FEATURE | hogan’s noIse
Time
4-dimensional
flat spacetime
(no gravity)
over time. Hawking showed that for that
to be true, a black hole must increase its
entropy by an amount greater than the
entropy carried by a body that falls into
the hole.
Bekenstein calculated that the entropy
of a black hole is entirely determined by
its effective surface area, or event horizon,
not its volume. The event horizon is the
imaginary surface that surrounds a black
hole and marks the point of no return:
Any entity— be it a planet or a string
quartet — that gets closer to the hole than
the event horizon is doomed to fall in.
In the 1990s, two scientists dramatically extended this idea into a “
holographic principle” that states that a
volume of space can be entirely described
by what happens on its boundary. Nobel
laureate Gerard ’t Hooft of the University of Utrecht in the Netherlands first
proposed the idea. Stanford physicist
Leonard Susskind then gave the idea
a more precise description according
to the precepts of string theory, which
holds that each elementary particle can
be represented by tiny, vibrating snippets of string in nine or 10 dimensions of
space, rather than the usual three.
Applying the holographic principle
to the real world has proven challeng-
ing. It can be difficult to relate a theory
about a volume of space with, say, five
dimensions, to a simpler theory that
envisions a universe that is restricted
to the boundary, or surface, of that vol-
ume — a universe with one less dimen-
sion. But in 1997, Juan Maldacena,
Hogan is hoping that his holographic
uncertainty principle will be a similarly
important result in a full theory of quan-
tum gravity.”
This larger size of the tiles within the
volume becomes noticeable only at very
large distances from the holographic sur-
face, Hogan notes. A sensitive device that
could measure changes in length in two
perpendicular directions at large dis-
tances from the surface might therefore
be sensitive to this fundamental limit of
encoding information, he says.
now at the Institute
for Advanced Study in
Princeton, N.J., used
string theory to show
that in one model, there
truly is a one-to-one correspondence between
the description of a volume of space in a higher
dimensional theory that
includes gravity and a
lower dimensional theory — the boundary of
that space — in which
gravity plays no role.
Consider, once again,
According to the holo-
graphic principle, the infor-
mation on the surface must
be exactly the same as that
contained within the vol-
ume. But that can be true
only if the volume is much
grainier, or blurrier, than
the Planck-length tiles on
the surface. In other words,
the tiles that fill the volume are much
bigger than those on the surface. Effec-
tively, the blurriness of the information
encoded on the surface becomes magni-
fied within the volume enclosed by the
hologram.
Hogan calls this magnification “the
holographic uncertainty principle.” He
sees it as an extension of the uncertainty
principle proposed by German physicist
Werner Heisenberg in 1927. Heisenberg
famously noted that the position and
momentum of a subatomic particle cannot both be precisely measured at the
same time.
“I think Hogan must see himself as a sort
of latter-day Heisenberg,” says Herzog.
“Just as Heisenberg provided us with
an uncertainty principle without a full-fledged theory of quantum mechanics,
5-dimensional
anti–de Sitter space
(supergravity)
Holographic twist according to physicist Juan maldacena’s
holographic principle, a theory of gravity in a particular 5-D model
of spacetime (right) called anti–de sitter space is equivalent to a
theory without gravity in a 4-D flat spacetime.
