Professor of Physics and Astronomy, Barnard College of Columbia University; Author, Black Hole Blues and Other Songs from Outer Space (forthcoming, March 29, 2016)
Physicist, Columbia University; Author, A Madman Dreams of Turing Machines

I used to take for granted an assumption that the universe is infinite. There are innumerable little things about which I've changed my mind but the size of the universe is literally the biggest physical attribute that has inspired a radical change in my thinking. I won't claim I "believe" the universe is finite, just that I recognize that a finite universe is a realistic possibility for our cosmos.

The general theory of relativity describes local curves in spacetime due to matter and energy. This model of gravity as a warped spacetime has seen countless successes beginning with a confirmation of an anomaly in the orbit of mercury and continuing with the predictions of the existence of black holes, the expansion of spacetime, and the creation of the universe in a big bang. However, general relativity says very little about the global shape and size of the universe. Two spaces can have the same curvature locally but very different global properties. A flat space, for instance, can be infinite but there is another possibility, that it is finite and edgeless, wrapped back onto itself like a doughnut — but still flat. And there are an infinite number of ways of folding spacetime into finite, edgeless shapes, a kind of cosmic origami.

I grew up believing the universe was infinite. It was never taught to me in the sense that no one ever tried to prove to me the universe was infinite. It just seemed a natural assumption based on simplicity. That sense of simplicity no longer resonates as true once we have confronted that there must be a theory of gravity beyond General Relativity that involves the quantization, the discretization, of spacetime itself. In cosmology we have become accustomed to models of the universe that invoke extra dimensions, all of which are finite and it seems fair to imagine a universe born with all of its dimensions finite and compact. Then we are left with the mystery of why only three dimensions become so incredibly huge while the others remain curled up and small. We even hope to test models of extra dimensions in imminent laboratory experiments. These ideas are not remote and fantastical. They are testable.

People have said to me they were very surprised (disappointed) that I suggested the universe was finite. The infinite universe, they believed, was full of infinite potential and so philosophically (emotionally) so much richer and more thrilling. I explained that my suggestion of a finite universe was not a moral failing on my part, nor a consequence of diminished imagination. More thrilling was the knowledge that it does not matter what I believe. It does not matter if I prefer an infinite universe or a finite universe. Nature is not designed to satisfy our personal longings. Nature is what she is and it's a privilege merely to be privy to her mathematical codes.

I don't know that the universe is finite and so I don't believe that it is finite. I don't know that the universe is infinite and so I don't believe that it is infinite. I do see, however, that our mathematical reasoning has led to remarkable and sometimes psychologically uncomfortable discoveries. And I do believe that it is a realistic possibility that one day we may discover the shape of the entire universe. If the universe is too vast for us to ever observe the extent of space, we may still discover the size and shape of internal dimensions. From small extra dimensions we might possibly infer the size and shape of the large dimensions. Until then, I won't make up my mind.