The Quantum Dictionary

In the popular sci-fi movie the Matrix, the world experienced by humanity is just an illusion created by a computer programme. That, laughs Mark Van Raamsdonk, might be strangely close to the truth. According to the theory of the universe that he ascribes to, the world we see around us is a projection from a set of rules written in simpler, lower-dimensional physics—just as the 2D code in a computer’s memory chip creates an entire virtual 3D world.

Van Raamsdonk spends his time as a professor at the University of British Columbia (UBC), Vancouver, thinking deeply about such things, and has made a significant advance: the metaphorical chip holding all the programming for our universe, he concluded in 2010, stores information like a quantum computer.

Now theoretical physicists, including 40-year-old Van Raamsdonk, are trying hard to figure out the programming language being used by that chip. "We’re trying to construct a dictionary," says Van Raamsdonk, that allows physicists to translate descriptions of our complex universe into simpler terms. If they succeed, they will have found the biggest jigsaw piece in the puzzle of a Grand Unified Theory—something that can describe all of the forces of our universe, at all scales from the atomic to the galactic. That puzzle piece is, specifically, something that can describe gravity within the framework of quantum mechanics, which governs physics on small scales. Such a unified theory is needed to explain the extreme scenarios of a black hole or the first moments of the universe.

Van Raamsdonk started out with a strong interest in maths—in high school he was a member of the Canadian team for the maths Olympiad—and that’s what he intended to pursue in university. But in his first year he realized he was more attracted to the complexities of theoretical physics. "I thought physics was only about things you could observe directly: electrical circuits and the motion of objects, and that for every little situation there would be an equation to describe it," he says. "As I learned more I realized how much could be derived from deeper principles. You learn about things like quantum mechanics. It’s amazing that anyone even figured it out. There’s a really beautiful mathematical theory underlying nature."

As a grad student at Princeton in the second half of the 1990s, Van Raamsdonk found himself wrapped up in the so-called Second Superstring Revolution. The first revolution, which took place around 1985, had simply proposed that string theory—which posits that elementary particles can be described by the vibrations of tiny strings—could be interpreted as a quantum theory that has gravity in it. At that point, physicists were deeply concerned that the beautiful mathematics of quantum mechanics, while able to describe the strong, weak and electromagnetic forces, failed horribly at trying to describe the final fundamental force of gravity. Trying to unify quantum mechanics and gravity had become the holy grail of theoretical physics. String theory offered a possible way to unite them. "People thought hey, maybe this would be the answer. But they understood relatively little about it," says Van Raamsdonk.

Holographic Universe

Then in 1998, a Princeton graduate published a paper that would become one of the most famous in theoretical physics: Juan Maldacena proposed that to understand quantum gravity through string theory, you can look instead to the much more ordinary, well-described system of quantum mechanics called quantum field theory (Adv. Theor. Math. Phys. 2, 231–252 (1998)). The more complex theory, he argued, was exactly equivalent to the simpler one: physicists just had to work out the code or dictionary that would translate the rules of one to the other. This idea is often popularly described as the holographic theory of the universe, since it seems that all the information about our complex multi-dimensional world can be described using a simpler, lower-dimensional language—just as a 3D image is projected from the 2D screen of a hologram, or a 3D computer gaming world created from a 2D memory chip. "After that, people wrote thousands of papers just testing whether that could be true," says Van Raamsdonk.

Although, so far, nobody has given a direct proof of Maldecena’s conjecture, its mathematical consistency has been confirmed time and again. As a computational tool, it is even being used to help condensed matter physicists predict the properties of exotic materials in the lab (see "The Black Hole and the Babel Fish"). "No one has actually proven it, but we’re as certain about it as about anything in physics," says Van Raamsdonk.

So Van Raamsdonk started to dedicate his time to figuring out how this works, and what the rules are for going from one set of math to the other. This was such a hot topic at the time, he notes, that of the 20 or so fellow PhD students in his programme at Princeton, about half went into string theory. In 2000, while still doing his first postdoc, Van Raamsdonk was lured back to his undergraduate alma-matter, UBC, with a job offer that let him delve into these ideas.

His biggest insight to date was described in a 2010 essay, which won an award that year from the Gravity Research Foundation and accolades from colleagues: "Everyone knows about this essay," says black hole theoretician and FQXi member Ted Jacobson from the University of Maryland in College Park. The paper addresses one of the most basic features of our universe—its shape. Van Raamsdonk started by imagining that the metaphorical computer determining the features of our universe is a quantum computer: instead of having ordinary information-carrying ’bits’ that must exist in either an ’1’ or ’0’ state (like current that must be either on or off), this sort of computer has quantum bits (or qubits) that can exist as a 1, 0, or something in between, all at the same time. In order for a quantum computer to perform any useful calculations, these fuzzy qubits have to be connected to each other through a phenomenon called entanglement, where the state of one qubit helps to determine the state of a neighbour.

Van Raamsdonk considered what would happen if one split the 2D quantum computer memory card in two, so that one half could not entangle with the other. In such a case, he showed mathematically, the geometry of the resulting 3D world would also be split in two—like a balloon being pinched into two separate balloons, or into two parallel universes that can’t communicate with each other. Keep splitting the memory card and you keep fragmenting the universe. If the chip has no entanglement at all, with every qubit operating independently, then the universe is just a mass of independent atoms with no connection to each other. That’s not the universe we live in. So the ’instructions’ at the core of our universe, Van Raamsdonk concluded, must involve entanglement. "To have classical spacetime you have to entangle all the parts of your memory chip," he says.

"What Mark has done is put his finger on a key ingredient of how space-time is emerging: entanglement," says Gary Horowitz, who studies quantum gravity at the University of California Santa Barbara. Horowitz says this idea has changed how people think about quantum gravity, though it hasn’t yet been universally accepted. "You don’t come across this idea by following other ideas. It requires a strange insight," Horowitz adds. "He is one of the stars of the younger generation."

With his $60,000 FQXi grant, Van Raamsdonk is pushing his work further, by identifying characteristic features of gravitational physics (like black holes, or the everyday gravitational attraction between two ordinary objects) and asking how to rewrite these phenomena in terms of quantum field theory; or, to look at things the other way, by investigating which properties of quantum theory, like entanglement, are required to give rise to the features we see around us in our universe.

"This whole set of questions about the dictionary is really a question about how the information about our universe is stored," Van Raamsdonk says. While the long-term goal is to formulate a working theory of quantum gravity, this work might also reveal interesting things about quantum information theory itself. "I’m very glad he has grabbed onto this thread and is pursuing it," says Jacobson.

Whether re-writing the laws of gravity so they work on a quantum scale will have any impact beyond the sphere of theoretical physics is uncertain. There are no clear applications in sight, though presumably one might need such a theory to, say, construct a wormhole to get your spaceship from one part of space to another. No one, laughs Horowitz, is building a wormhole in their lab quite yet. Indeed the whole idea of quantum gravity remains in the theoretical realm. "Mark’s ideas so far have not led to any testable predictions," says Horowitz. "But that’s not surprising when you’re dealing with something so remote from everyday experience."

But there is one way that Van Raamsdonk makes practical contact with a holographic dictionary —of sorts—in his daily life. In his spare time, he plays alto saxophone: music being, funnily enough, another area where 2D instructions are brought to life in a multi-dimensional world. "I haven’t thought about it like that," laughs Van Raamsdonk. But then, "part of the appeal of music is that you don’t have to think."