Ep. 79: How Big is the Universe?

[Fraser]

We’re ready to complete our trilogy of discovery about the universe. We’ve learned that it has no center; rather everywhere is its center and nowhere. We discovered that the universe seems to be flat. It not open, it is not closed, it is flat. If that doesn’t make any sense, you need to listen to the previous show because there’s no way I could give that an explanation. So now we want to know: “How big is it?” Does it go on forever or is it finite in scale? How much of it can we see?

More...

[damian1727]

cool cant wait to listen to this show

[SingleDad]

ok I'm over thinking,and haven't finished the show yet, but... why aren't the photons that where fired 13bil light-year, and traveled 78 bil light-years to get here... didn't it go past the speed of light to get here... ouch! stop it hurts!! =p

[SingleDad]

ok guys question from Megan. Could the CMBR be the out edge of like a bubble, and beyond that is nothing void?

[damian1727]

the cmbr is the heat left over from the BB .. its everywhere...

beyond our horizon is like where they used to draw dragons on old maps

ie we dont know but for sure there is alot more of what we see around us and a lot else besides....and as you know void can cause all sorts of problems ! lol

[Steve Limpus]

ok guys question from Megan. Could the CMBR be the out edge of like a bubble, and beyond that is nothing void?

Hi Megan

Good question. One of the big problems I think, is that if the CMBR was the edge of the universe (instead of just the limit we can see because of the age of the universe and the speed of light), we would have to infer Earth is at the centre of that universe. The Cosmological Principle (and the Copernican Principle) argue that we should not consider Earth to occupy a special place in the Universe (however special Earth is to us!).

Every time in history that people thought we were the centre of the Universe, it turned out they were wrong!

I loved this show by the way!

"Space is big. You just won't believe how vastly, hugely, mind- bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space."
Douglas Adams, The Hitchhiker's Guide to the Galaxy

[Steve Limpus]

ok I'm over thinking,and haven't finished the show yet, but... why aren't the photons that where fired 13bil light-year, and traveled 78 bil light-years to get here... didn't it go past the speed of light to get here... ouch! stop it hurts!! =p

This is how I understand it:

The photon has travelled 13.7 billion lightyears to get here, but the place the photon started from has since been carried away by the expanding universe, and is now 78 billion lightyears away.

It also means when the photon started out, that place was a lot closer than 13.7 billion lightyears to this place - that original distance has expanded to 13.7 billion lightyears in the meanwhile. (And, of course, the Earth wasn't even here then, just some hydrogen gas floating about that would eventually become the Milky Way, Earth, people... just in time for that photon to hit WMAP. Weird huh?)

[Guustaaf]

Towards the end of this episode you guys talk about the observable universe, and it being 1/100th cubed. Should this not be one millionth instead of one ten thousandth?

Thanks,
Guustaaf

[themank]

So, a question for a future episode of Astronomy Cast. It's been rattling around for a while but episode 79 served as a good motivator for me to ask it...

Considering how little we can actually measure and study of the universe, apparently our best guess seems to be the cube root of very little, how can we make such remarkably intricate theories about the first few slivers of a nanosecond after the Big Bang? On one hand it sure seems like a lot of recent evidence suggests we may have mistaken the elephant's leg for a tree.

I mean, remarkable details of Big Bang theory seem pretty widely accepted, such as the temperature at each instant, the primitive particle and force interactions, etc, and then, almost as an afterthought as we review our notes, we stumble on inflation, dark matter and dark energy?

I get the feeling it's as if, in the dark, we've accidentally walked into the closet rather than the house, then lit a candle and crafted an entire theory of residential construction based on an exhaustive examination of the clothes rod.

I love the podcast. Thanks for all the hard work. It's an exciting and amazing time to be paying attention to cosmology, eh? (but, then, when isn't?)

[Steve Limpus]

I mean, remarkable details of Big Bang theory seem pretty widely accepted, such as the temperature at each instant, the primitive particle and force interactions, etc, and then, almost as an afterthought as we review our notes, we stumble on inflation, dark matter and dark energy?

I just hope we're all around for the next Newton or Einstein... and I hope our world hasn't become too greedy, and too venal, and too shallow, for minds such as theirs. I'm sure it is a very beautiful tree...

But I like elephants too.

[clint]

Towards the end of this episode you guys talk about the observable universe, and it being 1/100th cubed. Should this not be one millionth instead of one ten thousandth?

I was wondering the same thing when I listened to this part of the show:
100 squared = 10.000
100 cubed = 1.000.000

[Fraser]

Yes, we definitely made a math error there.

[mtaylor]

I am new the the Astromony Cast forum, so let me first add to the chorus that the podcast is absolutely terrific. I look forward to each week's "episode" for the commute.

I have a question about the metaphor that everyone uses concerning the expanding universe -- that we are on the surface of the balloon.

So suppose I am on the surface and I take out my ruler and measure an object one foot away. To test this, I nail (OK tape, its a balloon after all) the ruler at point A and at point B. One foot. The balloon expands. Next time I look -- its still one foot. The balloon expanded, but so did the ruler. Relative to my world, on the surface of the balloon, the measurement did not change.

I think in the last episode Dr. Gay said that gravity and chemistry keep mass together while the universe expands around things. This is difficult to understand. It seems to be saying that "mass" exists independent of "space." That one can add "space" without making the mass any bigger.

Can someone explain this to a dense non-science type such as myself.

[Steve Limpus]

Hi MTaylor,

Welcome to the forum.

Some people add to the balloon analogy.

Imagine you have attached coins to the balloon - as the balloon expands, the distance between the coins stretches, but the coins remain the same size. The coins are analogous to galaxies, or more accurately clusters of galaxies.

The universe expands, but only on the largest scales where expansion overwhelms gravity, electromagnetism and the nuclear forces that binds us, earth, and galaxies together.

It's said that if you clipped a very (very!) long tape measure to a distant galaxy, waited a while then wound it back in, your tape measure would be longer when you were done.

Nature hasn't provided long tape measures, but it has provided light, and light is observed to stretch between distant galaxies (red-shift).

[mtaylor]

Thanks Steve, but I am still confused.

Granted if one attached an object to the balloon, it would not expand while the balloon did. But if I understand the metaphor, the surface of the balloon is the two-dimensional substitute for the 3 dimensional world in which we live. We are to suppose that we are two dimensional beings living "in" the surface, not "on" it. There is nothing "outside" or "on" the surface of the balloon, unless it is a 4th or 5th dimensional object.

Sorry if this is taking a metaphor to far, but its always bothered me.

[mtaylor]

Sorry, had another thought. What if its not space that getting bigger, but time getting slower. You never hear about time. Suppose that the farther you get away from here, the slower time is. That would explain the appearance that the universe was expanding and red shifting -- wouldn't it?

[Steve Limpus]

Thanks Steve, but I am still confused.

Granted if one attached an object to the balloon, it would not expand while the balloon did. But if I understand the metaphor, the surface of the balloon is the two-dimensional substitute for the 3 dimensional world in which we live. We are to suppose that we are two dimensional beings living "in" the surface, not "on" it. There is nothing "outside" or "on" the surface of the balloon, unless it is a 4th or 5th dimensional object.

Sorry if this is taking a metaphor to far, but its always bothered me.

lol... that is a metaphor too far. You'll need to pretend the coins and the surface of the balloon are in the same dimension, while not forgetting we have 'subtracted' a dimension from our 3d reality (which you obviously have a good handle on from the rest of your post).

You'll probably come across another common analogy that places ants on the 2d surface - same thing applies, the idea is to imagine the ants exist in the same dimension, not the next higher dimension they occupy in reality.

Invasion of the Fifth Dimension Ants!

You don't happen to have Spielbergs number?

[Steve Limpus]

Sorry, had another thought. What if its not space that getting bigger, but time getting slower. You never hear about time. Suppose that the farther you get away from here, the slower time is. That would explain the appearance that the universe was expanding and red shifting -- wouldn't it?

That's a great point. Time is the 4th dimension of spacetime of course, and the metaphors so far have not included time.

I'm fairly sure time 'slowing down' would not have the effect you describe, I'm not even sure it can (slow down that is, aside from relativistic effects which I think are quite a different beast).

I usually try to imagine 4d spacetime as a 3d loaf (one dimension subtracted again) - time being 'slices' of the loaf. Relativity means you can slice the loaf at different angles, so that different angled slices will include different events. The slices are always ordered from back to front (past to future - the arrow of time) due to increasing entropy (or disorder) in the universe. Then my brain melts.

Other than that, someone else might be able to help. Or you could post your question at Q&A, some of the folks over there are pretty damn smart. It's a great question, you're bound to get some great replies.

http://www.bautforum.com/questions-answers/

[mtaylor]

Thanks again. BTW. I read this explantion for the time dimension: time is the distance from the center of the balloon to the surface. I find this a useful metaphor because there is no "direction" as such to time, but for the ants on the surface, it always pushes outward.

[Vanamonde]

I do not believe the time was that dimension inside the balloon analogy - it was a fourth spatial dimension. I just listened to the followup Q & A show and that reinforces this view.

The current thinking is there is probably 11 or more dimensions to the universe(s). But for the discussion on the shape and size of this universe, I think we can stick with three we experience, at least extra spatial dimension for the curvature of space in a way we cannot perceive and then one for time.

And, yes, this trilogy on the shape, size, and center of the universe is one of my favorites. I am almost done with the current Astronomy Cast! It is sooooo kwel - one of the best finds on the Net that I have heard in years!

I promise to donate right after I recover from the bill I have to pay to the warlords on April 15th.

[cosmoboy]

If I did the arithmetic correctly if one uses the 71 km/MPs number agreed upon, one can work out that the universe at 13.7 billion light years is expanding away from us so fast that any EM emissions emitted at that distance would be red shifted to DC from our viewpoint.

It just so happens that the age of the universe is agreed to be 13.7 billion years. Is this an interesting coincidence or is it that these numbers are derived from one another in some non-obvious way. (According to the material I read, the two numbers seemed to be derived independently.)

If this is correct, Wouldn't all the high frequency light emitted from a sphere just shy of 13.7 B light years from us be red shifted to something like the Cosmic Background radiation?

[Steve Limpus]

The photon has travelled 13.7 billion lightyears to get here, but the place the photon started from has since been carried away by the expanding universe, and is now 78 billion lightyears away.

Since this post I have been reading some more - and these figures are incorrect (the figure of 78 billion light years that is). This figure was widely reported in popsci literature but was a misunderstading of a paper by Neil Cornish et al.

It is more accurate to say that the the CMBR was emitted some 13.7 billion years ago (about 380,000 years after the Big Bang). The surface of last scattering was at that time roughly 40 million light years away (from the particles that would become the Milky Way and Earth). The photons travelled about 13.7 billion light years to reach earth. The surface of last scattering (where the CMBR was emitted) is now roughly 46 billion light years away. (Not 78 billion.)

78 billion light years was actually the lower bound established, by examination of the CMBR, for the fundamental domain of the universe, or in other words the minimum size of a multiply connected manifold such as the 3-torus or hyper-dodecahedron mentioned by Pamela and Fraser. You could think of it as like a minimum diameter of the universe, if it is small enough that we are able to see 'around' it to the back of our own heads (albeit our own heads a long time ago). The researchers were looking for matching circle pairs in the patterns of the CMBR.

This figure was mis-reported in popular press as the radius of the universe. This article is typical:

http://www.cnn.com/2004/TECH/space/0...ide/index.html

Interestingly, researchers are having another go with a more refined search that will rule out a universe smaller than about 86 billion light years or so if they don't find the patterns they are looking for. When you consider that the diameter of the observable universe is about 92 billion light years - it is looking less and less likely that we live in a multiply connected universe smaller than the observable universe.

That might make it difficult for us to ever work out the shape of the universe (but that's just my opinion).

[Steve Limpus]

If I did the arithmetic correctly if one uses the 71 km/MPs number agreed upon, one can work out that the universe at 13.7 billion light years is expanding away from us so fast that any EM emissions emitted at that distance would be red shifted to DC from our viewpoint.

It just so happens that the age of the universe is agreed to be 13.7 billion years. Is this an interesting coincidence or is it that these numbers are derived from one another in some non-obvious way. (According to the material I read, the two numbers seemed to be derived independently.)

The redshift of the CMBR is something like z=1100, which apparently means the size of the observable universe is quite close to the hubble horizon, just co-incidentally I think. Some one might be able to elaborate.

If this is correct, Wouldn't all the high frequency light emitted from a sphere just shy of 13.7 B light years from us be red shifted to something like the Cosmic Background radiation?

I may have mis-understood you here, but it sounds like you have just described the CMBR.

Welcome to the forum by the way.

[dcl]

I've decided to enter this discussion and have reviewed its history. There seems to be no clear convergence toward a concensus, so I'm offering my own view in the hope that it will become a nucleus around which a concensus can coagulate. On March 28, 2008, I started a thread entitled "The Shape of the Universe", in which I summarized my finding, derived from extensive reading and study, that the universe appears to have the basic shape of an expanding four-dimensional hypersphere the contents of which are embedded in its three-dimensional "surface". That description appears at the beginning of the thread entitled "The Shape of the Universe". The following is based on that description.

The oldest feature of the universe that we can observe is the Cosmological Microwave Background Radiation (CMBR). According to the most recent published findings from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite, the universe came into existence 13.7 billion years ago. The CMBR is believed to have been emitted 380,000 years later when the hot primordial plasma had cooled enough so that protons and electrons could combine into stable hydrogen atoms, the resulting radiation being the CMBR. What we see now comprises what is referred to as "the known universe". It appears to have a radius of 13.7 billion light years. However, the structures that emitted the light by which we see them now have been continuing to recede from us during the past 13.7 billion years, so the known universe now has a radius much larger than 13.7 billion light yearsmuch. A simple calculation based on the measured recesson velocity of the CMBR and 13.,7 billion years yields 78 billion years as the current radius of the known universe.

But the CMBR does not mark the outer boundary of the universe. To see how the CMBR fits into the complete picture of the universe, including how it changes over time, it is useful to examine the picture of the universe described in my Forum thread entitled "The Shape of the Universe". There, the universe is described as the three-dimensional "surface" of a four-dimensional hypersphere. We live at a point in that "surface", and the CMBR that we see occupies an expanding two-dimensional spherical surface embedded in that "surface" with us in its center. People elsewhere in the universe see their own CMBRs as expanding spherical shells with themselves at their centers.

We have no way of knowing how large spherical shells representing the CMBRs are compared to the "surface" of the hypersphere. WMAP has been unable thus far to detect any curvature in the "surface" of the hypersphere. Some people have erroneously taken to indicate that the "surface" is precisely flat and that the universe is infinite in extent. That conclusion cannot be correct since expansion at a finite rate over a finite time results in a finite number, not an infinite one. However, it is probably safe to conclude that the volume of each of the above-described spheres representing local CMBRs on the "surface" of the hypersphere are much smaller than the volume enclosed within the "surface" of the hypersphere.

The above picture may be difficult to visualize. If you don't succeed at first, keep on trying. Or ask me for help.

[Vanamonde]

On March 28, 2008, I started a thread entitled "The Shape of the Universe", in which I summarized my finding, derived from extensive reading and study, that the universe appears to have the basic shape of an expanding four-dimensional hypersphere the contents of which are embedded in its three-dimensional "surface".

Old news. The latest is, against all expectations, the universe is flat (in that parallel lines stay parallel) and the hypersphere will not work. Try a hyper-torus.

Meanwhile, back on topic, Max Tagmark wrote this paper for the late great John Wheeler's 09th birthday (in 2003), http://arxiv.org/PS_cache/astro-ph/p.../0302131v1.pdf on "Parallel Universes" where he states:

The most distant visible objects are now about 4×10²⁶ meters away, and a sphere of this radius defines our observable universe, also called
our Hubble volume, our horizon volume or simply our universe.

...and there is a footnote to explain that 4×10²⁶ meters is about 40 billion light years. In a rewrite for Scientific American, he adjusts it to 46 billion light years. That gives a diameter of 92 billion years.

p.s. that article is a First Class Mind Bender. Don't operate heavy machinery for about four hours after you read it.

[Steve Limpus]

The gives a diameter of 72 billion years.

Don't ya hate typos.

EDIT: oh ok, you saw that already!

I know you favour the hyper-torus, but I still feel the margin of error scientists admit for observations of flatness (2% out to the cosmic light horizon) allows for curvature.

It's reasonable that the universe beyond what we observe is huge, certainly huge enough that a curvature of less than 2% is possible.

Efforts to prove that hyper-torus is the correct solution (and hyper-dodecahedron too) have been unsuccsessful out to a significant portion of the observable universe - so no one knows really.

As I tried to point out to dcl before he went south on me, I just happen to like the hypersphere he also favors. Can't prove it, just like it.

[Vanamonde]

Oops, sorry, Steve, about the slowness of that correction.

Hey, I LIKE the hypersphere. I was just going by what Dr. Gay said in the Astronomy Cast about the universe being flat. True, she points out at one point in the early universe, it was one gram out of a septillion from being open or closed and that is sooooo weird.

But if we are voting on it, I vote for a closed hypersphere with a Big Crunch in X trillion years. So much more satisfying than a long dragged out Heat Death. And less get rid of this dark energy, make the dark matter baryonic (make it planets, lots and lots of planets), and not have any inflationary epicycles PLEASE!

But then, of course, everything is subject to change in the face of new evidence.

[Steve Limpus]

Lots of planets: I'll second that! Nice, blue and green ones...

[dcl]

Thank you, Vanamonde and Steve Limpus, for your comments on my 1:11 AM 4/17/2008 contribution. My responses follow:

Vanamonde: Old news. The latest is, against all expectations, the universe is flat (in that parallel lines stay parallel) and the hypersphere will not work. Try a hyper-torus.

Despsite assertions to the contrary, WMAP has not determined that the universe is flat. Neither it nor any other measure can distinguish between absolute flatness and slight curvature. All a measurement can do is place limits on measurements of radius of curvature. Absolute flatness is represented by a single point within a measurement range, and that range can never be reduced to zero. It follows that no measurement can ever determine that the universe is flat. If the universe is extremely large but finite, it will be extremely difficult if not impossible to detect curvature.

The shape of the hypertorus is too contrived to be a plausible representation of the shape of the universe. It has been described as starting with a cube, the line between one pair of opposite faces then being stretched, bent into a circle, and the ends joined, thereby achieving the shape of a doughnut.

Vanamonde: The most distant visible objects are now about 4x1026 meters away, and a sphere of this radius defines our observable universe, also called our Hubble volume, our horizon volume or simply our universe.

This geometry, a sphere with a radius of 40 billion light years, fits into a hypersphere. It appears to me to NOT fit into a hypertorus. In any case, In any case, what is the source of the 4x1026 figure?

Vanamonde: ...and there is a footnote to explain that 4x1026 meters is about 40 billion light years. In a rewrite for Scientific American, he adjusts it to 46 billion light years. That gives a diameter of 92 billion years.

That 4x1026 meters is about 40 billion light years is correct. I would like to know how the original figure was derived and the basis for adjusting it to 46 billion light years.

Steve Limpus: As I tried to point out to dcl before he went south on me, I just happen to like the hypersphere he also favors. Can't prove it, just like it.

I'm not aware that I "went south" on you, whatever that means. Please explain. If there is a misunderstanding, I would like to clear it up.

I agree that validity of the hypersphere cannot be proven. I adopt it because it seems to be the simplest model that seems consistent with the data. This is consistent with a philosophy known as "Occam's razor", which says that the simplest model that seems to fit the data is likely to be the correct one. Hypertori, doughnuts, and dodecahedrons seem unlikely to be valid because of their seemingly unnecessary complexity.

Vanamonde: Hey, I LIKE the hypersphere. I was just going by what Dr. Gay said in the Astronomy Cast about the universe being flat. True, she points out at one point in the early universe, it was one gram out of a septillion from being open or closed and that is sooooo weird.

Via email, I questioned Dr. Gay's basis for saying that the universe has the topology of a doughnut. I found her response disappointing.

Vanamonde: But if we are voting on it, I vote for a closed hypersphere with a Big Crunch in X trillion years. So much more satisfying than a long dragged out Heat Death. And less get rid of this dark energy, make the dark matter baryonic (make it planets, lots and lots of planets), and not have any
inflationary epicycles PLEASE!

A big crunch now seems to ruled out by dark energy. Heat Death seems inevitable for the same reason. The possibility of dark matter being baryonic seems to have been ruled out.

[Steve Limpus]

I'm not aware that I "went south" on you, whatever that means. Please explain. If there is a misunderstanding, I would like to clear it up.

Um, that would have been this bit:

Much of the remainder of that thread strikes me as a mixture of uninformed juvenile speculation and gibberish.

But not to worry, I'm over it now.