In Search of a Quantum Spacetime

Physics is so hot these days that even equations scribbled on a blackboard are laminated and sold as art. "Oh, that’s just for my friend who’s an artist," laughs Sean Carroll, when I ask him about the temporary blackboard covered in diagrams that I can see leaning against his office wall during our Skype conversation.

The theoretical physicist based at the California Institute of Technology, in Pasadena, usually uses blackboards more conventionally. You’ll often find him chalking up equations with his students on his current area of study: how the deepest levels of reality are connected to higher levels of behavior we see in the world around us. With the help of a grant of over $60,000 from FQXi he hopes to explain the very emergence of space and time using quantum physics.

At the heart of this research is a puzzle that has been vexing physicists for nearly a century: how to unite Einstein’s theory of gravity, general relativity, with the quantum laws that govern the atomic world. The general theory of relativity describes spacetime as a fabric in which massive objects like stars and planets are embedded. Gravity manifests because heavier objects, such as stars, cause this fabric to bend more, drawing lighter objects, like planets, around spacetime’s contours towards them.

But spacetime’s relation to quantum mechanics still eludes physicists. Carroll believes the misfit between the two theories persists because people usually approach the problem the wrong way around. "People usually start from ’classical’ theories—where objects have precise positions and velocities as outlined by Isaac Newton—and then quantise them," says Carroll. "Instead we need to start with the quantum world and ask ’what does it looks like classically?’" he says.

In quantum mechanics you can’t say precisely where a particle is if you know its momentum. Instead physicists describe its behaviour mathematically by a wavefunction in a multidimensional space, known as "Hilbert space." From the wavefunction you can work out the probability of observing the particle in different locations. You can also see what it would look like in the classical world: whether it is a particle moving in one, two or three-dimensions.

Now Carroll is taking a step back and looking at the big picture, by investigating the quantum wavefunction of the entire universe. It’s something physicists have tried before, with mixed results. Carroll is attempting to approach the problem in a new way, without relying on any pre-existing structures or boundary conditions.

It’s a bold idea, but if it works, Carroll could come up with a quantum mechanism for generating space and time. This line of thought was inspired by the framework laid down by physicist Juan Maldacena of Princeton University in the late 1990s. It states that for a particular type of hypothetical "Anti de Sitter" spacetime (which is similar to ours, but is curved differently) the information on a surface surrounding a volume of space is equivalent to the information contained inside the volume. Carroll describes the correspondence as an "enormously big and fun playground for theoretical physicists" because it has enabled them to find new relationships between quantum phenomena on the surface and gravitational effects within.

Entangling Quantum Threads

In particular, physicists have been investigating entanglement—the spooky ’action at a distance’ that can connect pairs of quantum particles so that their behavior is eternally interconnected—within Maldecena’s framework. They have found hints that making and breaking entanglement on the surface can change the geometry of space within the volume. This suggests that quantum entanglement may be the thread from which spacetime’s fabric is woven.

While these findings are tantalising, Carroll notes that its implications are limited because we do not actually live in a space that is shaped like Anti-de Sitter space. Carroll aims to search for similar connections, but in a more realistic setting. "We’re trying this approach relating quantum entanglement to geometry in Hilbert space, which is much closer to the real world," says Carroll.

Working with Caltech graduate student Charles Cao, Carroll contends that by essentially looking at the entanglement between different parts of the wavefunction of the universe you can reconstruct the underlying geometry of spacetime. "There’s even a hint that if you poke it a little to perturb its state, then you get a non-flat geometry that looks like it may obey something like Einstein’s equations for gravity," enthuses Carroll. "But there’s an enormous amount of work to be done before can say anything like that with any confidence, but that’s the kind of huge ambition we have before us."

Mark Trodden, a cosmologist based at the University of Pennsylvania, says this is a promising project in a field that has shown significant progress in recent years. "It seems clear that the underlying laws of nature must be quantum mechanical," says Trodden. "The question of whether one can recover spacetime itself from the ideas of quantum mechanics, thereby understanding how all our classical notions arise from quantum theory, is a fascinating one."