Date: October 25, 2011

Title: Visualizing the Expanding Universe

Podcaster: Rob Knop

Organization: Quest University Canada

Links: http://www.mica-vw.org
My home page: http://www.sonic.net/~rknop
MICA Public Events.

Description: A way to wrap your mind around the phenomenon of the expansion of our universe.

Bio: Rob Knop obtained a PhD in Physics from Caltech in 1997. He then worked with the Supernova Cosmology Project and was part of the discovery that the expansion of the Universe is accelerating. After six years as an assistant professor at Vanderbilt University, he worked in the computer industry for two years. He now teaches physics the new college Quest Unviersity in British Columbia. He gives regular astronomy talks in Second Life in association with the Meta-Institute of Computational Astronomy.

Sponsor:This episode of “365 Days of Astronomy” has been sponsored by the Lake County Astronomical Society in northeast Illinois.

Transcript:

Hello, and thank you for listening to 365 Days of Astronomy! I am Rob Knop, Professor of Physical Science at Quest University Canada.

A couple of weeks ago, on October 12th, I gave a podcast here about the discovery of the accelerating Universe. On October 17th, Rob Sparks and Tom Matheson of the National Optical Astronomical Observatories also talked about that, Tom Matheson having been a member of one of the teams that made that discovery. Today, I want to talk about it from a more theoretical point of view. Now, by theoretical, I don’t mean speculative! One of the problems we have in science outreach is that “theory” in common parlance means something different from what it does in science. I don’t mean to say that this is “in theory” in that it’s all something that we’ve speculated about but don’t have any data on. Rather, I want to talk about our mathematical description of the expanding Universe– the mathematical description that has been held up by comparisons with data from observations. Instead of talking about the observations, I want to talk about the description that these observations have led us to– the theory that underlies our understanding of these observations.

What does it _mean_ to say that the Universe is accelerating? To answer that, I have to start by talking about what it means to say that the Universe is expanding. It sort of means exactly what you’d think, but also sort of doesn’t mean what you’d think it means. The obvious part is: all of the galaxies in the Universe are getting farther and farther away from each other. That’s just what you’d expect if somebody told you that the Universe is expanding.

The general name of the theory we have for the history of our Universe is the Big Bang. Although this theory nicely fits with the observation of an expanding Universe, we’ve known about the expansion of the Universe longer than we’ve accepted the Big Bang theory as a good description of the history of our Universe. The expansion of the Universe was discovered in the late 1920’s; it was only in the 1960’s that the Big Bang theory became the one that most astronomers accepted as the best description of the history of our Universe.

The problem with the Big Bang is that the name of the theory implies things that aren’t actually part of the theory. In particular, it implies that it’s a gigantic explosion. While it shares some similarities to explosions, it also has some key differences. In particular, you probably think of the Big Bang saying that the Universe all started at one point, which everything is now rushing away from. That description brings in a few conceptual difficulties, however. It suggests that there is a point out there in space somewhere that was the location where the Big Bang happened, and everything is rushing away from it. However, this is not what the actual Big Bang theory says.

Where was the Big Bang? Cup your hands in front of you. If you’re driving while you listen to this, only cup one hand in front of you. That space inside your hands? Right there, that’s where the Big Bang happened. It also happened at a point in deep intergalactic space five billion light-years away. The Big Bang happened everywhere! We’re still within the aftermath of the event that we call the Big Bang, and all of the space around us, including all of the space in and around all of the galaxies we can see, was the space where the Big Bang event happened.

Another reason the Big Bang theory isn’t a great name is that the current version of the theory doesn’t actually include the moment of Bang itself. A pure classical theory, such as you might have read about in “A Brief History of Time” by Stephen Hawking, and such as is described by Einstein’s equations of General Relativity interpreted by scientists such as Friedman, Robertson, Walker, and Lemaitre, does include a singularity, a moment in the past where the Universe has infinite density. However, when your physical theory predicts a singularity, it usually means that you’ve extrapolated it past the realm where it applies. And, indeed, that’s the case here. We know that a pure classical theory can’t completely describe our Universe, because when we get to small enough scales we have to take into account Quantum Mechanics. Unfortunately, while we have these two great, well-tested theories, Quantum Mechanics and General Relativity, they don’t play well together. Roughly speaking, General Relativity deals with the very massive, and Quantum Mechanics deals with the very small. When you get to a regime where both are relevant– such as at the center of a black hole, or at the moment of the Big Bang– and you try to use the two of them together, you get nonsensical results. In other words, we don’t have a complete theory of physics. As such, our Big Bang theory, which is based on our more fundamental theories of physics, can’t actually address the moment of bang itself.

So how does the Universe start in our modern version of the Big Bang theory? It starts in an extremely hot and dense state. If you look out in the sky, with the most powerful telescopes, you can see what we call the “observable universe”. Because the speed of light is finite, and because the age of the Universe is finite, light has only had time to reach us from a certain distance. That distance makes up the observable universe. In the observable universe, there are something like 100 billion galaxies. However, that’s not all the galaxies that there are. If you go to the edge of the observable universe, further off there are going to be more galaxies, pretty much like the ones inside the observable universe. The edge of the observable universe isn’t a real boundary, it’s just as far away as we’ve had time to see. As best we can tell, the Universe is infinite: as far as you go, there keep being more galaxies, pretty much like all of the other galaxies.

So, back to the hot and dense state that is “the beginning” in our current version of the Big Bang theory. If the Universe is infinite now, it was always infinite! Infinity is hard to wrap your brain around, and it’s much easier to think about the Big Bang as all rushing away from one point, but in fact that’s not the case. There is no spot in the Universe that you can identify as the center. At the earliest epochs where we can say anything solid about what the Universe was like, all of the 100 billion galaxies that are within our observable universe were squashed down into about the volume of a pea. That’s a lot of mass in a very small volume. However, remember that that pea of hot and dense stuff isn’t the whole universe; it’s a pea shaped region within a much larger, possibly infinite soup of stuff, a pea shape defined not by any physical boundaries but only by the stuff that you and I will be able to look at 13.7 billion years later.

If the Universe is not an explosion, if you can’t visualize it as a bunch of matter, from which galaxies eventually form, rushing away from one point, how can you visualize it? It’s difficult because visualizing infinity is difficult. So, instead, I shall give you a version of a finite Universe that shares some characteristics with our infinite Universe. That is: the surface of a uniform rubber balloon. It’s important to realize that I’m talking about a two-dimensional Universe here, that the Universe is represented by the _surface_. Creatures in our model Universe could move east-west, or north-south, but they cannot leave the surface. This is different from the surface of the Earth. You can leave the surface, however briefly, just by jumping.

Stick your left arm out straight in front of you. Now, stick your right arm pointing out straight to the right, perpendicular to your left arm. Now, look straight up, perpendicular to your two arms. Now, imagine a direction that’s perpendicular to both of your arms _and_ to the direction you’re looking. Tough, huh! That direction would be a fourth spatial dimension, which doesn’t exist in our Universe. By the same token the third spatial dimension– what we call “up and down”– doesn’t exist in this two dimensional model Universe.

Imagine galaxies as spots on this balloon. You can think of them as pennies pasted on the balloon, for example. Think, then, about light traveling from a galaxy in one part of this two-dimensional Universe to a galaxy at another spot. Suppose that the two galaxies are half-way around the circumference of the ball from each other. The light wouldn’t go what we would think of as “directly”, through the inside of the ball, but rather it would travel along the surface of the ball, curving around to reach the destination galaxy, all the while moving within the universe, that is, along the surface.

Now allow the balloon to expand. As it does so, clearly all of the galaxies are getting farther apart from each other. However, there’s no spot within the Universe– that is, _on the surface_ of the balloon– that you can identify as the center of the expansion. Every galaxy gets farther apart from every other galaxy, and every point on the balloon is equivalent.

Now run the expansion back in time. As we go back in time, the 2d model universe gets smaller and smaller, and the pennies that represent our galaxies get closer and closer together. Eventually, we’re looking far enough back that the pennies would all start to be on top of each other. At this point, we have to quash the pennies down into more dense soupy matter so that we can keep shrinking our Universe.

Keep going, as far as you want. As the ball keeps getting smaller, still there is no point on the surface of the ball that you can identify as the location where the Big Bang happened. Indeed, everything everywhere on the surface of the ball is equally dense. Our real Universe is like that. The Big Bang happened everywhere, and we’re still within it. If we look at the expansion of the Universe by looking at the rate at which galaxies are getting farther away from us, it looks just like we are right at the center of the expansion… but it would look like that to astronomers in any galaxy, for all points are equivalent.

Of course, our Universe is three-dimensional. Also, as best we can tell, it’s infinite. The surface of a ball, while it has no boundaries, isn’t infinite. Our Universe is more like the equivalent of an infinite two-dimensional rubber sheet, which you can expand by pulling it apart uniformly in all directions and everywhere at once. In three dimensions, you might think of it as being like an infinite loaf of raisin bread. The raisins represent the galaxies. As the bread rises, it expands uniformly in all directions. (Don’t put our universe in a breadpan.) The raisins all get farther apart, but for an infinite loaf of raisin bread, there’s no spot that you can identify as the center of the loaf.

The expansion of our Universe is often explained as galaxies flying apart from each other. While this is fine, at least for relatively nearby galaxies, that description runs into some conceptual problems when you start to talk about larger scales. As such, when trying to explain what the mathematics of the expanding Universe say, cosmologists more often will say that “space itself expands”. That is, as the Universe expands, there is more space between the galaxies. But what does this really mean? Really, the distance between the galaxies went up. When we say that “space itself expands” or that there is “more space”, it implies that space is somehow stuff, which isn’t quite right. However, this description is by and large a better description of the expansion than is saying galaxies are moving away from us with speeds that depend on the distance. And, indeed, one of the conceptual difficulties with it– that there is more “stuff” there in between the galaxies as “space itself expands”– may turn out not to be a conceptual difficulty at all!

So, the Universe’s expansion is accelerating. Imagine again our 2d model universe, the surface of a rubber balloon. You would expect the gravity of all those galaxies pulling on each other to try to slow down the expansion of our Universe. As time goes by, we’d expect the rate at which our balloon is getting bigger to get slower and slower. Indeed, that’s what the mathematics of General Relativity applied to our Universe as a whole say: the expansion of the Universe should be slowing down because of the gravitational effect of the matter in the Universe. However, when we went and measured the expansion history of the Universe, we measured that it is speeding up! For that to happen, there must be something in the Universe that has a negative gravitational effect, something that forms a sort of anti-gravity. Dark Energy is the name we give to whatever it is that is causing the acceleration. We really don’t know what Dark Energy is, but one of the most likely explanations is something called vacuum energy.

Vacuum energy is the energy density left over in space when you take out everything from a region of space. Take out all the atoms, take out all the neutrinos, take out all of the light, take out all of the Dark Matter. (Dark Matter is different from Dark Energy.) Once you’ve taken everything out, and have nothing left, you’d expect that that region of space has a zero energy density, for there’s nothing there. However, it turns out from quantum field theory that it’s possible that the vacuum left behind still has some residual energy; we call that residual energy vacuum energy. And, if vacuum energy exists, it would have the property of causing the Universe to accelerate exactly as we’ve observed it to.

So, in that sense, when we say that “space itself expands”, or that there is “more space” between the galaxies, in a sense there really is! If there is vacuum energy, then the density of that vacuum energy is probably a universal constant, or close to it. That means that if you have more space, you’ve got more vacuum energy. There really is more stuff, now in the form of vacuum energy, in between the galaxies as space itself expands.

A lot of this is mind-blowing stuff. It involves trying to visualize infinity, which is difficult. It also involves trying to visualize a description of space given to us by general relativistic equations that don’t match the kind of space that our brains evolved to understand. If there are a few pithy points I want you to take away from this it’s the following. First, the Big Bang is a great theory widely supported by observations, but it doesn’t include a single moment of Bang; rather, it just starts from a hot dense state where everything is much closer together, but it’s all still spread out. Second, the Big Bang didn’t happen all at one point, but happened everywhere, and we’re still inside it. Third, there is no center point to the Universe that things are rushing away from; rather, everything is moving away from everything else, and every point in the Universe is equivalent to the center.

I realize that this leaves a lot of unanswered questions. What happens when light moves through the Unvierse? What does it _mean_ to move through the Universe? What is the Universe expanding into? If you have questions that you’re still confused about, please leave them in the comments at the bottom of the blog entry associated with this podcast on 365daysofastronomy.org. I’ll collect the comments and try to address them in a future podcast.

Have a good day, and enjoy your accelerating expansion!

End of podcast:

365 Days of Astronomy
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