Put your right hand on your right temple, and your left on your left temple. Now gently squeeze; don't let up.
Okay. Now you are ready for a conversation with Arlie Petters, the energetic, broadly smiling man in the striped short-sleeve shirt and comfortable brown slacks who has come to meet you at a Barnes & Noble café. Many topics will come up. He will wonder whether amoebas could join the conversation. He will suggest searching the solar system for tiny black holes as a practical business enterprise. And he will say things like, "I don't see why reality should contain only three spatial dimensions." Again with the beaming, cheerful smile. "Do you?"
Now that he mentions it, maybe there are no good reasons for limiting reality to three spatial dimensions, but you are rather used to it that way, and … it's a good thing you didn't order coffee, because you could not pick up the cup: You need both hands to hold your skull together.
Perhaps Petters, a Duke professor of mathematics and physics, smiles so much because once he decided that he may have an entire extra physical dimension to work with, the usual limitations that make the rest of us so grumpy stopped pinching quite so tight. An additional dimension might enable him to be two places at once—saving money on daycare, perhaps, or at least making it easier to pick a child up there; or it might offer limitless extra time, or … space, or … something.
But maybe Petters is so cheerful because, if everything goes just right with a NASA satellite scheduled to launch any day now, it's possible that his name will be forever linked to the physical evidence that disproves Einstein's general theory of relativity. Or not exactly disproves Einstein's brilliant conflating of space, time, energy, and matter. "I would say that he missed something," Petters says. Something that, if it turns out to be true, "would give us a complete philosophical shift in our understanding of the physical world,"by proving that the physical universe has four, not three, spatial dimensions, making ours, when you include time, a five-dimensional universe. "It's a very exciting idea," Petters says.
He opens a clasp envelope and produces a sheaf of scrawled notes on lined paper, including a simple graph: an X- and a Y-axis, on which a straight dashed line angles down from left to right, with a sine wave superimposed. "The telltale wiggle," he calls it.
Here's the idea. The Gamma-ray Large Area Space Telescope (GLAST), scheduled to be launched into Earth orbit by NASA in February, will spend its time looking at gamma rays, the most energetic form of light there is—billions of times more energetic than the waves our eyes can perceive; millions of times stronger than even X-rays. The result should be new information about things like pulsars and supernovae, the kind of unimaginably massive energy sources that emit gamma rays and exist at the very edge of our current understanding of physics.
But with the new telescope, Petters and his colleague in this project, Charles Keeton, a Rutgers University astronomer, saw an opportunity to go even further. That graph that Petters produced, which he calls a "back of the envelope calculation," resulted from a flurry of e-mail messages between the two a couple of years ago when they heard about the telescope. The graph represents how gamma rays would bend—the "wiggle" in the graph—if they happened to pass a tiny but massive object called a braneworld black hole.
A black hole—not the braneworld kind, but the kind that most of us have heard of, even if we still don't quite comprehend what it is—is a massive object like a star or many stars that has collapsed into an unimaginably small and dense space with a gravitational pull so strong that even light cannot escape it. Einstein's theories predicted the existence of black holes, since verified by scientists. A braneworld black hole is a special kind of black hole. It's tiny, the size of an atomic nucleus or smaller, but has the mass of an asteroid. For now, its existence is theoretical. Proof will come only if a specific variant of the string theory of gravitation, which disagrees with Einstein's theory, turns out to be true.
But ignore that for a moment. For now, just keep in mind that Petters and Keeton want to look for the wiggle they predict they will find in the gamma-ray graph if the gamma rays happen to pass by one of those braneworld black holes. These wiggles are the subject of Petters' research.
They're caused by gravitational lensing, a process by which light (of any electromagnetic wavelength) is bent in the warped conditions of space and time that occur near massive objects like planets, stars, or black holes. Einstein predicted this phenomenon, and it was first observed during a 1919 total eclipse of the sun, when background stars viewed directly past the darkened sun appeared slightly out of position. The sun's mass had actually bent the rays of light from those distant stars. The phenomenon was regarded as a brilliant proof of the warping of space and time described in Einstein's general theory of relativity. Such lensing, now better understood, thanks in part to Petters, can produce not only bent but also multiple images of distant objects. What's more, objects with certain masses affect light of specific wavelengths according to specific signatures. Subjected to mathematical analysis, these signature bends yield secrets about the objects that cause them.
"Imagine dropping a pebble into a pond," Petters says. The pebble generates waves, with peaks and valleys: Big rock, big waves; tiny pebble, smaller waves. That is, an object massive enough to be a gravitational lens leaves a signature pattern affecting a specific wavelength of light. And those tiny black holes predicted by the braneworld theory would produce a wiggle in the specific electromagnetic range that the GLAST will be measuring, once it's in orbit.
Okay, braneworld black holes. These currently exist only on the blackboards of scientists who believe in a certain variation of string theory. String theory is a cosmological theory that considers the tiniest building blocks of matter to be something like vibrating strings rather than particles. The mathematics of this complex model end up requiring additional dimensions for everything to work out, though in most versions, extra dimensions are treated as little more than convenient theoretical constructs.
But a variant of string theory developed by Lisa Randall of Harvard University and Raman Sundrum of the Johns Hopkins University posits the universe we perceive as a sort of three-dimensional membrane (hence "braneworld") floating in a multidimensional universe. Petters loves the pragmatic elegance: "In braneworld, what I like is that this fourth dimension extends to infinity. In other string-theory models, it's this tiny, curled-up dimension," kind of stuffed into an inexpressibly small space like the end of a fiddlehead fern. In those models, the fourth dimension doesn't affect anything except strings. "They're not letting it loose," he says.
As he tries to explain the added spatial dimension, he runs his fingers along the café tabletop. "Imagine we are beings that live only on this desk," he says. That is, we're two-dimensional beings, inhabiting this flat, two-dimensional space. "That's not a limit of our eyes or ears, that's a limit of our physical existence." His eyes grow large: "You can't get off this table." He cites the famous Victorian satire Flatland, a book about two-dimensional creatures who receive a visit from a sphere and are simply unable to comprehend its three-dimensionality. He thinks a minute, then takes an intellectual step backward, to first principles.
"There are two acts of faith that go into science," he says. The first is that "the physical world is understandable to the human mind." The second, that "you can model it mathematically—quantitatively."
Then we're back to life on the tabletop. "That first postulate, that physical reality is accessible, is not quite right—not all of it. Think of an amoeba," he says. "It's a tiny entity that's wiggling around on this desk," in this essentially two-dimensional space. "Now think of our conversation. It completely transcends that amoeba, because of its wiring." That is, it completely lacks the capacity to perceive us: Living on its tabletop, it's going to think the universe has the limits of its perceptions.
"Who are we to think we are any different than this amoeba in the full spectrum of reality?" Petters says. Just because we can't think of where that fourth spatial dimension would be, and lack the capacity to perceive it, doesn't mean it's not there.
Charles Keeton, Petters' partner in the paper they published about that telltale wiggle, cites a common way to try to imagine this extra dimension: "People often draw a piece of paper standing vertically," he says. "The third dimension," poking outward from both sides of the two-dimensional paper, "is perpendicular to both dimensions. Braneworld would have a fourth dimension perpendicular to all three dimensions" that we now perceive.
That's about as good a description as anybody can come up with—we seem to be like those tabletop amoebas, doomed to our limited understanding of reality. Still, take for comfort these words by perhaps the most famous journalist of our generation, uttered when she, too, was trying to comprehend a five-dimensional reality: "It had height, length, breadth," she said, "and a couple of other things." Those are the words of Lois Lane, describing Superman's nemesis Mr. Mxyzptlk, who came from the fifth dimension, wore a derby hat, and could be forced to return to his five-dimensional space only if tricked by Superman into saying his own name backwards. Looking at Mr. Mxyzptlk's five-dimensional manifestation, Lane said, "made my head hurt."
But hard as it may be for two-dimensional comic-book characters, or even us three-dimensional types, to wrap our minds around spatial four-dimensionality, the point is that the braneworld model puts it there, and that Petters and Keeton have found a way to look for its signature through the data gathered by the GLAST satellite.
That takes us back to the tiny black holes of braneworld. In an Einsteinian universe, black holes of that size could be created only in the conditions present at the dawn of the universe, and any created then would have evaporated by now. But according to the braneworld universe, they would not have evaporated and so would still exist to put their signature juju on that gamma-ray vibration.
If you find the interference pattern in the gamma rays, you've found a tiny braneworld black hole. That tiny black hole doesn't fit in Einstein's equations. Ergo, if you find the braneworld black hole, you demonstrate that the braneworld theory, not Einstein's, is correct. And scientists will probably start spending a lot of time looking for ways to investigate a fourth spatial dimension.
Petters leans back in his chair. "The way I look at this is, remember when we thought the world was flat?" He shakes his head. "Think of the poor elementary-school kids who will have to learn geometry into the fourth dimension." He imagines possible consequences of a fourth spatial dimension, wondering, for example, whether people will instantly try to develop weapons based on the incredibly high energy with which particles will move between dimensions. On the other hand, he recalls that in Flatland, a three-dimensional being—like you—could put a finger right into the middle of a two-dimensional being—like a square—without penetrating its boundaries: You could poke its insides without going through its "skin." Similarly, a being from four spatial dimensions might be able to poke you in, say, the spleen—from the inside. "But that's like spooks, right?" Petters asks. "That's like ghosts. You can run with this metaphor." He smiles. "It's almost like science fiction."
Yes, like science fiction. But tiny black holes the size of atomic particles, four spatial dimensions, gravity bending light? That isn't like science fiction. That stuff is all in a day's work.
A mathematician's search for evidence of tiny black holes could disprove Einstein's general theory of relativity—and open up a whole new dimension.
January 31, 2008