Cosmic dioramas

Move over Harry Potter, and take your invisibility cloak with you. Alice’s looking glass may be the latest bit of literary magic worthy of physics laboratories.

Rather than using substances known as metamaterials to hide objects in plain sight, some scientists instead want to use the strange materials to build windows into worlds with fundamentally different physics. Peering in may reveal how other universes operate and how this universe — the one that avid J.K. Rowling and Lewis Carroll readers reside in — could have begun.

Metamaterials can be engineered to have features very different from those of everyday matter. By altering electric and magnetic properties, scientists can make metamaterials that bend, twist or otherwise manipulate light. The power to turn light in unusual ways brought about a cloaking craze and introduced the possibility of superlenses with unprecedented focusing power.

Last year, a group of physicists at the University of California, Berkeley proposed a type of metamaterial that, if built, could trap light the way a black hole does (SN: 10/10/09, p. 10). The math describing processes in that material resembles the equations governing black holes.

Now Igor Smolyaninov of the University of Maryland in College Park has developed additional “strange schemes,” as he calls them. Metamaterials, it turns out, can serve as broader cosmic dio­ramas, manipulating light to replicate the shape of spacetime.

“In metamaterials, we have a situation in which we have optical spacetime,” Smolyaninov says. “And we can engineer the properties of spacetime.”

Joseph Polchinski of the University of California, Santa Barbara’s Kavli Institute for Theoretical Physics says he was skeptical after first reading about the work. He is not convinced that the analogs Smolyaninov proposes would include enough detail to probe the questions that he and others in his field really care about. But Polchinski’s doubt soon became tempered by curiosity.

“Without being able to say where this is going, I think it is interesting,” he says. “There is nothing like having a real physical system in your hands to start thinking about things in a new way.”

When Alice stepped through her looking glass, she entered a distorted world. Words appeared backward on the page, clocks had human faces and floating was a reasonable way to get around. Some physicists have proposed that far more bizarre worlds lie beyond the visible universe. These worlds could have different laws of physics, different numbers of dimensions and different curvatures of spacetime surfaces. But because these multiple universes (known collectively as the multiverse) aren’t visible, they would be hard to study.

Smolyaninov suggests a solution online at arXiv.org and in an upcoming Journal of Optics. Metamaterials, he claims, can be made to mimic the multiverse. He says the idea is straightforward: Pockets with different properties could be designed to replicate adjacent universes. The pockets could be created so light can’t escape — as in the black hole scenario — or so that light can move among them.

And just as some physicists believe that some dimensions of the visible universe could be compactified — shrunk down really small — the same could be emulated for dimensions in other universes. One pocket universe with two compactified and two extended dimensions could sit next to a space with three compactified dimensions and one extended dimension, for example.

Analog systems have been beneficial to theorists over and over again, says metamaterials expert Ulf Leonhardt of the University of St. Andrews in Scotland. He suspects that something could be gleaned from this system too. “In some areas of theoretical astrophysics, people are just relying on theory,” he says. “They have been relying on theory for a very long time.”

The idea that space can have compactified dimensions has been around for a while. In the 1920s, Polish mathematician and physicist Theodor Kaluza proposed that an extra dimension might exist beyond the three of space and one of time that are typically experienced. Soon after, Swedish physicist Oskar Klein proposed that such an additional dimension of space could be wrapped up into a small loop. Because it would be too tiny to see, the dimension wouldn’t be like those that people know and love, the ones that allow moving forward or back, up or down and side-to-side. Yet particles would notice it. Adding the extra dimension did for electromagnetism what general relativity did for gravity — it gave the field a geometric underpinning.

A common way to think about a compactified dimension is to consider an ant walking along a garden hose. From far away, the garden hose appears one-dimensional — the ant can move only along its length. But zoom in closer, and it becomes obvious that the ant can also loop around the hose’s circumference, so a second dimension is available. Just as this second dimension is hidden from a distant observer, an extra curled-up dimension may be hidden from people in the real world.

Smolyaninov calls the Kaluza-Klein idea “a stone of theoretical physics.” And although his original proposal for a metamaterial multiverse focused on universes with fewer dimensions, he reports online September 6 at arXiv.org that metamaterials could mimic a world with five or more dimensions. Simulating higher dimensional spaces could make the analogs more interesting to string theorists, who propose the existence of many dimensions too small to see.

In the materials that Smolyaninov dreams of creating, photons can occupy an infinite number of quantum states. Some type of change, in temperature perhaps, could make the unusual material — if constructed just right — revert to a state in which photons can’t occupy so many positions. When this transformation happens, the particles have to be emitted, like a bunch of kids getting kicked out of a game of musical chairs all at once. Those emitted photons would create a flash of light.

“It looks like a Big Bang situation,” Smolyaninov says. Such a flash could emulate the birth of the universe.

And the flash could be made in a second way, Smolyaninov argues. Consider the dimensions that people experience (leaving Kaluza-Klein out of the picture for now). There are three of space and one of time; the time dimension behaves differently, so it gets its own special math to describe it. But when what’s called a metric signature change occurs, a timelike dimension can take on spacelike qualities, or vice versa. Metamaterials could also replicate the math behind this type of transformation, Smolyaninov and Evgenii Narimanov of Purdue University in West Lafayette, Ind., propose in the Aug. 6 Physical Review Letters.

Smolyaninov notes that theorists have discussed the idea of two timelike dimensions before. But, says Leonhardt, these ideas remain controversial in cosmology. “There’s no consensus about what would happen if one spatial dimension became a timelike dimension,” he says. In some ways, this uncertainty makes the proposed analog more exciting. “You can go ahead and try it and see what happens.”

Polchinski agrees: Very few people think that a metric signature change occurred during the Big Bang, and differential equations don’t seem to have meaningful solutions in a world with two times. Still, he notes, if the system can be built, the math must work out.

So can you build it? Christopher Davis, a colleague of Smolyaninov’s at the University of Maryland, says no: “You cannot build what he talks about from real materials.”
Smolyaninov responds, “not yet.” He is betting on advances in nanofabrication and hoping to drum up some excitement for new optical technologies until then.

While the new technologies may lead to practical devices, the metamaterial multiverse is more speculative.

Smolyaninov is careful to emphasize that the similarities he sees between spacetime and metamaterials are mathematical, not necessarily physical. He doesn’t know whether what lies on the other side of his proposed looking glass accurately represents reality.

“Maybe the whole universe is built in the same way,” Smolyaninov says. “If it is true or not, you just don’t know.”