S C H E M A T I C B Y H T K Y M / W I K I P E D I A ( C C B Y - S A 3 . 0 )

embedded in the infalling material is forever inaccessible. However, in the 1970s, Stephen Hawking of the U.K.’s University of Cambridge suggested that normally ephemeral pairs of particles that appear in the quantummechanical vacuum could be ripped apart at the horizon, with one sucked inside and the other escaping.

One consequence of this escaping “Hawking radiation” is that the black hole will eventually evaporate completely. At that time (usually ridiculously far in the future), information that had been carried in would not just be inaccessible, but gone forever, violating the quantum rule that it is always preserved. Physicists argued about how to resolve this “black-hole information paradox” for decades, but they largely came to accept that the information was somehow carried away in quantum “entanglement” between different radiated particles. In 2004, Hawking famously agreed, conceding a bet with the California Institute of Technology’s John Preskill.

 

The Universe as a Hologram

Important support for this consensus came from a tool proposed in 1997 by Juan Maldacena of the Institute for Advanced Study in Princeton, NJ. It is called the AdS/CFT correspondence because it allows a mathematical mapping between a particular model of spacetime (AdS) and a class of quantum models (CFT).

Intriguingly, although the gravitational and quantum systems are equivalent, the quantum system has one fewer spatial dimension, somewhat like the surface of the gravitational system. This is an example of a “holographic” universe, so called because it resembles the way that a flat holographic film can encapsulate a three-dimensional image. Black holes constructed in this idealized universe can evaporate while conserving information. Carroll said the hope is that looking at such explicit examples will “reveal general principles,” although he stresses that other approaches should also be explored.

The AdS/CFT framework has also
yielded other insights, including new
ways to study complex quantum-
mechanical systems like supercon-
ductors by looking at the correspond-
ing gravitational model. It also re-
of one bit requires an energy expendi-
ture of a few billionths of a picojoule
(at room temperature). This puts a
lower bound on the energy needed
for computation, because the output
of a logic gate usually compresses
the information in its inputs. Fortu-
nately, current electronics devices
use millions of times more energy per
operation, so the limit is not (yet)
important practically.

Quantum Information

Even this fundamental limit could in principle be avoided, however, by making all computations reversible, retaining enough information to reconstruct the original input. For researchers working on candidate components for quantum computers, this turns out to be immediately relevant, because these devices always operate reversibly, and this needs to be incorporated in circuit design.

Indeed, according to quantum me-
chanics, the mathematical evolution
of any system is restricted to “unitary”
transformations, which “basically
means that whatever information you
have, it always is there in some form,”
said theoretical physicist Brian Swing-
le of the University of Maryland. “May-
be it’s very hard to read it out in some
sense, but it’s there.”
Quantum information should still
be conserved even when it is scrambled
by interactions with the environment,
which can be viewed as a larger quan-
tum system. Although such interactions
are often viewed as uncontrolled noise
that causes “decoherence” that scram-
bles quantum information, quantum
error-correction schemes exploit the
overall reversibility of the combined sys-
tem to ensure the desired information
is preserved where it is needed.

Actually, “classical” ( non-quan-tum) physics also follows microscopic equations that pay no attention to the direction of time. Indeed, physicists have long struggled to describe how such deterministic processes lead to the apparent loss of information embodied in increasing entropy, since the final state contains all of the details needed to reconstruct the initial state. “Information is just as preserved classically as in quantum,” said Sean Carroll, a theoretical physicist at the California Institute of Technology (Caltech) in Pasadena, CA.

 

Beyond the Horizon

It is in the quantum realm, however, that information has raised the most profound conceptual challenges. This is most apparent in the field of quantum gravity, which aims to reconcile quantum mechanics and general relativity.

Traditionally, quantum mechanics plays out on a “stage” of unchanging spacetime, Swingle said. “If you try to make that stage dynamical, as happens in general relativity, where the geometry of spacetime is changing as a function of time, then combining those two things is hard.”

The gravitational and quantum frameworks can usually agree to disagree, since they apply to very large and small scales respectively. However, their conflict becomes unavoidable for physicists studying black holes, which are both extremely massive and relatively compact. In this reconciliation effort, information plays a central role.

Once anything falls within a black hole’s “event horizon,” from which even light cannot escape, it should have no more influence on outside space. In particular, any information

 

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A schematic of the Maxwell’s demon thought experiment.