Date: February 23, 2010

Title: Where IS the Center of the Universe?

Podcaster: Rob Knop

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

Description: A discussion of the center of the 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. This semester, he’s teaching physics at Belmont University in Nashville, and next fall will join 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.

Today’s sponsor: This episode of “365 Days of Astronomy” is sponsored by The Planetary Society, celebrating 30 years of inspiring the people of Earth to explore other worlds, understand our own, and seek life elsewhere. Explore with us at planetary.org.

This episode of “365 Days of Astronomy” has also been sponsored by Tom Foster.

Transcript:

Where IS the center of the Universe?
I’m Dr. Rob Knop. I’m associated with the Meta-Institute of Computational Astronomy (on the web at http://www.mica-vw.org), and will be joining the faculty of Quest University next fall.

Before I address the question as to where the center of the Universe is, I want to step back a bit and point out why some people might expect there to be a center to the Universe. It might seem obvious, but it’s worth pointing out why you might think that, so that we can tackle the issue head-on. We know that the Universe is expanding, and that it has expanded a whole lot from a very hot and very dense state to the Universe that we see around us today. The name for the theory that describes this evolution is the Big Bang. The Big Bang is often described as an explosion, although, for reasons I’ll discuss shortly, that’s not really a great way to think about it. However, the result of the Big Bang is that everything is rushing away from everything else. Indeed, if we look at other nearby galaxies, we see them moving away from us in exactly the way particles flung out from an explosion in an expanding cloud of debris would see other particles moving way from them.

And, so, given that we describe the Universe has having started in a Big Bang, it’s very natural to ask, where did this Big Bang happen? What is the center point that everything else is rushing away from?

Alas, it turns out that this isn’t really a meaningful question. It is based on a misunderstanding of what the Big Bang theory really says about the Universe… which in turn comes very naturally from the fact that even though the Big Bang is a great theory that is confirmed by a wide range of observations, it’s a poorly named theory in that it doesn’t really describe a gigantic cosmic explosion. The truth is, there IS no center to the Universe. Where did the Big Bang happen? It happened everywhere. Where you are sitting right now– that’s where the Big Bang happened. But it also happened where I’m sitting, and in the Andromeda Galaxy, and at the location of a galaxy observed to be a billion light years away from us.

How can we have an expanding Universe without having a center point that everything is expanding away from? In an attempt to explain this, I want to think about a two-dimensional model of the Universe, which we as hyperdimensional 3D creatures can look down upon and understand. This model of a 2D universe is the surface of a rubber balloon. To be more precise, this is a perfectly spherical balloon; there’s no special point such as a blowhole anywhere on the surface of the balloon. (If you’re worried about how we’re going to blow air into it to make it expand, remember that this is just a thought experiment. You can imagine the balloon getting bigger without worrying about the technical details of exactly how to make that happen.)

Now, the key point here is that the Universe is the surface of the balloon. Galaxies in this model universe exist just on the surface. Creatures within this universe can move around only on the surface. The concept of moving off of the surface of the balloon is not meaningful to them. We, in our three-dimensional space, can move left-right, forward-backward, and up-down… but we don’t even have a concept for a fourth spatial dimension that would be perpendicular to all of those first three. Likewise, for the creatures who live in the surface of this balloon, they can move left-right and forward-backward, but they don’t have a concept of up-down, for that would take them out of the surface of the balloon, which would mean leaving their universe. And, indeed, it is entirely possible to describe this two dimensional space mathematically without reference to any other than the two dimensions of the space itself— dimensions which you might think of as longitude and latitude.

Now let the balloon expand. If you have a bunch of galaxies in this model 2D universe– imagine, for instance, coins pasted on the surface of the balloon– clearly they’re all getting farther away from each other. There’s no doubt that the creatures living within this 2D Universe would be able to measure that it’s expanding. They would see that the distance from one galaxy to the next was getting bigger and bigger with time. Yet, where, on the surface of this balloon, would you point at and say the center of the expansion is? The answer is, nowhere. No one point on the balloon is special compared to any other point. Everything is getting farther away from each other, but there’s no point on the balloon that you would call the center.

Now, we, as hyperdimensional 3D creatures can identify a point we’d call the “center” of the balloon. But that point we identify is not on the surface of the balloon, and thus is not part of the universe of that surface in which our hypothetical 2D creatures live. You’ve got an expansion with no center. Indeed, if you run this backwards, at one point the balloon may have been very small, with all the stuff in the balloon very close together– which would mean that the matter in this 2d universe was very dense. The balloon universe then expanded from that point to what you see now. Every point on the surface was part of the original hot dense state; there’s nothing within that universe that is “outside” the original hot dense state. But it did get bigger, and everything did get farther away from each other.

Our Universe is similar, only we have three spatial dimensions. The 2D creatures who live within the surface of the balloon can describe the mathematics of their curved universe without any reference to a third dimension, using only the two spatial dimensions of their universe. Likewise, the space of our own Universe may itself be curved, but we only need our three familiar spatial dimensions to build a complete mathematical description of this. Back in the extremely early Universe, everything was much, much closer together than it is now, so everything was very dense. But it was all there. Space got bigger, and everything got farther apart from each other, but just as the whole balloon was there at the beginning of its expansion, all of space was compressed together into the early Universe in our Universe. And, just as there is no point on the surface of that balloon that you can identify as the center point, the special point, of the balloon, there’s no point in the Universe that we can identify as being the “center” of our Universe, or the one special place where the Big Bang happened. There IS no center to the Universe.

Is your mind straining with the visualization yet? I’m going to try to push it one step further. It turns out that the balloon is not the best two-dimensional model of the space of our real Universe. The surface of a balloon is what we’d call “spatially closed”. If you start at one point on the balloon, and walk as straight as you can in one direction, you’ll eventually go all the way around the balloon and come back to where you started. And, indeed, it was possible that our Universe had a three-dimensional geometry equivalent to this. However, just over ten years ago, astronomers made measurements that told us that the Universe as a whole is much closer to spatially flat. This means that a better two-dimensional model for the Universe would be a rubber sheet, instead of a balloon.

Now, you’ll very quickly point out that a sheet– just like a piece of paper– has a very easily identifiable center. But this isn’t just any rubber sheet… it’s an infinite rubber sheet. Infinity is one of those things that can cause your brain to tie itself into knots as you try to visualize it. The point, though, is this. Pick any point on this rubber sheet. At any time, there will be an infinite amount of sheet in any direction you look. As such, you can’t find any point on the rubber sheet that looks any different from any other point, so with an infinite rubber sheet, it’s impossible to define any point as the center.

It turns out that a very, very large balloon is very much like an infinite rubber sheet. If the balloon is so huge that over the size you can see you can’t tell that it’s curved, it will in practice appear to you just like a rubber sheet. This, in fact, is a concept that you’re familiar with. After all, we know that the surface of the Earth is curved, but in your every day life you walk around on the Earth and can see that the ground looks flat. You use maps of your city, and maybe even your whole country, on flat pieces of paper. So, to be perfectly honest, the measurements we have don’t prove that our Universe is the three-dimensional equivalent of an infinite flat rubber sheet… it may still be the equivalent of the surface of a balloon. But, if it is, the curvature is so small that we can’t detect it over the size of everything that we’re able to see.

What happens with the Big Bang and the expansion of the Universe in the case of an infinite rubber sheet? It is just the same as the balloon. As the universe expands, imagine stretching the rubber sheet in all directions at the same rate. Now, this does introduce a conceptual problem. With a finite sheet, you can go a certain distance and reach an edge. You can imagine the empty bit outside that sheet in that same direction, and that empty bit is what a finite flat rubber sheet would be expanding into. But if it’s an infinite rubber sheet, you can’t ever reach an edge… which means that it’s not expanding into anything. The question “what is the Universe expanding into” is a hard question to deal with, because it doesn’t have an answer. It’s not expanding into “nothing”… rather, the answer is that it’s a meaningless question, because there’s no “outside” of the Universe, at least not within the three spatial dimensions that we live in. You can’t go across the edge and get outside of our Universe any more than you can get outside of an infinite rubber sheet, or you can get outside of the surface of a balloon, by moving in the dimensions of the surface.

If an infinite rubber sheet is expanding, early on it was much smaller and much denser… but already infinite. It’s just that it was in a sense a smaller infinite size than it is now. As it expands, the density goes down, and everything gets farther apart from everything else, but one thing doesn’t change: however far you go in any direction, there’s still more rubber sheet outside it. That was true in the very early Universe, and that’s true now. So, just as in the balloon example, there’s no point you can identify as the center, there’s no point you can identify as the one point that everything is moving away from. Everything is moving away from everything else.

This is what the Big Bang really is. You will often hear it incorrectly described as a cosmic explosion with everything moving away from one point. In fact, the theory doesn’t address what it’s named after, the moment of Bang itself! Our current knowledge of Physics doesn’t allow us to understand what happened at that time, and it may well be that it wasn’t a single moment in time. The Big Bang theory describes the Universe evolving from a very hot, very dense state, where everything was a soup of fundamental particles, to the state we see today of stars and galaxies, Dark Matter clumped around galaxies, and Dark Energy spread throughout everything. But everything is not rushing away from one point; rather, everything is getting farther away from everything else. There IS no center to the Universe. All of space was squished together there in the early Universe. The Big Bang happened everywhere. The Universe is just bigger now.

End of podcast:

365 Days of Astronomy
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