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.
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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