Our innate perception that the world is three-dimensional could be an extraordinary illusion.
Hawking's radiation process allowed him to determine the proportionality constant between
black hole entropy and horizon area: black hole entropy is precisely one quarter of the
event horizon's area measured in Planck areas. (The Planck length, about 10-33 centimeter,
is the fundamental length scale related to gravity and quantum mechanics. The Planck area
is its square.) Even in thermodynamic terms, this is a vast quantity of entropy. The entropy
of a black hole one centimeter in diameter would be about 1066 bits, roughly equal to the
thermodynamic entropy of a cube of water 10 billion kilometers on a side.
The World as a Hologram
The GSL allows us to set bounds on the information capacity of any isolated physical
system, limits that refer to the information at all levels of structure down to level
X. In 1980 I began studying the first such bound, called the universal entropy bound,
which limits how much entropy can be carried by a specified mass of a specified size
[see box on opposite page]. A related idea, the holographic bound, was devised in 1995
by Leonard Susskind of Stanford University. It limits how much entropy can be contained
in matter and energy occupying a specified volume of space.
In his work on the holographic bound, Susskind considered any approximately spherical
isolated mass that is not itself a black hole and that fits inside a closed surface of
area A. If the mass can collapse to a black hole, that hole will end up with a horizon
area smaller than A. The black hole entropy is therefore smaller than A/4. According to
the GSL, the entropy of the system cannot decrease, so the mass's original entropy cannot
have been bigger than A/4. It follows that the entropy of an isolated physical system with
boundary area A is necessarily less than A/4. What if the mass does not spontaneously
collapse? In 2000 I showed that a tiny black hole can be used to convert the system to a
black hole not much different from the one in Susskind's argument. The bound is therefore
independent of the constitution of the system or of the nature of level X. It just depends
on the GSL.
We can now answer some of those elusive questions about the ultimate limits of information
storage. A device measuring a centimeter across could in principle hold up to 1066 bits--
a mind-boggling amount. The visible universe contains at least 10100 bits of entropy,
which could in principle be packed inside a sphere a tenth of a light-year across.
Estimating the entropy of the universe is a difficult problem, however, and much
larger numbers, requiring a sphere almost as big as the universe itself, are entirely
But it is another aspect of the holographic bound that is truly astonishing. Namely, that
the maximum possible entropy depends on the boundary area instead of the volume. Imagine
that we are piling up computer memory chips in a big heap. The number of transistors--the
total data storage capacity--increases with the volume of the heap. So, too, does the total
thermodynamic entropy of all the chips. Remarkably, though, the theoretical ultimate
information capacity of the space occupied by the heap increases only with the surface
area. Because volume increases more rapidly than surface area, at some point the entropy
of all the chips would exceed the holographic bound. It would seem that either the GSL or
our commonsense ideas of entropy and information capacity must fail. In fact, what fails
is the pile itself: it would collapse under its own gravity and form a black hole before
that impasse was reached. Thereafter each additional memory chip would increase the mass
and surface area of the black hole in a way that would continue to preserve the GSL.
This surprising result--that information capacity depends on surface area--has a natural
explanation if the holographic principle (proposed in 1993 by Nobelist Gerard 't Hooft of
the University of Utrecht in the Netherlands and elaborated by Susskind) is true. In the
everyday world, a hologram is a special kind of photograph that generates a full three-
dimensional image when it is illuminated in the right manner. All the information
describing the 3-D scene is encoded into the pattern of light and dark areas on the
two-dimensional piece of film, ready to be regenerated. The holographic principle
contends that an analogue of this visual magic applies to the full physical description
of any system occupying a 3-D region: it proposes that another physical theory defined
only on the 2-D boundary of the region completely describes the 3-D physics. If a 3-D
system can be fully described by a physical theory operating solely on its 2-D boundary,
one would expect the information content of the system not to exceed that of the description
on the boundary.
A Universe Painted on Its Boundary
Can we apply the holographic principle to the universe at large? The real universe is
a 4-D system: it has volume and extends in time. If the physics of our universe is
holographic, there would be an alternative set of physical laws, operating on a 3-D
boundary of spacetime somewhere, that would be equivalent to our known 4-D physics.
We do not yet know of any such 3-D theory that works in that way. Indeed, what surface
should we use as the boundary of the universe? One step toward realizing these ideas is
to study models that are simpler than our real universe.
A class of concrete examples of the holographic principle at work involves so-called
anti-de Sitter spacetimes. The original de Sitter spacetime is a model universe first
obtained by Dutch astronomer Willem de Sitter in 1917 as a solution of Einstein's
equations, including the repulsive force known as the cosmological constant. De Sitter's
spacetime is empty, expands at an accelerating rate and is very highly symmetrical. In
1997 astronomers studying distant supernova explosions concluded that our universe now
expands in an accelerated fashion and will probably become increasingly like a de Sitter
spacetime in the future. Now, if the repulsion in Einstein's equations is changed to
attraction, de Sitter's solution turns into the anti-de Sitter spacetime, which has
equally as much symmetry. More important for the holographic concept, it possesses a
boundary, which is located "at infinity" and is a lot like our everyday spacetime.
Using anti-de Sitter spacetime, theorists have devised a concrete example of the
holographic principle at work: a universe described by superstring theory functioning
in an anti-de Sitter spacetime is completely equivalent to a quantum field theory
operating on the boundary of that spacetime [see box above]. Thus, the full majesty
of superstring theory in an anti-de Sitter universe is painted on the boundary of
the universe. Juan Maldacena, then at Harvard University, first conjectured such
a relation in 1997 for the 5-D anti-de Sitter case, and it was later confirmed for
many situations by Edward Witten of the Institute for Advanced Study in Princeton,
N.J., and Steven S. Gubser, Igor R. Klebanov and Alexander M. Polyakov of Princeton
University. Examples of this holographic correspondence are now known for spacetimes
with a variety of dimensions.
This result means that two ostensibly very different theories--not even acting in spaces
of the same dimension--are equivalent. Creatures living in one of these universes would
be incapable of determining if they inhabited a 5-D universe described by string theory
or a 4-D one described by a quantum field theory of point particles. (Of course, the
structures of their brains might give them an overwhelming "commonsense" prejudice in
favor of one description or another, in just the way that our brains construct an innate
perception that our universe has three spatial dimensions; see the illustration on the
The holographic equivalence can allow a difficult calculation in the 4-D boundary
spacetime, such as the behavior of quarks and gluons, to be traded for another,
easier calculation in the highly symmetric, 5-D anti-de Sitter spacetime. The
correspondence works the other way, too. Witten has shown that a black hole in
anti-de Sitter spacetime corresponds to hot radiation in the alternative physics
operating on the bounding spacetime. The entropy of the hole--a deeply mysterious
concept--equals the radiation's entropy, which is quite mundane.
The Expanding Universe
Highly symmetric and empty, the 5-D anti-de Sitter universe is hardly like our
universe existing in 4-D, filled with matter and radiation, and riddled with
violent events. Even if we approximate our real universe with one that has
matter and radiation spread uniformly throughout, we get not an anti-de
Sitter universe but rather a "Friedmann-Robertson-Walker" universe. Most
cosmologists today concur that our universe resembles an FRW universe, one
that is infinite, has no boundary and will go on expanding ad infinitum.
Does such a universe conform to the holographic principle or the holographic bound?
Susskind's argument based on collapse to a black hole is of no help here. Indeed, the
holographic bound deduced from black holes must break down in a uniform expanding
universe. The entropy of a region uniformly filled with matter and radiation is
truly proportional to its volume. A sufficiently large region will therefore violate
the holographic bound.
In 1999 Raphael Bousso, then at Stanford, proposed a modified holographic bound, which
has since been found to work even in situations where the bounds we discussed earlier
cannot be applied. Bousso's formulation starts with any suitable 2-D surface; it may be
closed like a sphere or open like a sheet of paper. One then imagines a brief burst of
light issuing simultaneously and perpendicularly from all over one side of the surface.
The only demand is that the imaginary light rays are converging to start with. Light
emitted from the inner surface of a spherical shell, for instance, satisfies that
requirement. One then considers the entropy of the matter and radiation that these
imaginary rays traverse, up to the points where they start crossing. Bousso conjectured
that this entropy cannot exceed the entropy represented by the initial surface--one
quarter of its area, measured in Planck areas. This is a different way of tallying
up the entropy than that used in the original holographic bound. Bousso's bound refers
not to the entropy of a region at one time but rather to the sum of entropies of locales
at a variety of times: those that are "illuminated" by the light burst from the surface.
Bousso's bound subsumes other entropy bounds while avoiding their limitations. Both the
universal entropy bound and the 't Hooft-Susskind form of the holographic bound can be
deduced from Bousso's for any isolated system that is not evolving rapidly and whose
gravitational field is not strong. When these conditions are overstepped--as for a
collapsing sphere of matter already inside a black hole--these bounds eventually fail,
whereas Bousso's bound continues to hold. Bousso has also shown that his strategy can
be used to locate the 2-D surfaces on which holograms of the world can be set up.
Researchers have proposed many other entropy bounds. The proliferation of variations on
the holographic motif makes it clear that the subject has not yet reached the status of
physical law. But although the holographic way of thinking is not yet fully understood,
it seems to be here to stay. And with it comes a realization that the fundamental belief,
prevalent for 50 years, that field theory is the ultimate language of physics must give way.
Fields, such as the electromagnetic field, vary continuously from point to point, and they
thereby describe an infinity of degrees of freedom. Superstring theory also embraces an
infinite number of degrees of freedom. Holography restricts the number of degrees of
freedom that can be present inside a bounding surface to a finite number; field theory
with its infinity cannot be the final story. Furthermore, even if the infinity is tamed,
the mysterious dependence of information on surface area must be somehow accommodated.
Holography may be a guide to a better theory. What is the fundamental theory like? The
chain of reasoning involving holography suggests to some, notably Lee Smolin of the
Perimeter Institute for Theoretical Physics in Waterloo, that such a final theory must
be concerned not with fields, not even with spacetime, but rather with information
exchange among physical processes. If so, the vision of information as the stuff the
world is made of will have found a worthy embodiment.
Jacob D. Bekenstein has contributed to the foundation of black hole thermodynamics
and to other aspects of the connections between information and gravitation. He is
Polak Professor of Theoretical Physics at the Hebrew University of Jerusalem, a member
of the Israel Academy of Sciences and Humanities, and a recipient of the Rothschild
Prize. Bekenstein dedicates this article to John Archibald Wheeler (his Ph.D. supervisor 30 years ago).
Wheeler belongs to the third generation of Ludwig Boltzmann's students: Wheeler's Ph.D. adviser, Karl
Herzfeld, was a student of Boltzmann's student Friedrich Hasenöhrl.
In the 1950s, while conducting research into the beliefs of LSD as a psychotherapeutic tool,
Grof had one female patient who suddenly became convinced she had assumed the identity of a
female of a species of prehistoric reptile. During the course of her hallucination, she not
only gave a richly detailed description of what it felt like to be encapsuled in such a form,
but noted that the portion of the male of the species's anatomy was a patch of colored scales
on the side of its head.
What was startling to Grof was that although the woman had no prior knowledge about such
things, a conversation with a zoologist later confirmed that in certain species of reptiles
colored areas on the head do indeed play an important role as triggers of sexual arousal.
The woman's experience was not unique. During the course of his research, Grof encountered
examples of patients regressing and identifying with virtually every species on the
evolutionary tree (research findings which helped influence the man-into-ape scene
in the movie Altered States). Moreover, he found that such experiences frequently
contained obscure zoological details which turned out to be accurate.
In later research, Grof found the same range of phenomena manifested in therapy sessions
which did not involve the use of drugs. Because the common element in such experiences
appeared to be the transcending of an individual's consciousness beyond the usual boundaries
of ego and/or limitations of space and time, Grof called such manifestations "transpersonal
experiences", and in the late '60s he helped found a branch of psychology called "transpersonal
psychology" devoted entirely to their study. Although Grof's newly founded Association of
Transpersonal Psychology garnered a rapidly growing group of like-minded professionals and
has become a respected branch of psychology, for years neither Grof or any of his colleagues
were able to offer a mechanism for explaining the bizarre psychological phenomena they were
witnessing. But that has changed with the advent of the holographic paradigm.
As Grof recently noted, if the mind is actually part of a continuum, a labyrinth that is
connected not only to every other mind that exists or has existed, but to every atom,
organism, and region in the vastness of space and time itself, the fact that it is able
to occasionally make forays into the labyrinth and have transpersonal experiences no
longer seems so strange.
The holographic prardigm also has implications for so-called
hard sciences like biology. Keith Floyd, a psychologist at Virginia Intermont College, has
pointed out that if the concreteness of reality is but a holographic illusion, it would no
longer be true to say the brain produces consciousness. Rather, it is consciousness that
creates the appearance of the brain -- as well as the body and everything else around us
we interpret as physical. Such a turnabout in the way we view biological structures has
caused researchers to point out that medicine and our understanding of the healing process
could also be transformed by the holographic paradigm. If the apparent physical structure
of the body is but a holographic projection of consciousness, it becomes clear that each of
us is much more responsible for our health than current medical wisdom allows. What we now
view as miraculous remissions of disease may actually be due to changes in consciousness
which in turn effect changes in the hologram of the body.
Similarly, controversial new healing techniques such as visualization may work so well
because in the holographic domain of thought images are ultimately as real as "reality".
Even visions and experiences involving "non-ordinary" reality become explainable under
the holographic paradigm. In his book "Gifts of Unknown Things," biologist Lyall Watson
discribes his encounter with an Indonesian shaman woman who, by performing a ritual dance,
was able to make an entire grove of trees instantly vanish into thin air. Watson relates
that as he and another astonished onlooker continued to watch the woman, she caused the
trees to reappear, then "click" off again and on again several times in succession.
Although current scientific understanding is incapable of explaining such events,
experiences like this become more tenable if "hard" reality is only a holographic projection.
Perhaps we agree on what is "there" or "not there" because what we call consensus reality is
formulated and ratified at the level of the human unconscious at which all minds are infinitely
interconnected. If this is true, it is the most profound implication of the holographic paradigm
of all, for it means that experiences such as Watson's are not commonplace only because we have
not programmed our minds with the beliefs that would make them so. In a holographic universe
there are no limits to the extent to which we can alter the fabric of reality.
What we perceive as reality is only a canvas waiting for us to draw upon it any picture
we want. Anything is possible, from bending spoons with the power of the mind to the
phantasmagoric events experienced by Castaneda during his encounters with the Yaqui
brujo don Juan, for magic is our birthright, no more or less miraculous than our
ability to compute the reality we want when we are in our dreams. Indeed, even our
most fundamental notions about reality become suspect, for in a holographic universe,
as Pribram has pointed out, even random events would have to be seen as based on
holographic principles and therefore determined. Synchronicities or meaningful
coincidences suddenly makes sense, and everything in reality would have to be
seen as a metaphor, for even the most haphazard events would express some underlying symmetry.
Whether Bohm and Pribram's holographic paradigm becomes accepted in science or dies an ignoble
death remains to be seen, but it is safe to say that it has already had an influence on the
thinking of many scientists. And even if it is found that the holographic model does not
provide the best explanation for the instantaneous communications that seem to be passing
back and forth between subatomic particles, at the very least, as noted by Basil Hiley,
a physicist at Birbeck College in London, Aspect's findings "indicate that we must be
prepared to consider radically new views of reality".