From Robert Lawrence Kuhn, host and creator of Closer To Truth:

Extra dimensions seem the stuff of science fiction. We’re familiar with three dimensions—length, width, height. But what about other dimensions? What could that mean? What would they be like? And, anyway, why would we care?
What about the fourth dimension—time? Not as metaphor but as fact. Now, some speak of 10 or 11 dimensions, a factor in string theory, as the foundation of the cosmos. Is deep reality so strange?
Physicist Lawrence Krauss, who is passionate about origins, explains how this counterintuitive idea developed. “The idea of extra dimensions has been around for a long time in different contexts,” he says, “partly because people crave an ‘unknown universe’ in one form or another.”
Consider the origin of time as a fourth dimension, which was Einstein’s great intuition in his special theory of relativity (needed in order to maintain the speed of light as a constant, even when light sources are moving relative to one another).
“If you think of the world as four-dimensional—time being the extra dimension,” Krauss says, “then space and time become personal in that when I’m moving with respect to you, what I’m really kind of doing is rotating in this four-dimensional space, so my space is your time and your time is my space. So time is like an extra dimension, not exactly like space—but suddenly [with Einstein’s relativity], we live in this four-dimensional universe.”
Einstein’s radical insight enabled other scientists to wonder what else might be lurking within the foundations of the forces of reality.
Physicist Michio Kaku explains that “in three dimensions, there’s not enough room to account for all the laws of physics. But when you go into hyperspace, then the laws of physics fit together beautifully, like a jigsaw puzzle.” Kaku explains that “there are certain ‘magic’ numbers in mathematics, numbers which have spectacular properties. A 13-dimensional universe or a 15-dimensional universe would be unstable. Particles would prefer to collapse down to 10 or 11 dimensions because the mathematics shows these are the most stable and self-consistent.”
Where are these higher dimensions? “Look at smoke,” Kaku says. “Smoke permeates throughout a room in three dimensions, but smoke never disappears. Smoke never floats off into the fourth dimension. Therefore, a fourth, fifth, sixth dimension has to be smaller than smoke. Atoms, too, don’t suddenly drift away into hyperspace. Therefore, these higher dimensions have to be smaller than an atom, or else our universe would drift away.” But gravity, Kaku adds, might “ooze, escape, into these higher dimensions, and that could explain why gravity is so weak.”
Nobel laureate David Gross explains that even though extra dimensions had been contemplated before string theory, “one of the surprising things that came out of string theory was that we had to have more than the three spatial dimensions that we see around us. And, of course, since we don’t see these extra dimensions, either they have to be very small or (as was discovered more recently) there could be large extra dimensions in what are called warped geometries. The stuff of which we’re made could be stuck in the three dimensions that are visible.”
Particle theorist Nima Arkani-Hamed says that “other dimensions are curled up into a very small size. The usual analogy is like looking at a garden hose from very, very far away. The hose looks like a line, but as you get closer, you see it has a little thickness, a little circle there, with a finite size.” (The term of art is “compactified.”) “And so if you went around this other dimension, you would very rapidly come back to the same place,” Arkani-Hamed explains.
“Branes are a crucial part of this picture,” he adds, referring to the so-called “branes” of cosmology, where our whole three-dimensional universe could be floating in some fourth-dimensional or nth-dimensional space. “There are many different scenarios now which exploit branes and extra dimensions to do interesting things; they have experimental consequences, so they will live or die on a near-term timescale.”
Ten or 11 dimensions of space and time, all but our common three dimensions astonishingly tiny. Speculation, yes, but based on good theory. And they may explain the inexplicable—like why gravity is so incredibly weak compared with other forces like electromagnetism.
I’m almost getting this … but then lose it again. So how is it that extra dimensions, fiendishly complicated, make the world simpler?
Juan Maldacena, an unassuming “string theory rock star,” says that “we know that these extra dimensions are not infinitely big and equal to the other three dimensions because we know we are not moving in the extra dimensions. But the question is whether elementary particles can in some sense move in the extra dimensions. The idea is that perhaps the laws of physics are simpler when we add extra dimensions because some of the complications we see in the laws of physics in our three dimensions are due to the fact that the same particles are doing different things in these extra dimensions.”
Simpler? It seems more complicated! “Yes,” Maldacena agrees, “it does seem more complicated, but in a way it is simpler … because the idea is that you have simpler laws in extra dimensions [e.g., unifying fundamental forces, particularly gravity with electromagnetism] that rise to more complicated laws in our common dimensions. So, that’s the beauty, if you will, of extra dimensions.”
The point is that extra dimensions reduce the complexities of our three-dimensional world by explaining and unifying laws in those extra dimensions. Extra dimensions make the laws of physics simpler. What a realization!
But there’s sharp disagreement: Some scientists reject extra dimensions.
Mathematician Roger Penrose says, “I just don’t think these extra dimensions are stable. They will just collapse.” He adds, “Maybe these string theories’ ideas can have value in theories which don’t require extra dimensions.”
It’s the great human quest: To dig up the foundational structures of mass and energy, space and time. The drive is for simplicity: to explain how the world works concisely and elegantly. (When theories are complicated, then there is likely another theory, simpler and thus deeper.)
And simplicity, when it’s found, is breathtaking. That’s the magnetic appeal of extra dimensions. To show how the “atomic zoo” of what seem to be very different particles are really different manifestations of the same, singular “atomic animal.”
Unity from diversity. The wonder of it all. But do extra dimensions really exist? Either way, the exhilaration of exploration brings us closer to truth.

Robert Lawrence Kuhn speaks with Lawrence Krauss, Michio Kaku, David Gross, Nima Arkani-Hamed, Juan Maldacena, and Roger Penrose in “Are There Extra Dimensions?”—the sixth episode in the new season of the Closer To Truth: Cosmos, Consciousness, God TV series (45th in total).
The series airs on PBS World (often Thursdays, twice) and many other PBS and noncommercial stations. Every Thursday, participants will discuss the current episode.

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