Black Hole Computers

Home , Seth Lloyd

BLACK HOLE COMPUTER may sound absurd but is proving to be a useful conceptual tool for researchers studying cosmology and fundamental physics. And if physicists are able to create black holes in particle accelerators—as some predict will be possible within a decade—they may actually observe them perform computation.

AEGRE FRAGILIS catelli conubium santet incredibiliter quinquennalis appar at us bellis.Catelli suffragarit perspicax ﬁ ducia suis, quod pretosius umbraculi adquireret Caesar. Cathedras agnascor quinquennalis saburre. quod pretosius umbraculi adquireret Caesar.

COPYRIGHT 2004 SCIENTIFIC AMERICAN, INC. In keeping with the spirit of the age, researchers can think of the laws of physics as computer programs and the universe as a computer BY SETH LLOYD AND Y. JACK NG BLACK HOLE COMPUTERS

hat is the difference between a computer and a black hole? This question sounds like the start of a Microsoft joke, but Wit is one of the most profound problems in physics today. Most people think of computers as specialized gizmos: stream- lined boxes sitting on a desk or ﬁ ngernail-size chips embedded in high-tech coffeepots. But to a physicist, all physical systems are computers. Rocks, atom bombs and galaxies may not run Linux, but they, too, register and process information. Every electron, photon and other elementary particle stores bits of data, and every time two such particles interact, those bits are transformed. Physi- cal existence and information content are inextricably linked. As physicist John Wheeler of Princeton University says, “It from bit.” JEAN-FRANCOIS PODEVIN

www.sciam.com SCIENTIFIC AMERICAN 53 COPYRIGHT 2004 SCIENTIFIC AMERICAN, INC. Black holes might seem like the ex- information. The principle itself is not Paola Zizzi of the University of Padova ception to the rule that everything com- new. In the 19th century the founders says, “It from qubit.” putes. Inputting information into them of statistical mechanics developed what presents no diffi culty, but according to would later be called information theory When Gigahertz Is Too Slow Einstein’s general theory of relativity, to explain the laws of thermodynamics. the confluence of physics and in- getting information out is impossible. At first glance, thermodynamics and formation theory fl ows from the central Matter that enters a hole is assimilated, information theory are worlds apart: maxim of quantum mechanics: at bot- the details of its composition lost irre- one was developed to describe steam en- tom, nature is discrete. A physical sys- trievably. In the 1970s Stephen Hawking gines, the other to optimize communica- tem can be described using a fi nite num- of the University of Cambridge showed tions. Yet the thermodynamic quantity ber of bits. Each particle in the system that when quantum mechanics is taken called entropy, which limits the ability acts like the logic gate of a computer. Its into account, black holes do have an out- of an engine to do useful work, turns spin “axis” can point in one of two di- put: they glow like a hot coal. In Hawk- out to be proportional to the number of rections, thereby encoding a bit, and can ing’s analysis, this radiation is random, bits registered by the positions and ve- fl ip over, thereby performing a simple however. It carries no information about locities of the molecules in a substance. computational operation. what went in. If an elephant fell in, an The invention of quantum mechanics in The system is also discrete in time. elephant’s worth of energy would come the 20th century put this discovery on a It takes a minimum amount of time to out—but the energy would be a hodge- fi rm quantitative foundation and intro- fl ip a bit. The exact amount is given by podge that could not be used, even in duced scientists to the remarkable con- a theorem named after two pioneers of principle, to re-create the animal. cept of quantum information. The bits the physics of information processing, That apparent loss of information that make up the universe are quantum Norman Margolus of the Massachusetts poses a serious conundrum, because the bits, or “qubits,” with far richer proper- Institute of Technology and Lev Levitin laws of quantum mechanics preserve in- ties than ordinary bits. of Boston University. This theorem is formation. So other scientists, includ- Analyzing the universe in terms of related to the Heisenberg uncertainty ing Leonard Susskind of Stanford Uni- bits and bytes does not replace analyz- principle, which describes the inherent versity, John Preskill of the California ing it in conventional terms such as force trade-offs in measuring physical quanti- Institute of Technology and Gerard ’t and energy, but it does uncover new and ties, such as position and momentum or Hooft of the University of Utrecht in surprising facts. In the fi eld of statisti- time and energy. The theorem says that the Netherlands, have argued that the cal mechanics, for example, it unknot- the time it takes to fl ip a bit, t, depends outgoing radiation is not, in fact, ran- ted the paradox of Maxwell’s demon, on the amount of energy you apply, E. dom—that it is a processed form of the a contraption that seemed to allow The more energy you apply, the shorter matter that falls in [see “Black Holes for perpetual motion. In recent years, the time can be. Mathematically, the and the Information Paradox,” by Leon- we and other physicists have been ap- rule is t ≥ h/4E, where h is Planck’s con- ard Susskind; Scientifi c American, plying the same insights to cosmology stant, the main parameter of quantum April 1997]. This past summer Hawk- and fundamental physics: the nature of theory. For example, one type of experi- ing came around to their point of view. black holes, the fi ne-scale structure of mental quantum computer stores bits on Black holes, too, compute. spacetime, the behavior of cosmic dark protons and uses magnetic fi elds to fl ip Black holes are merely the most ex- energy, the ultimate laws of nature. The them. The operations take place in the otic example of the general principle universe is not just a giant computer; it is minimum time allowed by the Margo- that the universe registers and processes a giant quantum computer. As physicist lus-Levitin theorem. From this theorem, a huge variety of conclusions can be drawn, from lim- Overview/Cosmic Computers its on the geometry of spacetime to the ■ Merely by existing, all physical systems store information. By evolving computational capacity of the universe dynamically in time, they process that information. The universe computes. as a whole. As a warm-up, consider the ■ If information can escape from black holes, as most physicists now suspect, limits to the computational power of a black hole, too, computes. The size of its memory space is proportional ordinary matter—in this case, one kilo- to the square of its computation rate. The quantum-mechanical nature of gram occupying the volume of one liter. information is responsible for this computational ability; without quantum We call this device the ultimate laptop. effects, a black hole would destroy, rather than process, information. Its battery is simply the matter it- ■ The laws of physics that limit the power of computers also determine the self, converted directly to energy per precision with which the geometry of spacetime can be measured. The Einstein’s famous formula E = mc2. precision is lower than physicists once thought, indicating that discrete Putting all this energy into fl ipping bits, “atoms” of space and time may be larger than expected. the computer can do 1051 operations per second, slowing down gradually as the

54 SCIENTIFIC AMERICAN NOVEMBER 2004 COPYRIGHT 2004 SCIENTIFIC AMERICAN, INC. EXTREME COMPUTING What is a computer? That is a surprisingly complex question, although they may not accept input or give output in a but whatever precise definition one adopts, it is satisfied form that is meaningful to humans. Natural computers are not just by the objects people commonly call “computers” inherently digital: they store data in discrete quantum but also by everything else in the world. Physical objects states, such as the spin of elementary particles. Their can solve a broad class of logic and mathematics problems, instruction set is quantum physics.

INPUT COMPUTATION OUTPUT bits 12 MEMORY: 10 MEMORY: ■ hertz 9

A keyboard and associated circuitry The pulses interact, guided by devices The pulses, having been processed, encode information as voltage pulses such as transistors, which perform are translated into meaningful in a wire. logical operations such as NOT. patterns of light. bits bits SPEED: 10 31 MEMORY: 10 MEMORY: ■ hertz 20 Consisting of one kilogram of hot The particles interact. Collisions can As particles leave the volume, their plasma in a one-liter box, this device be arranged to perform operations properties can be measured and accepts data encoded as particle such as NOT: a collision can cause translated. The system slowly winds positions, velocities and spins. particles to ﬂ ip. down as its energy degrades. bits bits SPEED: 10 16 MEMORY: 10 MEMORY: ■ hertz 35 This black hole consists of one On their descent, particles interact The hole emits radiation, named after kilogram in a volume 10–27 meter much as in the ultimate laptop, except physicist Stephen Hawking. New in radius. Data and instructions are that gravity also plays a role. The theories suggest that the radiation encoded in matter and dropped in. governing laws are not yet understood. carries the computational output. SPEED: 10 SPEED: BLACK HOLE ULTIMATE LAPTOP ORDINARY LAPTOP ALFRED T. KAMAJIAN KAMAJIAN T. ALFRED

www.sciam.com SCIENTIFIC AMERICAN 55 COPYRIGHT 2004 SCIENTIFIC AMERICAN, INC. By preparing the material that falls into a black hole, A HACKER COULD PROGRAM IT to perform any desired computation. energy degrades. The memory capacity 100 giga-gigahertz. In fact, the system Schwarzschild radius, is directly propor- of the machine can be calculated using is too fast to be controlled by a central tional to its mass. thermodynamics. When one kilogram clock. The time it takes a bit to fl ip is ap- A one-kilogram hole has a radius of of matter is converted to energy in a li- proximately equal to the time it takes a about 10–27 meter. (For comparison, ter volume, its temperature is one bil- signal to travel from one bit to its neigh- a proton has a radius of 10–15 meter.) lion kelvins. Its entropy, which is pro- bor. Thus, the ultimate laptop is highly Shrinking the computer does not change portional to the energy divided by the parallel: it acts not as a single processor its energy content, so it can perform 1051 temperature, corresponds to 1031 bits of but as a vast array of processors, each operations per second, just as before. information. The ultimate laptop stores working almost independently and com- What does change is the memory capac- information in the microscopic motions municating its results to the others com- ity. When gravity is insignifi cant, the and positions of the elementary particles paratively slowly. total storage capacity is proportional to zipping around inside it. Every single bit By comparison, a conventional com- the number of particles and thus to the allowed by the laws of thermodynamics puter fl ips bits at about 109 times per sec- volume. But when gravity dominates, it is put to use. ond, stores about 1012 bits and contains interconnects the particles, so collective- Whenever particles interact, they a single processor. If Moore’s law could ly they are capable of storing less infor- can cause one another to fl ip. This pro- be sustained, your descendants would be mation. The total storage capacity of a cess can be thought of in terms of a pro- able to buy an ultimate laptop midway black hole is proportional to its surface gramming language such as C or Java: through the 23rd century. Engineers area. In the 1970s Hawking and Jacob the particles are the variables, and their would have to fi nd a way to exert precise Bekenstein of the Hebrew University of interactions are operations such as ad- control on the interactions of particles Jerusalem calculated that a one-kilo- dition. Each bit can fl ip 1020 times per in a plasma hotter than the sun’s core, gram black hole can register about 1016 second, equivalent to a clock speed of and much of the communications band- bits—much less than the same computer width would be taken up in controlling before it was compressed. the computer and dealing with errors. In compensation, the black hole Engineers would also have to solve some is a much faster processor. In fact, the Weak magnetic field –35 (low energy) knotty packaging problems. amount of time it takes to fl ip a bit, 10 In a sense, however, you can already second, is equal to the amount of time it purchase such a device, if you know the takes light to move from one side of the right people. A one-kilogram chunk of computer to the other. Thus, in contrast matter converted completely to ener- to the ultimate laptop, which is highly Time gy—this is a working defi nition of a 20- parallel, the black hole is a serial com- megaton hydrogen bomb. An exploding puter. It acts as a single unit. nuclear weapon is processing a huge How would a black hole computer Strong magnetic field amount of information, its input given work in practice? Input is not problem- (high energy) by its initial confi guration and its output atic: just encode the data in the form of given by the radiation its emits. matter or energy and throw it down the hole. By properly preparing the material From Nanotech to Xennotech that falls in, a hacker should be able to Time if any chunk of matter is a com- program the hole to perform any desired puter, a black hole is nothing more or computation. Once the material enters FIRST LAW of quantum computation is less than a computer compressed to its a hole, it is gone for good; the so-called that computation takes energy. The smallest possible size. As a computer event horizon demarcates the point of no spin of a proton encodes a single bit, shrinks, the gravitational force that its return. The plummeting particles interact which can be inverted by applying a components exert on one another be- with one another, performing computa- magnetic fi eld. The stronger the fi eld is—the more energy it applies—the comes stronger and eventually grows so tion for a fi nite time before reaching the faster the proton will fl ip. intense that no material object can es- center of the hole—the singularity—and

cape. The size of a black hole, called the ceasing to exist. What happens to matter KAMAJIAN T. ALFRED

56 SCIENTIFIC AMERICAN NOVEMBER 2004 COPYRIGHT 2004 SCIENTIFIC AMERICAN, INC. as it gets squished together at the singularity depends on the details of quantum CLASSIFYING COMPUTERS gravity, which are as yet unknown. The output takes the form of Hawk- The ultimate laptop and black hole computer embody two different approaches ing radiation. A one-kilogram hole gives to increasing computing power. The ultimate laptop is the supreme parallel off Hawking radiation and, to conserve computer: an array of processors working simultaneously. The black hole is the supreme serial computer: a single processor executing instructions one at a time. energy, decreases in mass, disappearing altogether in a mere 10–21 second. The peak wavelength of the radiation equals the radius of the hole; for a one-kilo- 0.1 m Ultimate laptop consists gram hole, it corresponds to extremely of a collection of particles intense gamma rays. A particle detector that encode and process can capture this radiation and decode it bits. Each can execute an instruction in 10–20 second. for human consumption. In that time, signals can Hawking’s study of the radiation move a distance of only –12 that bears his name is what overturned 3 × 10 meter, which is roughly the spacing between the conventional wisdom that black holes particles. Therefore, communication is much are objects from which nothing whatso- Signal ever can escape [see “The Quantum Me- slower than computation. Subregions of the computer chanics of Black Holes,” by Stephen W. work almost independently. Hawking; Scientifi c American, Janu- ary 1977]. The rate at which black holes 3 × 10–12 m radiate is inversely related to their size, Black hole so big black holes, such as those at the Black hole computer also center of galaxies, lose energy much more consists of a collection slowly than they gobble up matter. In the of particles. Because of future, however, experimenters may be gravity, they encode fewer bits, giving more energy able to create tiny holes in particle accel- 1.5 × 10–27 m per bit. Each can execute an erators, and these holes should explode instruction in 10–35 second, almost immediately in a burst of radia- which is the time it takes for a signal to cross the hole. tion. A black hole can be thought of not Therefore, communication as a fi xed object but as a transient congre- is as fast as computation. gation of matter that performs computa- The computer operates as a single unit. tion at the maximum rate possible. Escape Plan the real question is whether two or more systems remain correlated how distant it may be. The information Hawking radiation returns the answer across the reaches of space and time. can be decoded using the results of the of the computation or merely gibber- Entanglement enables teleportation, in measurement as the key [see “Quantum ish. The issue remains contentious, but which information is transferred from Teleportation,” by Anton Zeilinger; Sci- most physicists, including Hawking, one particle to another with such fi del- entifi c American, April 2000]. now think that the radiation is a highly ity that the particle has effectively been A similar procedure might work for processed version of the information beamed from one location to another at black holes. Pairs of entangled photons that went into the hole during its forma- up to the speed of light. materialize at the event horizon. One tion. Although matter cannot leave the The teleportation procedure, which of the photons fl ies outward to become hole, its information content can. Un- has been demonstrated in the labora- the Hawking radiation that an observer derstanding precisely how is one of the tory, fi rst requires that two particles be sees. The other falls in and hits the sin- liveliest questions in physics right now. entangled. Then a measurement is per- gularity together with the matter that Last year Gary Horowitz of the Uni- formed on one of the particles jointly formed the hole in the fi rst place. The versity of California at Santa Barbara with some matter that contains informa- annihilation of the infalling photon acts and Juan Maldacena of the Institute for tion to be teleported. The measurement as a measurement, transferring the in- Advanced Study in Princeton, N.J., out- erases the information from its original formation contained in the matter to the lined one possible mechanism. The es- location, but because of entanglement, outgoing Hawking radiation. cape hatch is entanglement, a quantum that information resides in an encoded The difference from laboratory tele-

ALFRED T. KAMAJIAN KAMAJIAN T. ALFRED phenomenon in which the properties of form on the second particle, no matter portation is that the results of this “mea-

www.sciam.com SCIENTIFIC AMERICAN 57 COPYRIGHT 2004 SCIENTIFIC AMERICAN, INC. Evolution of Black Hole Theory “Objects so dense that nothing, not even light, can escape”— energy can leak out of a black hole, and most now think this deﬁ nition of black holes has become a cliché of newspaper that information (which describes the form that the energy articles and freshman astronomy lectures. But it is probably takes) can, too. These diagrams show a black hole from a wrong. Physicists have argued since the mid-1970s that hypothetical viewpoint outside spacetime.

CLASSICAL VIEW, based on Virtual-particle pair HOROWITZ-MALDACENA MODEL prequantum physics, holds suggests that the outgoing that a blob of matter falling particle carries away not just through the hole’s outer raw mass but also information. rim—the event horizon—can The particle is quantum- neither escape nor send out its mechanically entangled with information. It hits the center its infalling partner, which in of the hole—the singularity— turn gets entangled with the where its mass is assimilated blob. The entanglement beams and its information lost. the blob’s information out.

Matter Event horizon

HAWKING MODEL is a ﬁ rst stab at considering quantum effects. Pairs of virtual particles materialize at the event horizon (red and blue balls). One member of each Quantum pair, like other matter, falls teleportation to the singularity. Its partner ﬂ i e s o u t w a r d . T h e p a r t i c l e spins are random and do not Singularity carry any information about the infalling blob.

surement” are not needed to decode the past June one of us (Lloyd) showed that in waves in the branes and can eventually information that was teleported. Horo- the Horowitz-Maldacena mechanism is leak out. Earlier this year Samir Mathur witz and Maldacena argued that the an- robust; it does not depend on what ex- of Ohio State University and his collabo- nihilation does not have a variety of pos- actly the fi nal state is, as long as there is rators modeled a black hole as a giant sible outcomes—only one. An observer one. It still seems to lead to a small loss of tangle of strings. This “fuzzyball” acts on the outside can calculate this unique information, however. as a repository of the information car- outcome using basic physics and thereby Other researchers have proposed es- ried by things that fall into the black unlock the information. It is this conjec- cape mechanisms that also rely on weird hole. It emits radiation that refl ects this ture that falls outside the usual formula- quantum phenomena. In 1996 Andrew information. Hawking, in his recent ap- tion of quantum mechanics. Though con- Strominger and Cumrun Vafa of Har- proach, has argued that quantum fl uc- troversial, it is plausible. Just as the ini- vard University suggested that black holes tuations prevent a well-defi ned event ho- tial singularity at the start of the universe are composite bodies made up of multi- rizon from ever forming [see “Hawking may have had only one possible state, so dimensional structures called branes, a Theory,” by Graham P. Collins; News it is possible that the fi nal singularities in- which arise in string theory. Informa- Scan, October]. The jury is still out on

side black holes have a unique state. This tion falling into the black hole is stored all these ideas. KAMAJIAN T. ALFRED

Cyberspacetime The process of mapping the geometry the energy available to each satellite (so the properties of black holes are of spacetime is a kind of computation, in that their clocks tick more slowly). Ei- inextricably intertwined with those of which distances are gauged by transmit- ther way, the measurement becomes less spacetime. Thus, if holes can be thought ting and processing information. One precise. Mathematically, in the time it of as computers, so can spacetime it- way to do this is to fi ll a region of space takes to map a region of radius R, the self. Quantum mechanics predicts that with a swarm of Global Positioning Sys- total number of ticks by all the satellites 2 2 spacetime, like other physical systems, tem satellites, each containing a clock is R /lP . If each satellite ticks precisely is discrete. Distances and time intervals and a radio transmitter [see illustration once during the mapping process, the cannot be measured to infi nite precision; on next page]. To measure a distance, satellites are spaced out by an average 1/3 2/3 on small scales, spacetime is bubbly and a satellite sends a signal and times how distance of R lP . Shorter distances foamy. The maximum amount of in- long it takes to arrive. The precision of can be measured in one subregion but formation that can be put into a region the measurement depends on how fast only at the expense of reduced precision of space depends on how small the bits the clocks tick. Ticking is a computa- in some other subregion. The argument are, and they cannot be smaller than the tional operation, so its maximum rate is applies even if space is expanding. foamy cells. given by the Margolus-Levitin theorem: This formula gives the precision to Physicists have long assumed that the the time between ticks is inversely pro- which distances can be determined; it is size of these cells is the Planck length (lP) portional to the energy. applicable when the measurement appa- of 10–35 meter, which is the distance at The energy, in turn, is also limited. ratus is just on the verge of becoming a which both quantum fl uctuations and If you give the satellites too much energy black hole. Below the minimum scale, gravitational effects are important. If or pack them too closely together, they spacetime geometry ceases to exist. That so, the foamy nature of spacetime will will form a black hole and will no longer level of precision is much, much bigger always be too minuscule to observe. But be able to participate in mapping. (The than the Planck length. To be sure, it is as one of us (Ng) and Hendrik van Dam hole will still emit Hawking radiation, still very small. The average imprecision of the University of North Carolina at but that radiation has a wavelength the in measuring the size of the observable Chapel Hill and Frigyes Károlyházy of size of the hole itself and so is not useful universe is about 10–15 meter. Neverthe- Eötvös Loránd University in Hungary for mapping features on a fi ner scale.) less, such an imprecision might be de- have shown, the cells are actually much The maximum total energy of the con- tectable by precise distance-measuring larger and, indeed, have no fi xed size: stellation of satellites is proportional to equipment, such as future gravitational- the larger a region of spacetime, the larg- the radius of the region being mapped. wave observatories. er its constituent cells. At fi rst, this asser- Thus, the energy increases more From a theorist’s point of view, the tion may seem paradoxical—as though slowly than the volume of the region broader signifi cance of this result is that the atoms in an elephant were bigger does. As the region gets bigger, the car- it provides a new way to look at black than those in a mouse. In fact, Lloyd has tographer faces an unavoidable trade- holes. Ng has shown that the strange derived it from the same laws that limit off: reduce the density of satellites (so scaling of spacetime fl uctuations with the power of computers. they are spaced farther apart) or reduce the cube root of distances provides a back-door way to derive the Bekenstein- SETH LLOYD and Y. JACK NG bridge the two most exciting fi elds of theoretical physics: Hawking formula for black hole memo- quantum information theory and the quantum theory of gravity. Lloyd, professor of quan- ry. It also implies a universal bound for tum-mechanical engineering at the Massachusetts Institute of Technology, designed the all black hole computers: the number of fi rst feasible quantum computer. He works with various teams to construct and operate bits in the memory is proportional to the quantum computers and communications systems. Ng, professor of physics at the Uni- square of the computation rate. The pro- versity of North Carolina at Chapel Hill, studies the fundamental nature of spacetime. He portionality constant is Gh/c5—math- THE AUTHORS has proposed various ways to look for the quantum structure of spacetime experimen- ematically demonstrating the linkage tally. Both researchers say their most skeptical audience is their family. When Lloyd between information and the theories told his daughters that everything is made of bits, one responded bluntly: “You’re wrong, of special relativity (whose defining Daddy. Everything is made of atoms, except light.” Ng has lost credibility on the subject parameter is the speed of light, c), gen- because he is always having to turn to his sons for help with his computer. eral relativity (the gravitational con-

www.sciam.com SCIENTIFIC AMERICAN 59 COPYRIGHT 2004 SCIENTIFIC AMERICAN, INC. Computing Spacetime Measuring distances and time intervals is a type of computation and falls under the same constraints that computers do. It turns out that measurement is a much more slippery process than physicists had thought.

TO MAP A VOLUME of space, you might use a constellation of Global Positioning System –+ 1 x 10–22 cm satellites. They make measurements by sending signals and timing their arrival. For maximum precision, you need lots of satellites. But the number of satellites is limited: too many, and the entire system will collapse to a black hole. –+ 2 x 10–22 cm To measure a region twice the size, you can use twice as many satellites. Because the volume is eight times as great, the satellites must be spaced farther apart. Each covers a larger subregion ▲ RADIUS: 100 km + 3 x 10–22 cm and can devote less attention to individual SATELLITES: 4 – measurements, reducing their precision. SPACING: 90 km

▼ RADIUS: 200 km SATELLITES: 8 MEASUREMENT UNCERTAINTY is thus not fi xed SPACING: 150 km but can vary with the size of the object being INCREASE IN ERROR: 26% measured. The larger the object is, the fuzzier its detailed structure. That differs from everyday life, in which the measurement imprecision is independent of the object and depends only on how fi nely subdivided your ruler is. It is as though your choice of what to measure affects the fi n e - s c a l e s t r u c t u r e o f s p a c e t i m e .

it also follows directly visible matter, the dark matter and the from the fundamental so-called dark energy that is causing quantum limits to the pre- the universe to expand at an accelerated cision of measurement. rate. The observed cosmic energy density is about 10–9 joule per cubic meter, so The Answer Is ... 42 the universe contains 1072 joules of en- the principles of computation ergy. According to the Margolus-Levitin can be applied not just to the most com- theorem, it can perform up to 10106 op- stant, G) and quantum mechanics (h). pact computers (black holes) and tiniest erations per second, for a total of 10123 Perhaps most signifi cantly, the result possible computers (spacetime foam) but operations during its lifetime so far. In leads directly to the holographic prin- also to the largest: the universe. The uni- other words, the universe has performed ciple, which suggests that our three-di- verse may well be infi nite in extent, but it the maximum possible number of opera- mensional universe is, in some deep but has existed a fi nite length of time, at least tions allowed by the laws of physics. unfathomable way, two-dimensional. in its present form. The observable part To calculate the total memory capaci- The maximum amount of information is currently some tens of billions of light- ty of conventional matter, such as atoms, that any region of space can store seems years across. For us to know the results one can apply the standard methods of to be proportional not to its volume but of a computation, it must have taken statistical mechanics and cosmology. to its surface area [see “Information in place within this expanse. Matter can embody the most informa- the Holographic Universe,” by Jacob D. The above analysis of clock ticks also tion when it is converted to energetic, Bekenstein; Scientifi c American, Au- gives the number of operations that can massless particles, such as neutrinos gust 2003]. The holographic principle is have occurred in the universe since it be- or photons, whose entropy density is normally thought to arise from the un- gan: 10123. Compare this limit with the proportional to the cube of their tem-

known details of quantum gravity, yet behavior of the matter around us—the perature. The energy density of the par- KAMAJIAN T. ALFRED

ticles (which determines the number of had time to fl ip no more than once over far as we can tell, it is not producing a operations they can perform) goes as the course of cosmic history. So these single answer to a single question, like the fourth power of their temperature. unconventional bits are mere spectators the giant Deep Thought computer in the Therefore, the total number of bits is just to the computations performed at much science-fi ction classic The Hitchhiker’s the number of operations raised to the higher speeds by the smaller number of Guide to the Galaxy. Instead the uni- three-fourths power. For the whole uni- conventional bits. Whatever the dark verse is computing itself. Powered by verse, that amounts to 1092 bits. If the energy is, it is not doing very much com- Standard Model software, the universe particles contain some internal struc- putation. It does not have to. Supplying computes quantum fields, chemicals, ture, the number of bits might be some- the missing mass of the universe and ac- bacteria, human beings, stars and gal- what higher. These bits fl ip faster than celerating its expansion are simple tasks, axies. As it computes, it maps out its they intercommunicate, so the conven- computationally speaking. own spacetime geometry to the ultimate tional matter is a highly parallel com- What is the universe computing? As precision allowed by the laws of physics. puter, like the ultimate laptop and unlike Computation is existence. the black hole. These results spanning ordinary As for dark energy, physicists do not computers, black holes, spacetime foam know what it is, let alone how to cal- and cosmology are testimony to the culate how much information it can unity of nature. They demonstrate store. But the holographic prin- DARK ENERGY the conceptual interconnec- ciple implies that the universe SPEED: >10–18 hertz tions of fundamental physics. MEMORY: <10123 bits can store a maximum of 10123 Although physicists do not bits—nearly the same as the yet possess a full theory of total number of operations. quantum gravity, whatever This approximate equality that theory is, they know is not a coincidence. Our it is intimately connected universe is close to its criti- with quantum informa- cal density. If it had been tion. It from qubit. slightly more dense, it might UNIVERSE IS A COMPUTER have undergone gravitational consisting of two types of collapse, just like the matter components. Matter (red) is falling into a black hole. So it highly dynamic; it acts as a high- speed parallel computer. Dark energy meets (or nearly meets) the con- MATTER ditions for maxing out the number SPEED: 1014 hertz (gray) appears to be nearly static; it Universe 92 acts as a lower-speed serial computer. of computations. That maximum MEMORY: 10 bits Together the components have performed 2 2 number is R /lP , which is the same as as many operations as the laws of physics the number of bits given by the holo- allow. Computo, ergo sum. graphic principle. At each epoch in its history, the maximum number of bits MORE TO EXPLORE that the universe can contain is approx- Ultimate Physical Limits to Computation. Seth Lloyd in Nature, Vol. 406, pages 1047–1054; imately equal to the number of opera- August 31, 2000. Preprint available at arxiv.org/abs/quant-ph/9908043 tions it could have performed up to that From Computation to Black Holes and Space-Time Foam. Y. Jack Ng in Physical Review Letters, moment. Vol. 86, No. 14, pages 2946–2949; April 2, 2001. Erratum, Vol. 88, No. 13, article 139902(E); March 14, 2002. gr-qc/0006105 Whereas ordinary matter undergoes Computational Capacity of the Universe. Seth Lloyd in Physical Review Letters, Vol. 88, No. 23, a huge number of operations, dark ener- article 237901Z; June 10, 2002. quant-ph/0110141 gy behaves quite differently. If it encodes The Black Hole Final State. Gary T. Horowitz and Juan Maldacena in Journal of High Energy the maximum number of bits allowed by Physics, JHEP02(2004)008, 2004. hep-th/0310281 the holographic principle, then the over- Information: The New Language of Science. Hans Christian von Baeyer. Harvard University

ALFRED T. KAMAJIAN T. ALFRED whelming majority of those bits have Press, 2004.