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FQXI ARTICLE
December 21, 2014

The Holographic Universe
Take one universe. Turn it into a hologram. Find its quantum wavefunction. Understand the birth of the cosmos.
by Anil Ananthaswamy
FQXi Awardees: Alex Maloney
August 17, 2010
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ALEX MALONEY
McGill University
By 1988, when Alex Maloney was just twelve years old, holograms were well and truly "in." Scientists had only recently worked out how to capture these three-dimensional photographs and emboss them onto two-dimensional metallic film and soon—to every kid’s delight—they were appearing on credit cards, magazine and book covers, and bank notes. Maloney had little idea then that more than two decades on he would be ambitiously attempting to cast the entire universe as a hologram, in an effort to explain the mysteries of the cosmos in its infancy. But even at that young age he did know that he wanted to be a physicist.

"Even when I didn’t have a name for it, I sort of had a good idea of what I wanted to do," says Maloney, now at McGill University, Montreal. He credits his grandfather Dewitt Stetten, a prominent biochemist who would rather have been a mathematician or a physicist, for this insight. In his later years, Stetten went blind and it fell upon young Maloney to read to him. But this was no ordinary reading list. Maloney had to read aloud books like Men of Mathematics and a four-volume set on the history of mathematics, straining his young mind to the explain the illustrations in the books. And then came Stephen Hawking’s A Brief History of Time. Which prompts the question: did the twelve-year old Maloney understand the book? "You know, I don’t think anyone understood A Brief History of Time," says Maloney.

Even when I didn’t
have a name for it,
I sort of had a good idea
of what I wanted to do.
- Alex Maloney on physics
Still, this unusual introduction to physics and mathematics steered Maloney towards its confluence: string theory as it applies to cosmology. Maloney cut his teeth on string theory during his Ph.D. at Harvard under Andrew Strominger; later he spent a year at the Institute for Advanced Studies (IAS) in Princeton with Edward Witten. But it was the discovery of dark energy in 1998 that kindled his interest in cosmology. Astronomers had found that the expansion of the universe is accelerating, and they put it down to an inherent energy density of the vacuum of space. But no theory in physics can explain why dark energy has the value it does.

"I remember very clearly how excited everybody was by this set of discoveries," says Maloney. "Even though it didn’t have a direct influence on the thinking in string theory, it had an indirect influence."

String theory has been formulated as a candidate theory of quantum gravity, which can be applied in realms where both quantum mechanics and general relativity are important. But, unfortunately, it doesn’t offer any easy answers to mystery of dark energy; string theory’s intractable mathematics has made applying it to the problems of cosmology near impossible.

Hawking and Holograms

So now Maloney is turning to techniques that were forged to understand another arena where immense gravitational forces meet microscopic volumes and quantum gravity cannot be ignored: black holes. And that’s where holograms come in.

In the 1970s, Hawking and Jacob Bekenstein showed that the information stored in a black hole is proportional to its surface area rather than its volume. This encoding of three-dimensional information on a two-dimensional surface came to be called the holographic principle. In 1997, Juan Maldacena of the IAS formalized the principle, showing that the string theory description of a black hole is mathematically equivalent to a quantum field theory without gravity that describes the surface of the black hole.


"PROBABLY THE MOST INTERESTING QUANTUM GRAVITATIONAL
SYSTEM."

Alex Maloney assesses the universe.
Credit: Ephraim Brown
The upshot for physicists was that, thanks to this correspondence, the math got easier. Problems that were too tough to solve using string theory could now be answered by using the equations of the more amenable quantum field theory. And it helped unravel one of the most perplexing puzzles about black holes, the information paradox, that had stumped Hawking. In the 1970s, Hawking and Bekenstein realized that black holes should slowly emit particles, losing mass through Hawking radiation. That meant that, in the absence of any infalling matter, a black hole will eventually evaporate. The conundrum was: What happens to the information that was originally part of the black hole? Is it lost forever? If so, it violates a basic tenet of quantum mechanics that information is neither lost nor created.

The holographic principle came to the rescue; physicists used it to show that the information of the constituents of the black hole is actually encoded in the radiation that emanates from its surface. So no information is ever lost.

The next step, says Maloney, is to try and apply these sorts of ideas to "what’s probably the most interesting quantum gravitational system"—the universe as a whole.

Holography right now
is the most powerful
tool to understand
precise formulations of
quantum gravity.
- Alex Maloney
Maloney will have to treat the universe as a quantum gravitational system if he wants to uncover what happened immediately after the big bang. Quantum particles are described using a wavefunction—a mathematical object that can be used to work of the probability that the particle will have certain properties when it’s observed. So Maloney’s quest involves hunting for nothing less than the quantum wavefunction of the entire universe. The universe’s wavefunction will help chart things like its volume or its rate of expansion in a quantum mechanical manner. Instead of being sharply defined at every instant in time, these quantities will fluctuate because of the inherent uncertainties of any quantum mechanical system. Arriving at the right theory of quantum gravity is imperative for such work.

"Holography right now is probably the most powerful tool to understand precise formulations of quantum gravity," says Maloney.

But it won’t be easy. The correspondence that Maldacena found works in very particular circumstances. It deals with a simple form of spacetime, called anti de Sitter space, which is symmetric, finite, and mathematically pliant. The early universe, by contrast, is modeled by something called de Sitter spacetime.

"You might think that because they only differ by one word, the description is rather similar," says Maloney. "But it turns out that describing de Sitter space using holography is much more subtle, and much trickier."

Black-Hole Universe

One of the key differences is that the volume of de Sitter space changes with time. That makes sense when you want to describe the early universe, which is thought to have increased nearly 1060 times in its infancy, during a period of exponential expansion, known as inflation. "If space is being created, then you might think that information is being created, so there is a tension there (with) the idea that information can neither be created nor destroyed," explains Maloney. "This is one of the real puzzles of quantum cosmology. It’s very analogous to the black hole information problem."


LAUNCHING THE QUEST FOR A THEORY OF QUANTUM GRAVITY
The Ariane 5 launcher lifts-off from the European spaceport in Kourou
on 14 May 2009, carrying the Planck satellite.

Credit: European Space Agency
Maloney and his colleagues Robert Brandenberger, Jim Cline and Keshav Dasgupta at McGill plan to use their $117,120 FQXi grant to apply the holographic principle to de Sitter space. It’s going to be tough, but Maloney’s peers think he’s up to the job. Strominger says that Maloney "has some very creative ideas," adding that Maloney’s "main strength is his ability to discover new angles for looking at problems."

Treating the universe as a hologram might sound like just a nifty mathematical trick, with little relevance to reality. But if holographic techniques can be applied to de Sitter space, they can also be used to make predictions about patterns etched in the cosmic microwave background (CMB), the relic radiation left over by the big bang.

Maloney’s main strength
is his ability to
discover new angles.
- Andrew Strominger
Inflation is thought to have caused ripples in the density of matter in our universe’s early history, which have left their imprint on the CMB. In the simplest models of inflation, which do not involve quantum gravity, these patterns have a basic form; they are predicted to be scale invariant. That means that the power in the fluctuations of the CMB is the same regardless of the scale at which the sky is being studied. But measurements made by NASA’s WMAP satellite hint at a small deviation from scale invariance.

The European Space Agency’s Planck satellite, launched on 14 May 2009, will be trying to home in on those tantalizing hints offered by WMAP, and Maloney is eagerly awaiting the outcome. "Understanding how it deviates is a question that might be relevant for a theory of quantum gravity," says Maloney.

Maloney’s combining all that he’s learnt: mathematics and physics, general relativity and quantum mechanics. "Applying quantum gravity to quantum cosmology is a very exciting thing to be doing nowadays," he says. Those childhood days spent reading Hawking’s obscure musings to his grandfather are certainly paying off.

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