6,000 years. [12]

A recent calculation placed the visible universe at about 156 billion light years across. [13] This creates a dilemma of faster than light movement, but it is speculated that the expansion of space itself can exceed the speed of light even if the objects within it moving on their own can not. [13] As an analogy, imagine ants (galaxies), that can't walk faster than 20 centimetres per second, sitting on an elastic cord. Normally two ants moving away from each other could not exceed a speed of 40 cm/s relative to each other (speed of light). However, if the cord is stretched while the ants are moving (expansion of space), the ants' speed relative to each other can be greater.

## How big is space? Interactive views of the universe in varying scales December 4, 2014 1:35 PM Subscribe

It's interesting to note that we have literally no idea how big the universe is. The observable universe is at least 93 billion light years across, but it is certainly much larger and quite possibly infinite.

One thing that I find mind-boggling about that fact is that since the upper bound is infinity, and we have no other universes as data points, we can't even assign probabilities to any ranges of size. Like, we can't say there's a 90% chance that it's smaller than X light years, for any finite value of X, or that it's larger than Y for any value of Y over the minimum. That melts my brain.
posted by justkevin at 2:12 PM on December 4, 2014 [3 favorites]

When the topic of a huge universe comes up, I like to point at my favorite personal project. I last updated it about 8 years ago, but I still love to revisit it from time to time:

I really should go back and do more with that site. Maybe update the look to be more modern, add some more comparisons, perhaps add Android intregration so people can compare themselves to the universe.
posted by HappyEngineer at 2:39 PM on December 4, 2014

haricotvert: "If I were traveling at the speed of light, the universe would have no size because wherever I "went" I would leave and arrive at exactly the same time which means no distance could have been covered."

Nope.
posted by signal at 5:06 PM on December 4, 2014

'Space. It seems to go on and on forever. Then you get to the end, and a monkey starts throwing barrels at you.'

Phillip Fry
posted by Hello, I'm David McGahan at 5:21 PM on December 4, 2014 [1 favorite]

haricotvert: Depends on what you mean by the size of the universe. Usually what people mean is the distance traveled by photons in the cosmic microwave background, which was emitted about 13.8 billion years ago (Gya) when the universe went from being a hot ionized plasma, like the surface of the sun, to an electrically neutral gas. So it's common to think of the universe as being 13.8 billion light-years (Gly) in radius. But the expansion of the universe has carried those objects away from us since then they're now about 45 Gly away from us, and being carried away by cosmic expansion faster than the speed of light. (I'll just admit that I have a little trouble keeping the proper terminology straight.) And furthermore because we can see that the microwave background is very uniform in temperature, we have to infer that any edge or boundary or significant change in the structure of the universe is much larger than the portion inside of our observable horizon trillions of light-years, most likely. That's just the radius. The volume of the universe that we can see is a very tiny fraction of the universe's size.

In fact everything farther than 10 Gly or 15 Gly is beyond our "communication horizon": because the expansion of the universe is accelerating, any signal which we send towards them (such as a Metafilter commenter traveling near the speed of light) will never actually arrive. To the extent that it makes sense to talk about a speed-of-light observer finding the location of the CMB horizon, it actually wouldn't be terribly deformed from the sphere that we see.

There are lots of other issues at play, too. Cosmology is complicated.
posted by fantabulous timewaster at 5:50 PM on December 4, 2014 [6 favorites]

If I were traveling at the speed of light, the universe would have no size because wherever I "went" I would leave and arrive at exactly the same time which means no distance could have been covered.

We speak of the size of the Universe in the space-time foliation in which the CMB is isotropic.

In words that are not designed to convince you I went to grad school, when we talk about the size of the visible Universe, we are talking about the size in the rest-frame in which the background radiation from the afterglow of the Big Bang (the Cosmic Microwave Background - CMB) doesn't have a direction that appears to be hotter because of an observer's relative motion towards it.

Functionally, this nearly the same as the Earth's rest frame. The Sun is moving relative to the CMB at 371 km/s, which is pretty damn fast, but only 0.001c, so the relative gamma factor (the time-dilation or length-contraction factor) is about 1.000001. So we have to do corrections for this, but it's not a big change.

We use this rest frame because this is effectively the rest frame of the Big Bang. I do lose sleep occasionally wondering how the Universe picked that frame, but it had to pick something, so probably no big mystery there. So it picked that particular frame, and everything in the Universe that wasn't accelerated to huge velocities somehow is moving relatively slowly relative to that frame.

In this frame, working out the evolution of the Universe over time (to calculate, for example, the age or size) is much more straightforward than any other frame, which is why we use it. That should make sense: this is the frame that the Universe is flat and isotropic, so there's no special direction, and things are approximately the same everywhere which makes evolving differential equations forward in time tractable. The flatness and isotropic nature of the Universe is a non-trivial fact, you could have built a Universe much like ours that was not. Given that our Universe happens to have these properties (see my posts here on inflation for why that might be), we can speak of the size and age of the Universe in the unique special frame that the Universe itself picked.

Someone moving at 99.999999999. % of the speed of light since the birth of the Universe would measure different lengths and ages relative to themselves, but they would also see a CMB massively blueshifted in one direction and redshifted in the other, and so they too could work out that there is a special reference frame and all these Universal properties in that frame, same as any other observer (like us). Then they'd better start wondering what the hell they did to get moving so fast relative to it.

For a photon, of course, time does not exist, and the age of the Universe is a meaningless statement. Of course, photons also don't have much of a personality, so asking them about the timelessness of time is not a useful exercise.
posted by physicsmatt at 5:59 PM on December 4, 2014 [8 favorites]

Thanks for those terrific explanations, physicsmatt and fantabulous time waster. Very much appreciated!

Do astronomers believe that the universe actually exists past the point where its expansion exceeds light speed? It sounds to me like there would be some kind of "event horizon" due to the cosmic expansion -- that objects would appear to us to move slower and slower due to their acceleration away until they hit light speed and just stopped. Is that true, and if so, wouldn't that really be the end of the universe for all practical purposes?
posted by haricotvert at 6:50 PM on December 4, 2014

Your question is very good, and the answer is complicated because not only are there multiple ideas that need to be conveyed, but there are different answers depending on what sort of Universe we happen to be living in.

Executive summary: in our Universe, there exists a cosmic event horizon, beyond which we can never see the light from events occurring "now," due to the expansion of the Universe.

Now let's get into it. When we do cosmology, we work in a narcissistic frame of reference where we, the people doing the calculation, live in the center of the coordinate frame, at rest. Everything else then is receding away from us. Now, we could, if we wanted, translate our results over to another point in space, in which case that point would be at rest and everything recedes away from them, including us at the original center point.

The usual analogy is living on the surface of an inflating balloon: everyone on the balloon sees themselves at rest and the remainder of the surface moving away from them. The true "center" of the balloon is in a coordinate orthogonal to the surface, just as the "center" of the Universe is orthogonal to our 3-D space (it's back in time). However, any observer on the balloon surface could call themselves the "center" of the 2-D surface and work from there, and so any observer in the Universe can call their location the center of the 3-D surface for mathematical simplicity. (This assumes they are in the CMB rest frame, otherwise the observer sees special directions, but we already went over that.)

OK, so we sit in the center of our coordinate frame, and look around us. Since there is a cosmic speed limit, information can only propagate at the speed of light (or slower), so we are not aware of what's going on "now" elsewhere in the Universe. (Again, everything I'm going to say here will be using a specific slicing of time relative to the rest frame of the CMB) We have to wait until the light reaches us. Of course, as the light moves towards us, the Universe stretches due to cosmic expansion, and so the light takes longer to reach us than you would have expected if you just took the initial distance between the origin of the light and us at time of emission and divided that length by the speed of light. The light will also be red-shifted as it travels.

This means that at any given moment, there is the particle horizon: the furthest distance away from us at any moment at which we can see events occurring. Obviously, as the Universe gets older, our particle horizon gets larger: we can see "more" of the Universe because we have more time for the light to reach us. The size of the particle horizon at any moment depends on how the Universe's size changed at every moment from the "start" to today. That is, it is related to the integral of the rate of expansion of the Universe. This is driven by the types of energy density in the Universe, which we measure by a combination of particle physics (calculating how radiation drives expansion compared to non-relativistic massive particles, for example) and direct measurements of how fast distant objects seem to be receding from us as a function of their apparent distance.

Now, if the Universe was built only of matter and radiation, the particle horizon grows to infinity. That is, if you wait an infinite amount of time, you can, in principle, see infinitely distant events. Matter and radiation have specific meanings here: matter density dilutes as cube of the length scale increase, because if you have a room with matter in it, and make each side of the room twice as long while keeping the total amount of stuff the same, you have 1/2^3 the density. Radiation goes like scale^4, since the energy of radiation is in the wavelength, and that redshifts as the Universe expands.

There's a way of picturing this, called a Penrose diagram. I started trying to explain those here, but it's really hard to do without a picture, and so maybe I'll have to take it off-site.

Anyway, the point is that in a Universe of only matter and radiation, you can if you are patient see whatever you want, just due to how the Universe expands. However, we don't live in such a Universe. Our Universe has dark energy. Now, we don't know what the hell this stuff "is" on a level that makes a particle physicist like me happy. We don't know even how exactly it dilutes as the Universe expands. It is consistent, however, with not diluting at all as you increase the size of the Universe. Which is pretty nuts if you think about it. But such things are possible. If dark energy has that precise property, it's a "cosmological constant" (it could also dilute a little as the Universe expands, or even increase in density a little as the Universe expands. We need to make more precise measurements of the expansion history to reduce the error bars.)

With a cosmological constant, the expansion rate of the Universe will keep increasing. Since a cosmological constant is constant, eventually it will be the only stuff around that is important in terms of how the Universe expands, regardless of how much matter or radiation you started with, or how small your cosmological constant value is. Today, the Universe is 68% dark energy, but earlier in time it was less dominated by this type of energy. In the future, the relative amount of dark energy will grow asymptotically to 100%. The energy density of dark energy (Lambda) remains constant though (again, assuming it's a perfect cosmological constant).

In such a Universe, there is an event horizon: a distance beyond which the light from events that occur will never reach you, no matter how long you wait. This horizon is small if the cosmological constant is big, and large if the constant is small (small Lambda means small rate of acceleration, so we should see further before the Universe's acceleration kicks in enough). So our event horizon goes like 1/Lambda.

So, in a Universe like the one we thought we lived in prior to 1998, you can see everything, assuming you're immortal, patient, and willing to build impossibly good telescopes that can see impossibly low energies. In the real Universe, the one with a small non-zero Lambda, that one you can't. We have a horizon, and beyond that we can have no idea of what's going on. Ever.

Now, just to bend brains a bit more before I leave, I will remind the observant reader of a few things. We're talking about an event horizon, which defines a boundary between what I can in principle see and communicate with and what I can't. Black holes also have event horizons. Hawking proved that black hole event horizons radiate. They have to radiate because black holes have entropy, and they have to have entropy because otherwise there's a way to violate the 2nd law of thermodynamics (throw a high entropy system into a black hole. If the black hole doesn't have entropy, viola, you have the perfect trash compactor for entropy. This would be bad for physics. ) Later, it was realized that black hole entropy means that all the information inside a volume can be painted somehow onto the 2D surface of the horizon around the volume. This makes very little sense from the perspective of quantum field theory, but appears to be true. Look up my posts here about the Holographic Principle.

Since our Universe has Lambda not equal to zero (such a Universe is called a 'de Sitter' universe), we too have a horizon. Every observer has an event horizon, but that horizon is different for each observer, just as every observer can see themselves as the center point from which everything expands away from. All these horizons also have entropy, and radiate. According the Holographic Principle, everything that is occurring or can occur or will occur in our visible Universe is somehow painted onto the 2D cosmological event horizon. Fun, isn't it?
posted by physicsmatt at 6:50 AM on December 5, 2014 [17 favorites]

I suppose one point that might help is to clarify when we say "expansion of the universe" we aren't meaning "movement of matter away from the "center" or origin point of the big bang" but that space itself is literally expanding, not just a uniform cosmic empty space where "the universe" (i.e. the matter/energy we think of as "stuff") expands into. That's one of the trickiest ideas to get your head around, though once you grok that it helps simplify a lot of stuff.

It sounds that haricotvert groks that, but figured I'd drop that in for people who are reading this who might not.

I mean I think my understanding is (mostly) right in that regards?
posted by symbioid at 8:44 AM on December 5, 2014

Well - we theorize it from an information theoretic principle, but I don't know if we can say we "know" in the same sense we know E=MC^2 or even that black holes evaporate.

Not that I don't love that idea. I think theoretically it's a fun idea to mess with, and I know we have those laser interferometers testing things regarding this, but I haven't followed up on the latest news on that.

(says someone who occassionaly reads books on this and again - would prefer if a real physicist chimed in).

Speaking of - physicsmatt, you say the current universe fits a "deSitter universe" description, but it sounds like the tecnical definition of a deSitter Universe is one that doesn't contain Mass/Energy (matter) and thus requires mostly empty space? The wiki article makes it sounds like early/pre big-bang universe was deSitter space, and that eventually via expansion, the . well the matter will be "diluted" enough such that the effects of space expansion will be the dominant force and thus a real deSitter space again, whereas we're not technically in one now due to the local and networked effects of mass on the fabrice of space time. Is that reading correct?
posted by symbioid at 11:11 AM on December 5, 2014

Well, there's no purpose to the universe of physics, but that's all just a model (or, more accurately, a whole bunch of models). An incredibly useful model, but it's not the way things "really are". It's a kind of net cast over reality through the expedient of measurement -- and again, there's no question this is an immensely practical way of proceeding -- but most people mistake the resultant model for the real thing, and wind up asking questions like "What's the purpose?" which make no sense in the context of the model. "What's the purpose?" is an infinitely regressive question in the context of a hypothetical world of discrete objects and forces interacting with each other causally in space and time, because whatever purpose you came up with, there would then have to be a purpose FOR the purpose, and so on. But that just means that if you want to know why you're here, physics (or any kind of materialism) is the wrong model -- not that there's no purpose or that the universe actually is material.

That said, it is indeed liberating to realize that the physical model admits of no purpose as we habitually think of purposes. Definitely takes the pressure off! Then you can sit back and enjoy the stars.
posted by haricotvert at 12:46 PM on December 5, 2014 [1 favorite]

symboid, oops yes, you are correct. Right now we're not a perfect de Sitter because there's still matter and radiation density around. Asymptotically, we will approach perfect de Sitterness in the far future (modulo quantum fluctuations and other mysteries of the Universe we don't understand today). I got a bit sloppy and called our present Universe "de Sitter" since that's often how I refer to it in day-to-day work (since we're usually referring to asymptotic properties at that point). A certain laziness of language is surprisingly common in my line of work (figuring out when you can be lazy and when you can't is part of the grad school process).

Usually I remember to de-lazify when writing these things up here, or at least sneak it by you all with razzle-dazzle when I don't. Damn you for noticing (puts symboid on The List).
posted by physicsmatt at 4:15 PM on December 5, 2014 [1 favorite]

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## Age of universe

Basically, we can set an overall reference frame by using the temperature of the CMB. An observer anywhere in our universe, no matter their reference frame, can look at the CMB and measure its temperature (provided they have the right instrument).

We can define a global reference frame by the following two criteria:
1. An observer in the global reference frame sees a CMB which is has the same average temperature in every direction (that is, it has no dipole). This means that the observer is at rest with respect to the CMB.
2. At a given time t, the every observer sees the same temperature of the CMB. That is to say, we can define a global "now" by saying that all observers "now" see the same temperature of the CMB that we see (2.725K). These observers will see the total time passed since the big bang as being the same, so we can use the same time coordinate.

This is perhaps a bit technical. But the upshot is that the fact that our universe is, on average, the same in every location and in every direction means that there is a convenient choice of reference frame. With this convenient choice, we can talk about things like the age of the universe in a sensible way, in a way that observers on far-away galaxies will agree with.

## The Future

We are currently at the end of the first year.

 Length of Day increases by 1 second 1 January at 00:01:45 Constellations no longer recognisable 1 January at 00:03:30 East Africa splits off after Great Rift Valley flooded 1 January at 05:50 Mediterranean Sea closesGregorian Calendar has Northern Hemisphere Summer in late Deccember 2 January at 04:12 The Sun (and Earth) will have completed an orbit around the Galactic centre 6 January The Moon will be too far from the Earth to cause a Total Eclipse of the Sun 14 January Because of increase in Sun's luminosity, plate tectonics slows and stops This lowers atmospheric carbon dioxide to the point where photosynthesis stops Most higher plants die 14 January Atmospheric carbon dioxide falls to a level that kills all multi-cellular life 19 January The Sun's luminosity increases by 10% A wet green house effect causes the evaporation of the Earth's oceans 24 January All non-bacteriological life extinct 1 February Earth's liquid core solidifies shutting down the magnetic field 25 February Earth's surface temperature reaches 147 degrees killing all life 9 March The Moon's distance from the Earth has increased to the point where the Earth's axial tilt becomes chaotic 14 March Earth's surface conditions comparable to Venus now 26 March Andromeda Galaxy collides with our Galaxy - no effect on the Earth 7 April Sun begins to expand into a Red Giant star becoming hundreds of times more luminous 11 May Sun reaches its maximum size as a Red Giant and swallows the Earth 11 July Sun becomes a tiny White Dwarf star after shedding much of its mass 13 July Sun cools to the point where it is no longer emitting light 16 December The expansion of the Universe places all galaxies outside the Local Group beyond observation 6 years 7 months The 47 galaxies of the Local Group coalesce into one large galaxy 30 years Star formation ends as galactic gas depleted 650 years All stars are non-energy producing remnants 8000 years The Sun will have cooled to 5 degrees above Absolute Zero 65000 years

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## Lecture 2: Origins of Modern Science, Astronomy, and Astrobiology

Ancient Greek (i.e. Aristotelian) philosophy asserts that: The Earth is fixed and unmoving at the center of the Universe The laws on Earth are different than those in the Heavens Copernicus advocates heliocentric model, and begins the "Copernican Revolution" Kepler uses Tycho's data to refine model Galileo shows the Earth is not the center of the solar system Newton demonstrates that the very same laws of physics govern the Earth and Heavens. Physical estimates of the age of Earth indicate that it is much older than our records of human civilization Estimates of the scale of the Universe indicate it is very large By the mid-20th century, the key pieces of knowledge are in place for the development of astrobiology Technological advances turn philosophy into science.

Stars are pinpoints of light that appear to move from East to West. The Sun is a bright disk

1/2 degree across that moves East to West, but in one year moves relative 360 degrees relative to the stars (from West to East). The Moon is a pale disk

1/2 degree across that moves East to West, but in one month moves relative 360 degrees relative to the stars (from West to East), and has phases.

The Geocentric System Geocentric = Earth-Centered Anaximander of Miletus (611-546 BC) The first Greek philosopher to suggest a geocentric system: Earth was a flat disk (cylinder) fixed and unmoving at the center. Sun, Moon & Stars were affixed to rotating crystalline spheres centered on the Earth. Sun, Moon & Stars were physical objects.

Aristotle (384-322 BC) Pupil of Plato, tutor of Alexander. His On the Heavens refined previous systems 55 crystalline spheres within spheres Incorporated physical reasoning: Earth fixed and unmoving at the center as it was too big to move, including rotation. All spheres were in uniform circular motion.

The Aristotelian System makes certain basic assumptions: The Earth is a sphere, fixed & unmoving at the center of the Universe. Natural state of motion on Earth is rest. The natural state of the heavens is unceasing uniform circular motion. A rotating or revolving Earth is "unnatural".

The Aristotelian system makes a distinction between the heavens versus the Earth Heavens: Perfection Uniform circular motion Constant motion The Earth: Center of the Universe Sphere, fixed & unmoving Natural state of motion on Earth is rest.

The "rules" of the Earth do no apply to the heavens.
A basic assumption that affects all subsequent ideas.

The problem of the planets

Planets: (Greek: planetai = wanderers) Objects that move relative to the "fixed" stars. Stay within a few degrees of the Ecliptic. In general, the planets move eastward relative to the "fixed" stars. Sometimes, however, the planets appear to Slow down, stop, start moving westward, or RETROGRADE, stop again, and then resume moving eastward. Very hard to understand in the simple geocentric uniform motion picture.

Elaborated on a system of 'epicycles,' creating a geocentric model that explained retrograde motion Epicyclic models have a number of successes: Reproduces the retrograde motion of planets.

The Ultimate Geocentric System Ptolemy's final system was quite complex: 40 epicycles & deferents required. It provided accurate predictions of the motions of the planets, Sun, and Moon. It was to prevail virtually unchallenged for nearly 1500 years. Was rooted and associated with fundamentally Aristotelian ideas Essentially precludes even the notion of life elsewhere.

Sun at the center. Earth rotates about its axis Earth revolves about the Sun. + Explains retrograde motion naturally. - Didn't work much better, although it was more elegant. - No observational evidence (no parallaxes!)

Scientific Objections to Copernican Model No observational evidence of orbital motion: Parallax As Earth orbits around the Sun, it moves 2 AU from one side to another in 6 months. A nearby star would appear to shift position with respect to more distant stars. The apparent shift is the "stellar parallax" Parallax was not observed in Copernicus' time, suggest that the Earth does not move.

Brilliant German Mathematician Staunch Copernican Convinced the Universe was governed by physical laws. Obsessed with finding harmony in the heavens. Had a genius for data analysis Inherited Tycho's data Mars was the key to unlocking the secrets of planetary motion. Kepler began analyzing Tycho's data on the orbit of Mars. Last data point did not fit by 8 arcminutes Kepler listened to the data: Knew Tycho's data were accurate to 1-2 arcminutes. Kepler questioned his assumptions: Forced to abandon uniform circular motion. Concluded Mars' orbit was not a circle, but instead an ellipse with the Sun at one focus.

Italian contemporary of Kepler: Gifted mathematician Brilliant observer & experimenter Preferred experimentation and measurement to philosophical rhetoric. Staunch anti-Aristotelian Often at odds with the scholarly establishment Built a telescope and observed the sky Observed: Sunspots,mountains on the moon, -> showed that the heavens were not perfect phases of Venus -> showed that Venus orbits the Sun moons of Jupiter -> showed that there were other centers of motion other than the Earth

Newton Unified all motions into three simple laws. Replaced older, empirical or philosophical descriptions with quantifiable, physical explanations of the nature of the World. Explained the motion of all objects with the same set of self-consistent rules. Developed the law of Universal Gravitation which governs all things Demonstrated that the physical laws which govern motion are the same everywhere

The Copernican Revolution Completed We do not occupy a special or privileged place in the Universe. The Universe and everything in it can be understood and predicted using a set of laws ("rules"). The entire Universe obeys the same rules.

How Old is the Earth? James Ussher (1581-1656) Protestant Archbishop of Armagh Classical & biblical scholar Sought a critical chronology of human history, including the date of the Creation. Annals of the World (1658): Sunday, October 23, 4004 BC First Sunday after the Autumnal Equinox in 4004 BC (Julian Calendar).

All of the estimates from Ussher and before are based upon the same central assumption: Human history can be equated with the physical history of the Earth. Not surprising given the vestigial Aristotelian philosophy.

After the Copernican revolution, physical estimates of the Earth's age were sought. Example: Charles Darwin Theory of Natural Selection Slow changes in species over time Takes a long time for profound changes Concluded that the Earth probably had to be more than 500 million years old

Radioactive Dating of the Earth Oldest surface rocks known are 4.3 Gyr old The best estimate of the age of the Earth: 4.5 billion years Age of the Universe 14 billion years Civilization: less than 10,000 years

How big is the Universe? The Parallax View Stars are more distant than people thought All stellar parallaxes are less than 1 arcsecond Cannot measure parallaxes with naked eye. First observed in 1837 by Friedrich Wilhelm Bessel for the star 61 Cygni. Used a telescope Measured a parallax of 0.3-arcsec Means its distance is

630,000 times the distance to the Sun!

By the early 1900s, there were two lines of thought about the "Scale of the Universe" How big is the Milky Way? How distant are the Spiral Nebulae? Island Universe Hypothesis: Spiral Nebulae are much more distant than the "edge" of our Galaxy, and so very large (as big as our Galaxy). Nebular Hypothesis: The Spiral Nebulae are nearby, thus inside our Galaxy and and thus smaller than it.

Debate was ended in 1923 by Edwin Hubble Used the new 100 inch telescope on Mt. Wilson Found variable stars that he used to estimate the distance to Andromeda Nebula Found it was much further away than the size of the Milky Way, and thus was not in the Galaxy Also found that it was the same size as the Milky Way

The Birth of Astrobiology By the middle of the 20th Century, the key pieces of knowledge were in place We do not occupy a special or privileged place in the Universe. The Universe and everything in it can be understood and predicted using a set of laws ("rules"). The entire Universe obeys the same rules. The Universe is big! The Universe it old (but we are young)!

All that was required to turn astrobiology from philosophy to science was the development of technology.

See A Note about Graphics to learn why the graphics shown in the lectures are generally not reproduced with these notes.

## Lecture 19: Special and General Relativity

Result was a set of laws formulated from the perspective of an absolute "God's Eye View" of the Universe.

## Einstein's Challenge

• We cannot take a "God's eye view" of the Universe.
• We can only compare our view with that of other observers.
• All information we have is carried by light.
• But, light moves at a finite speed .

Result is an irreducible relativity of our physical perspective.

## Seeing the world

All information about the Universe is carried by light.

Speed of Light : c = 300,000 km/sec

• 65 mph = 0.028 km/sec = 9.3x10 -8 c
• light travel time in the lecture hall (front-to-back) =

Our everyday experience of the world is with phenomena at speeds much slower than the speed of light.

## 1st Postulate of Special Relativity

The laws of physics are the same for all uniformly moving observers.

"Uniformly" = "with a constant velocity "

• No such thing as "absolute rest".
• Any uniformly moving observer can consider themselves to be "at rest".

## 2nd Postulate of Special Relativity

The speed of light in a vacuum is the same for all observers, regardless of their motion relative to the source.

• The speed of light is a Universal Constant .
• We cannot send or receive information faster than the speed of light.

This has been experimentally verified in all cases.

## Essential Relativity

• Both measure the same speed of light
• Both find the same physical laws relating distance, time, mass, etc.
• But, both measure different distances, times, masses, etc. applying those laws.

The key is the role of light .

## The Relativity of Time: A Thought Experiment

Consider a simple photon clock:

• Laser fires to a mirror 1.5 meters away
• Light bounces to a detector
• Photon Path Length = 3 meters
• One "Tick" = Time of Flight = 3 meters / c = 10 -8 seconds

### Relativity with Dick & Jane

• Constant Relative Speed = 0.8 c
• Jane is carrying a photon clock
• Each measures how long it takes between "ticks" of Jane's photon clock.

### He Said, She Said.

• Jane's Speed = 0
• Dick's Speed = 0.8c
• Photon Speed = c
• Path Length = 3 m
• 1 Tick = 10 -8 sec
• Jane says: "My Clock Runs OK"
• Jane's Speed = 0.8c
• Dick's Speed = 0
• Photon Speed = c
• Path Length = 5 m
• 1 Tick = 1.67x10 -8 sec
• Dick says: "Jane's Clock is running slower ."

## Relative Time

Our result is true for all clocks.

• Times passes at different rates for observers moving relative to each other.
• At speeds small compared to c, the difference is very small.

Verified experimentally using atomic clocks on airplanes and satellites.

## Consequences of Relativity

• Do not measure the same times kept by clocks.
• Disagree on what events occur simultaneously.
• Do not measure the same lengths of objects.
• Do not measure the same masses for objects.

## Spacetime

• Space & Time are relative .
• United by light into Spacetime .
• Only spacetime has an absolute reality independent of the observer.

## Light the Unifier

• All uniformly moving observers see the same physical laws.
• All observers measure the same speed of light.

Special Relativity is restricted to uniformly moving ( unaccelerated ) observers.

But, objects are accelerated by gravity. (Newton: "They feel a gravitational force .")

Einstein took 8 years to generalize relativity.

This was to lead to a completely new theory of gravity.

## Newtonian Gravity

• Matter tells gravitation how to exert a Force .
• A Force tells matter how to accelerate .

A mass m is accelerated by another mass M:

## Einstein's Discontents

The force law (line 1) implies instantaneous knowledge of the distance, R, but information is only transmitted at the speed of light .

## The Principle of Equivalence

There is no distinction between gravitational and inertial accelerations.

## General Relativity

Gravitation binds matter to matter.

But how does matter "know" that the other matter is "out there"?

• Special Relativity used light to unify space & time into spacetime, but left matter separate.
• Need to unite matter & gravity with spacetime.

## Enter Geometry

Newton's laws lead to a geometric description of motion:

Use geometry to describe the paths of objects moving through space.

Need to describe the geometry of spacetime .

## The Shortest Path.

• The shortest path between two points is a straight line .
• Parallel lines stay parallel always.
• The shortest path is a curved line .
• Lines that start parallel can converge or diverge at some distance away.

## Curved Spacetime

• The least paths are curved lines.
• More mass = Greater spacetime curvature.
• Closer = Greater spacetime curvature.

A freely falling object follows a curved path.

## A New Theory of Gravity

Replaces the Newtonian idea of a "force" with the curvature of spacetime.

GR has so far withstood all experimental tests.

## The Precessing Orbit of Mercury

Mercury's orbit major axis precesses slowly by

### Einstein 1, Newton 0

• Spacetime curvature changes as Mercury gets closer to the sun on its orbit.
• Gives the orbit a little twist.
• This adds an extra 43 arcsec/century!!

## Bending of Starlight

Light travels on the shortest path through spacetime.

Data are from the 1922 Total Solar Eclipse.

Another Prediction: Gravitational Lenses (1980s)

## The Binary Pulsar

1975 : Hulse & Taylor discover a binary pulsar

• Accelerating masses emit Gravity Waves.
• Loss of energy from Gravity Waves should make the pulsars orbit closer.

Hulse & Taylor won the 1994 Nobel Prize for this discovery.

Newton's laws are approximations of GR.

#### Notes:

If you do not make this correction and instead measure the precession relative to the equinox, you get the values quoted in some books, namely 5600.73 arcsec/century observed, and 5557.62 arcsec/century predicted by Newtonian gravity. However, of the predicted 5557.62 arcsec/century, only

523 arcsec/century is actually due to the combined gravitational tugs of the other planets on Mercury the rest is due entirely to the poor choice of reference frame. The 43 arcsec/century discrepancy between observations and the Newtonian prediction, of course, remains unchanged.

## Is the age of the universe relative to an observer's location in that universe? - Astronomy

My bright teenage son, after considerable calculation, has concluded that the universe is approximately 162 sextillion miles wide. He based his calculation on the basic 186K mi/sec speed of light x the estimated 13.8 billion year age of the universe. When I pointed out that 13.8 billion years of expansion is not the same as 13.8 billion LIGHT years of expansion, he asserted that I was in fundamental error on that point. I don't mind being in error, but do mind that one of us, now, has clearly gone astray in his basic understanding. If it is me, please set me straight!

From the current rate of expansion of the Universe, astronomers infer that the age of the observable Universe is about 13.8 billion years. In other words, if we assume that the Universe has been expanding at a constant rate since the Big Bang, then the rate of expansion tells us how far back in time the expansion started, which we take to be the beginning of the Universe. If the Universe is 13.8 billion years old, then light has had 13.8 billion years to propagate, and so the statements "13.8 billion years old" and "13.8 billion light years apart" are completely equivalent.

The catch is going from light-years to miles. In the local Universe, we know the conversion, since for all intents and purposes we live in a locally flat, spatially "euclidean" Universe ("euclidean" just means that the three angles of a triangle on a surface add to 180 degrees this is true for a sheet of paper (which is flat), but not on the surface of a sphere or a saddle (which are both curved)). However, when we look at large distances we have to take the 4-dimensional curvature of the Universe into account. In essence, your son has calculated an accurate "radius" for the observable Universe provided that the Universe is flat (a sort of 4-dimensional sheet in spacetime in which light travels in straight lines), and that the rate of expansion of the Universe has remained constant.

Today, we think that half of your son's assumptions are right. Observations indicate that the Universe is either flat, or so big that the curvature is negligible. However, there is recent evidence that the rate of expansion of the Universe is increasing with time that is, galaxies are moving away from each other *faster* today than they were in the past. This means that the observable Universe is *more* than 13.8 billion years old. It also means that the energy density of the Universe at present is dominated by "dark energy", a substance with "negative mass" that pushes the Universe apart rather than pulling it together like regular matter does (sound like science fiction? It still is, for the most part, since scientists don't yet have any idea what dark energy is. ). The presence of dark energy also affects the curvature of the Universe in the past, which then throws off the conversion from light-years to miles. This is perhaps the best reason why cosmologists avoid using actual distances altogether, unless they are trying to figure out precisely what that conversion factor is.

After 13.8 billion years of expansion, is the universe 13.8 or 27.2 billion years "wide". My son asserts that because the expansion is one of space rather than matter, its total dimension = its time of expansion. This logic escapes me. If is is "expanding," surely it is doing so in all directions at once, thus yielding, to my (admittedly fallible) logic the necessity of its "furthest limits" moving diametrically away from each other. I.e., being two years separated in one year's expansion. Am I confusing time and distance here?

Note that in the above paragraphs I have been careful to use the term "observable Universe" rather than Universe. The Universe itself, or the maximum amount of space that we will eventually be able to see given an infinite amount of time, may well be infinite. In quoting a size of the Universe we infer how far we can see in one direction (13.8 billion light years), and how far we can see in the other direction (13.8 billion light years) and add the two to get a size (27.2 billion light years). An age of 13.8 billion light years in each direction therefore leads us to infer that we are at the centre of a sphere with radius 13.8 billion light-years, and hence that the Universe is 27.2 billion light-years "across". The trick, however, is that because the Universe is homogeneous and isotropic, every observer must measure a size of the Universe that is 27.2 billion light years. even ones that are at the "edge" of our observable Universe! This means that either the Universe is sufficiently curved that space doubles back on itself (like on the surface of a sphere), or that the actual Universe is much larger than the observable one. We currently think that the latter possibility is the case.