March 22, 2010

Big Bang for beginners-7: What lies beyond the edge of the universe?

(My latest book God vs. Darwin: The War Between Evolution and Creationism in the Classroom has just been released and is now available through the usual outlets. You can order it from Amazon, Barnes and Noble, the publishers Rowman & Littlefield, and also through your local bookstores. For more on the book, see here. You can also listen to the podcast of the interview on WCPN 90.3 about the book.)

For previous posts in this series, see here.

The idea of an infinite space that has always existed and in which everything else just moves around seems intuitively reasonable, at least to those who are comfortable with the concept of infinity. But the idea that there is no edge or boundary to the universe is much harder to grasp.

Going back to our raisin bread analogy, asking the question "What is beyond the edge of the universe?" is akin to asking what exists outside the space occupied by the dough. The answer is that there is no space outside the dough. The dough is all the space there is. This is where the raisin bread analogy starts to be misleading because we cannot help but view the dough as expanding inside the space of the oven, and it is hard to eliminate that unwanted extra image of oven walls. (If we wish, we can envisage a small portion of the dough and speak of the boundary of that portion alone, but that is not the boundary of space as a whole. It would be like speaking of the boundary of our Solar System or the Milky Way galaxy.)

To try to shake ourselves of the idea that the universe must have an edge (and center), let us try another analogy and imagine the old days when people thought the Earth was flat. A couple of natural questions for them would be to wonder where the center of the Earth was and what lay beyond the edge. There are three ways in which questions about center and edge become meaningless, as illustrated in the figure on the right which is taken from a NASA website.

Curved space.jpg

One is the bottom figure in which the flat Earth extended to infinity, so that there is no edge and no way to determine where the center is, since the location of the center of any object (such as a circle or sphere or anything else) is dependent on its relationship to the boundary of the object. No boundary means no center.

The second way to eliminate the edge and center as meaningful concepts is if the Earth is neither flat nor infinite in size but curved into a sphere, like the top figure. The idea of a center and an edge becomes meaningless here too. After all, what would it mean to refer to the edge of the surface of the Earth? Where on the Earth's surface would a center be located?

There is also a third option for the Earth and that is that it is infinite but not flat. Instead it is like the middle figure which is shaped at every point in space like a saddle that curves downward in the side-to-side direction (where the rider's legs dangle), curves upward in the front-back direction, and extends to infinity in all directions. (Apparently mathematicians have also been able to devise equations that represent a space that is saddle-shaped at every point but is finite. (The Runaway Universe, Donald Goldsmith (2000), p. 36.) But I have no idea if such a universe makes sense from a physical standpoint and am not going to consider it further.)

Which of these three models (spherical, saddle, or flat) was true of the Earth was an empirical question that was settled by careful observations and data. We now know that it is a sphere, or to be more precise, a slightly flattened sphere.

Something similar is true for the universe. Either it is infinite (either flat or saddle shaped) or it is finite in size and closed in on itself. All three shapes (flat, saddle, sphere) are analogous to the three possible options that we had for the Earth but much harder (even impossible) to visualize. Since we can see in three dimensions, visualizing a 2D surface as a sphere or flat or saddle-shaped is easy. But in the case of the universe, it is already in three dimensions and we cannot visualize how it curves. We can only deal with it mathematically. But the question of which one of these alternatives for the universe (infinite and flat, infinite and saddle, or finite) is one that can be answered by gathering relevant data. At present, our best estimate is that it is infinite and flat, a point I will return to in later posts.

If the universe is infinite and always has been infinite, what does it mean to say that the Big Bang started out as a 'small', highly dense and hot gas of quarks, gluons, electrons and photons? How can an infinite universe be small?

What is meant by 'small' in this context is that all the matter that now occupies the visible universe once occupied the small region that we identify as the space in which the Big Bang occurred.

Again we need an analogy to help us get a grip on this idea, though as with all analogies we must not take it too far because all analogies eventually break down. Think of a flat rubber sheet that extends to infinity. In a small region of the sheet, a Big Bang occurs that creates matter that is embedded in the rubber. If the sheet is then stretched in all directions (i.e., as space expands), the matter that is embedded will get pulled apart along with the sheet. So then instead of speaking of the absolute size of the universe at any time (the rubber sheet is and always has been infinite), we can meaningfully speak about by how much any given region of the sheet (i.e., the visible universe) has expanded since the Big Bang. (See here for a more thorough explanation.)

So even if the universe is infinite and always has been infinite, the visible universe that we can see could still have been concentrated in a small region in the distant past.

POST SCRIPT: Paralyzed by choice

Barry Schwartz talks with Stephen Colbert about why while some choice is good, too much choice can be bad, leaving people more dissatisfied.

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Hi Mano,

Very interesting, but now I am even more confused--I guess there is something wrong with the model in my head.

Does this mean that we have other evidence that the universe extends outside of observable space, or is this a necessary condition of the big bang theory but something that by definition we cannot have evidence (because it is unobservable)?

A few posts ago you said that "What the theory actually says is that the only space that exists is the space occupied by the matter produced in the Big Bang and that, as the matter spread out, it did not fill already existing empty space, but instead it was space itself that was expanding, carrying the matter along with it." and "There is no space outside of the dough."

Today's post seems to say that the "bread dough" exists to infinity in all directions, and there's a region of this bread dough that has raisins in it. As all of the bread dough expands the region with raisins in it also expands, but if you look at the region with the raisins in it it is still the same dough as when it was a very small amount of dough with highly dense raisin dispersion.

I feel like there's been a sudden switch in what terms mean. What we were originally calling "space" and "the universe" is now "the observable universe". And if the observable universe is only a region of the entire universe (which is apparently both infinite and expanding), then even if the observable universe isn't expanding into "empty space", it is still expanding with other space. This somehow seems different to me.

I think I can still work most of it out, but I am left with at least this question, "If the observable universe is a subspace of the whole (infinite) universe, and it is the region that the big bang occurred in (and the big bang occurred in ALL of this space), than mustn't there be some boundaries between the two?"


Posted by Jared A on March 22, 2010 11:11 AM

I am confused by the same thing as Jared.
>At present, our best estimate is that it is infinite and flat.

If that's true, then the analogy of the surface of a sphere having no center doesn't apply. There must be some point in space where the big bang started, and by conservation of momentum, it must be at the center of mass of the universe. We should at least be able to calculate the center of mass of of the known universe, right? And about the edge: We see stars in all directions. Shouldn't there be some stars that were formed from the very fastest particles in the big bang, that are the farthest out, that can see nothing in one direction? Like the raisins, even if the dough is infinite, there will still be raisins at the "edge" if there are a finite number of raisins, since there is a center of mass of the raisins.

Posted by Robert Allen on March 22, 2010 12:39 PM


I can clarify at least one thing for you. Remember that the big bang started at a single point. As this point expanded in three dimensions over time, all of observable space is expanded from that singularity. Space is expanding uniformly, too. This means that no particles are going "fastest". It's just that there is more space in between. I can't quite grasp how this means that there are not any particles "near the edge", although presumably this is what it means.


Posted by Jared A on March 22, 2010 02:07 PM

Jared and Robert,

Let me take a shot at clarifying this.

From an empirical standpoint, we only have the universe that we can see. And as far as we can see, there seems to be no end. One can say that the extreme of what we can see constitutes a boundary or an edge but this is an artifact of our technology.

There is no reason to think that that the number of raisins is finite. It is possible that we see only some of the raisins, those that are close enough. It may be that the dough and raisins extend (and have always extended) to infinity so the visible universe encompasses just our neighborhood and it is this space that we see expanding as part of the expansion of all space. Hence there would be no raisins at the edge because there is no edge.

Or it may be that the number of raisins and the amount of dough is finite but closed on itself so that again we would not see an edge. As I said, this option seems to be ruled out at present.

As for the question about the center of mass, if we compute the center of mass of the visible universe, it will be where we are. But this would be true wherever we happened to be located, since the Big Bang happened everywhere in space. So there is no 'real' center of mass, if by that we mean a unique point in space.

Hope that helps. Or at least does not confuse you even more!

Posted by Mano on March 22, 2010 02:35 PM

Mano said, "There is no reason to think that that the number of raisins is finite."

Or turtles?

Isn't is only a small step from here to the existence of multiple realities or universes sitting on top of each other.

Posted by dave on March 22, 2010 03:16 PM

Aha, thanks for the clarification. I think I can pinpoint where I was getting confused. I misread something on Wright's so everything wasn't fitting together properly.

So what's mechanically important about the big bang is how dense it started. We can't say how big the universe is or whether or not it even has a bounded size, but we can have an idea of how much it has expanded since it "started".

Posted by Jared A on March 22, 2010 05:23 PM


I don't think that follows from anything I have said so far which is consistent with a unique universe.

The multiverse hypothesis deals with the origins of the universe and the question of why the constants of nature in this universe has the values they have.

Posted by Mano on March 22, 2010 08:17 PM

Jared A,

Yep, you got it!

Posted by Mano on March 22, 2010 08:18 PM

Wow, I have to digest this for a day or two. Mano, I think I will have many questions!

Posted by Bill on March 23, 2010 04:39 AM

If we consider a distant point, as far away as we can see, then from that vantage point, even farther areas of the universe would be visible, right? And so homogeneity and isotropy would imply that even the parts of the universe we can't see are similar to our local area?

Posted by Paul Jarc on March 23, 2010 03:06 PM

Great explanation! Clarifying "Visible" vs. "Entire" totally clears it up for me. Wow, this is fascinating! So, based on the uniformity, wouldn't it then be extremely unlikely that the visible universe is the entire universe?


Posted by Robert Allen on March 23, 2010 06:06 PM


Yes, it is very unlikely that what we can see now is all that there is.

In fact, the most recent theories are that the universe is expanding so rapidly that galaxies are 'disappearing' over the far horizon. So if we had happened to come along a hundred billion or so years later, the only things we would see in the night sky would be the merged result of own Milky Way and the Andromeda galaxy, which are due to collide. The rest of the sky would be dark and people would have thought that there was nothing else in the universe.

The sky would be really boring and we would not have had the vast amounts of observational data that we have now to make all these great inferences.

Posted by Mano on March 23, 2010 08:41 PM


Yes, that implication is there.

Posted by Mano on March 23, 2010 08:55 PM