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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
AB AB AB AB AB AB
A schematic of the Maxwell’s demon thought experiment.