The Cosmic Hologram

An Indian emperor was angry with a guru for teaching that everything is maya: an illusion. To prove him wrong, the emperor invited the guru to his palace and set a stampeding elephant on him. As the guru ran away, the emperor shouted after him, "Why do you run so fast, seeing that my elephant is only an illusion?" The guru replied, "Oh emperor, my running too is an illusion, everything in this world is an illusion."

Andrew Strominger, a string theorist at Harvard University, is one of a number of physicists who surprisingly agree with the guru in this ancient story—just swap the word "maya" for "holographic" and you’re there. About ten years ago, Strominger had an outlandish idea. He mused that our universe is an image projected backwards in time from a hologram located at the boundary of the cosmos, in the infinite future. As the image projects into the past, it fades away, becoming grainy and undefined, eventually fading to nothing. It’s a bizarre notion, but over the past decade it has been gaining ever more credence, especially within the mathematical framework devised by string theorists. If correct, it could help explain how the universe, and time as we know it, came from nothing, as well as helping in the quest to unite quantum mechanics—the theory that governs particles on the small scale—and general relativity—which describes the large-scale cosmos—into one overarching theory of quantum gravity. "It’s one of the most speculative things I’ve ever worked on," admits Strominger. "But if it turns out to be right, then it’s one of the most interesting things I’ve ever done."

The contrast with big bang cosmology is stark: there is no flick of a switch and everything is suddenly here. Running time forwards in this story, you have a pleasingly slow, continual process of creation as more and more of the hologram comes into view. In this picture, mind-bogglingly, even living beings would be projections from the future. "It wouldn’t be the first time in physics when the unimaginable has been understood to be reality," retorts Strominger. He is sticking to his equations.

As crazy as this idea sounds, there’s good reason why we should listen to this physics guru. Physicists acknowledge the strides Strominger—who has been awarded a $73,000 FQXi grant—has already made in our understanding of the basic structure of quantum gravity, black holes and string theory. "He has a unique perspective, which often allows him to solve apparently complex problems in a simple and clear way," says Alex Maloney, who is based at McGill University, Canada. (Read more about Maloney’s FQXi-funded research in "The Holographic Universe.") "His work is often quite prescient, and it is only in retrospect—sometimes years or decades later—that many of his papers have been fully appreciated," Maloney adds.

Early on Strominger knew that physics was for him: "The universe is such an amazing and wonderful place, there’s nothing more enthralling than trying to understand it, and possibly make a small amount of progress," he says. But he is coy about his childhood and upbringing. The fact that he finished high school at 15, two years earlier than most, almost seems an embarrassment. Asked if he was a child prodigy, he says, "You’d better ask my parents!" He attributes his first appreciation of physics to his high school teacher, a Mexican immigrant to Boston, where he and his family lived at the time. "He didn’t even have a PhD but he just loved physics and had a great ability to communicate it," says Strominger.

Black Holes and Holograms

The roots of Strominger’s latest ideas about a projected universe go back to the 1970s, when physicists Stephen Hawking and Jacob Bekenstein calculated that the information content of a black hole (described mathematically by its entropy) is proportional to its surface area. This was surprising because most people expected it would be related to its volume. Their discovery has been dubbed the "holographic principle" because it shows that information about a three-dimensional black hole is encoded on its two-dimensional surface, just like a hologram.

Then in 1996 Strominger and his Harvard colleague Cumrun Vafa derived a precise statistical description of a black hole’s entropy in terms of microscopic energy states at the black hole’s surface. In particular, they made a connection with the equations usually used to describe the behaviour of particles: quantum field theory. They realized that the equations they were using to describe the properties of the black hole were similar to those used to describe a system of particles using quantum field theory, but in a universe without gravity.

A year later Juan Maldecena of the Institute for Advanced Study (IAS) in Princeton, New Jersey, independently found a mathematical equivalence between two kinds of universes: the first universe contains particles that obey quantum field theory, but does not contain gravity; the second universe contains strings and gravity and has a special type of negatively curved space-time geometry (called an "anti de Sitter universe"), such as that thought to be found inside black holes. This may seem like a lot of obscure mathematical shuffling, but it’s had a huge impact on theoretical physics. When physicists get stuck because their equations are too tough to solve, they can switch into the mirror universe where the math is often easier and finish their calculations there, before transferring their answers back again. (See "The Black Hole and the Babel Fish" for more about how the holographic principle is being used to predict the behavior of exotic materials in the lab.) "It is useful because problems that are hard in one formulation become easy in the other formulation," says Maldecena.

Maldecena’s conjecture linking these two universes has proven a spectacular mathematical success, says Strominger. "We understand it in amazing detail, it’s a very beautiful and precise statement and there is general agreement that there is overwhelming evidence that it is correct."

However, on the whole, the universe we see around us is not negatively curved, limiting the applications of Maldecena’s correspondence. In fact, in the late 1990s, astronomers discovered the opposite: that the expansion of the universe is accelerating—something they attribute to some kind of "dark energy" pushing it outwards. They now believe that soon after the big bang, dark energy dominated the universe, and it may do so again in the far future, pulling the cosmos apart so ferociously that matter is ripped apart and gravity cannot hold stars and planets together. A cosmos in which dark energy plays the biggest role is known as a "de Sitter universe" (in contrast to the anti de Sitter universe that makes up one half of Maldecena’s relationship). So the hunt has been on to find a similar correspondence principle to Maldecena’s, but for a de Sitter, rather than an anti de Sitter universe.

That has not been easy, explains Strominger. "It’s been very frustrating trying to understand de Sitter space within string theory, and I spent many years trying. It always ends up being complicated and not especially pretty," he says, adding modestly, "I just didn’t succeed—but then I don’t succeed in most things I do. But when you’re trying and not succeeding you’re always learning something."

Strange Gravity

Indeed, through this endeavor, Strominger learned of a little-known theory describing interacting particles by a Russian physicist Misha Vasiliev. Although it’s related to string theory, it includes a raft of new massless particles with unusual properties that have never been observed. "Everybody agrees that Vasiliev gravity is a strange theory. But nevertheless it seems to be mathematically self-consistent and in many ways much simpler to analyse than string theory," says Strominger. Crucially, Strominger and colleagues Tom Hartman also from IAS and Dionysius Anninos at Stanford University, California, found that the Vasiliev’s bizarre model for the universe easily accommodated de Sitter space.

Using Vasiliev’s model for gravity, Strominger and his colleagues have taken Maldacena’s correspondence for anti de Sitter space, and applied it to de Sitter space. It represents the first example of how a universe that is more physically similar to the one in which we live can be understood in terms of information at a boundary surface, holographically projected back in time. "This is a very radical thing, it amounts to a total revolution in the way that we view the universe," says Strominger. "We’re very far from seeing that this is how it works in our own universe, but nevertheless, it is a small step in the right direction. So people are interested in it and they want to take the next step," he says.

Maldecena agrees that the work is "very interesting" because it is the first example of the correspondence with positive curvature, which is more directly related to the universe we live in. Although it holds for a very special and somewhat strange theory of gravity, it gives a strong hint that our actual universe could one day be described using a similar correspondence, he adds. In turn, this will be a powerful tool for understanding quantum gravity and even how our universe emerged from nothing in the first place.

Strominger hopes to move his correspondence onto firmer ground, mathematically speaking, by finding more examples of how it can work. He has a lot of calculating planned for the next part of the journey, up to what he calls "the next bend in the road," including trying to find a solution that looks even more like the universe that we live in, starting with a big bang. "It’s not a vague question, we can translate it into some real mathematics and I expect we’ll be able to solve it in the next year or two," says Strominger.

Whether or not our universe is really a holographic projection from the future is still far from any sort of observational test because it has only been shown to work using this strange Vasiliev model for the universe, rather than our real universe. "We are asking the most difficult questions we can conceive of," says Strominger. "It takes a long time to understand what the question is, it takes a long time to understand the answer, and it takes an even longer time to test it. You have to be a little crazy to work on these things because they go on for years." We just have to hope that our holographic projections last long enough for physicists to test the answer—and perhaps upset a few emperors along the way.