arX

iv:q

uant

-ph/

0101

077

v1

17 J

an 2

001

100 Years of the Quantum

Max TegmarkDept. of Physics, Univ. of Pennsylvania, Philadelphia, PA 19104; max@physics.upenn.edu

John Archibald WheelerPrinceton University, Department of Physics, Princeton, NJ 08544; jawheeler@pupgg.princeton.edu

(An abbreviated version of this article, with much better graphics,was published in the Feb. 2001 issue of Scientific American, p.68-75.)

Abstract: As quantum theory celebrates its 100th birthday, spectacular successes are mixed withoutstanding puzzles and promises of new technologies. This article reviews both the successes ofquantum theory and the ongoing debate about its consequences for issues ranging from quantumcomputation to consciousness, parallel universes and the nature of physical reality. We argue thatmodern experiments and the discovery of decoherence have have shifted prevailing quantum inter-pretations away from wave function collapse towards unitary physics, and discuss quantum processesin the framework of a tripartite subject-object-environment decomposition. We conclude with somespeculations on the bigger picture and the search for a unified theory of quantum gravity.

“...in a few years, all the great physical constants willhave been approximately estimated, and [...] the only oc-cupation which will then be left to the men of science willbe to carry these measurement to another place of deci-mals.” As we enter the 21st century amid much brouhahaabout past achievements, this sentiment may sound fa-miliar. Yet the quote is from James Clerk Maxwell anddates from his 1871 Cambridge inaugural lecture express-ing the mood prevalent at the time (albeit a mood hedisagreed with). Three decades later, on December 14,1900, Max Planck announced his famous formula on theblackbody spectrum, the first shot of the quantum revo-lution.

This article reviews both the spectacular successes ofquantum theory and the ongoing debate about its con-sequences for issues ranging from quantum computationto consciousness, parallel universes and the very natureof physical reality.

THE ULTRAVIOLET CATASTROPHE

In 1871, scientists had good reason for their optimism.Classical mechanics and electrodynamics had poweredthe industrial revolution, and it appeared as though theirbasic equations could describe essentially all physical sys-tems. Yet some annoying details tarnished this picture.The amount of energy needed to heat very cool objectswas smaller than predicted and the calculated spectrumof a glowing hot object didn’t come out right. In fact, ifyou took the classical calculation seriously, the predictionwas the so-called ultraviolet catastrophe: that you wouldget blinded by light of ultraviolet and shorter wavelengthswhen you looked at the burner on your stove!

In his 1900 paper, Planck succeeded in deriving the cor-rect shape of the blackbody spectrum which now bearshis name, eliminating the ultraviolet catastrophe. How-

ever, this involved an assumption so bizarre that evenhe distanced himself from it for many years afterwards:that energy was only emitted in certain finite chunks, or“quanta”. Yet this strange assumption proved extremelysuccessful. Inspired by Planck’s quantum hypothesis, Pe-ter Debye showed that the strange thermal behavior ofcold objects could be explained if you assumed that thevibrational energy in solids could only come in discretechunks. In 1905, Einstein took this bold idea one stepfurther. Assuming that radiation could only transportenergy in such chunks, “photons”, he was able to explainthe so-called photoelectric effect, which is related to theprocesses used in present-day solar cells and the imagesensors in digital cameras.

THE HYDROGEN DISASTER

In 1911, physics faced another another great embar-rassment. Ernest Rutherford had convincingly arguedthat atoms consisted of electrons orbiting a positivelycharged nucleus much like a miniature solar system.However, electromagnetic theory predicted that such or-biting electrons would radiate away their energy, spiral-ing inward until they got sucked into the atomic nucleusafter about a millionth of a millionth of a second. Yethydrogen atoms were known to be eminently stable. In-deed, this was the worst quantitative failure so far in thehistory of physics, under-predicting the lifetime of hydro-gen by some forty orders of magnitude!

Niels Bohr, who had come to Manchester to work withRutherford, made a breakthrough in 1913. By postulat-ing that the amount of angular momentum in an atomwas quantized, the electrons were confined to a discreteset of orbits, each with a definite energy. If the electronjumped from one orbit to a lower one, the energy differ-ence was sent off in the form of a photon. If the electron

1

was in the innermost allowed orbit, there were no orbitswith less energy to jump to, so the atom was stable. Inaddition, Bohr’s theory successfully explained a slew ofspectral lines that had been measured for Hydrogen. Italso worked for the Helium atom, but only if it was de-prived of one of its two electrons. Back in Copenhagen,Bohr got a letter from Rutherford telling him he had topublish his results. Bohr wrote back that nobody wouldbelieve him unless he could explain the spectra of all theatoms. Rutherford replied, in effect: Bohr, you explainhydrogen and you explain helium and everyone will be-lieve all the rest.

Bohr was a warm and jovial man, with a talent forleadership, and that business of explaining all the restsoon become the business of the group that rose aroundhim at Copenhagen. The second author had the privilegeto work there on nuclear physics from September 1934to June 1935, and on arrival asked a workman who wastrimming vines running up a wall where he could findBohr. “I’m Niels Bohr”, the man replied.

THE EQUATIONS FALL INTO PLACE

Despite these early successes, physicists still didn’tknow what to make of these strange and seemingly adhoc quantum rules. What did they really mean?

In 1923, Louis de Broglie proposed an answer in hisPh.D. thesis: that electrons and other particles acted likestanding waves. Such waves, like vibrations of a guitarstring, can only occur with certain discrete (quantized)frequencies. The idea was so new that the examiningcommittee went outside its circle for advice on the ac-ceptability of the thesis. Einstein gave a favorable opin-ion and the thesis was accepted. In November 1925, Er-win Schrodinger gave a seminar on de Broglie’s work inZurich. When he was finished, Debye said in effect, “Youspeak about waves. But where is the wave equation?”Schrodinger went on to produce and publish his famouswave equation, the master key for so much of modernphysics. An equivalent formulation involving matriceswas provided by Max Born, Pasquale Jordan and WernerHeisenberg around the same time. With this new pow-erful mathematical underpinning, quantum theory madeexplosive progress. Within a few years, a host of hith-erto unexplained measurements had been successfully ex-plained, including spectra of more complicated atoms andvarious numbers describing properties of chemical reac-tions.

But what did it all mean? What was this quantity,the “wave function”, which Schrodinger’s equation de-scribed? This central puzzle of quantum mechanics re-mains a potent and controversial issue to this day.

Max Born had the dramatic insight that the wave func-tion should be interpreted in terms of probabilities. Ifwe measure the location of an electron, the probability

100%0% 25% 50% 75%Fraction of queens face up

FIG. 1. According to quantum physics, a card perfectlybalanced on its edge will by symmetry fall down in both di-rections at once, in what is known as a “superposition”. Ifan observer has bet money on the queen landing face up, thestate of the world will become a superposition of two out-comes: her smiling with the queen face up and her frowningwith the queen face down. In each case, she is unaware of theother outcome and feels as if the card fell randomly. If ourobserver repeats this experiment with four cards, there willbe 2 × 2 × 2 × 2 = 16 outcomes (see figure). In almost all ofthese cases, it will appear to her that queens occur randomly,with about 50% probability. Only in 2 of the 16 cases willshe get the same result all four times. According to a 1909theorem by the French mathematician Borel, she will observequeens 50% of the time in almost all cases (in all cases exceptfor what mathematicians call a set of measure zero) in thelimit where she repeats the card experiment infinitely manytimes. Almost all of the observers in the final superpositionwill therefore conclude that the laws of probability apply eventhough the underlying physics is not random and God doesnot play dice.

2

of finding it in a given region depends on the intensityof its wave function there. This interpretation suggestedthat a fundamental randomness was built into the laws ofnature. Einstein was deeply unhappy with this interpre-tation, and expressed his preference for a deterministicUniverse with the oft-quoted remark “I can’t believe thatGod plays dice”.

CURIOUS CATS AND QUANTUM CARDS

Schrodinger was also uneasy. Wave functions could de-scribe combinations of different states, so-called superpo-sitions. For example, an electron could be in a superpo-sition of several different locations. Schrodinger pointedout that if microscopic objects like atoms could be instrange superpositions, so could macroscopic objects,since they are made of atoms. In particular, seeminglyinnocent “microsuperpositions” could turn into “macro-superpositions”. As a baroque example, he describedthe famous thought experiment where a nasty contrap-tion kills a cat if a radioactive atom decays. Since theradioactive atom eventually enters a superposition of de-cayed and not decayed, it produces a cat which is bothdead and alive in superposition.

Figure 1 shows a simpler version of this Gedanken ex-periment that we will call Quantum Cards, again turn-ing a microsuperposition into a macrosuperposition. Yousimply take a card with a perfectly sharp bottom edgeand balance it on its edge on a table. According to classi-cal physics, it will in principle stay balanced forever. (Inpractice, this unstable card will of course get toppled inno time by say a tiny air current, so you could take a cardwith a thick bottom edge and use Schrodinger’s radioac-tive atom trigger to nudge it one way or the other.) Ac-cording to the Schrodinger equation, it will fall down ina few seconds even if you do the best possible job of bal-ancing it, because the Heisenberg uncertainty principlestates that it cannot be in only one position (straight up)without moving. Yet since the initial state was left-rightsymmetric, the final state must be so as well. The impli-cation is that it falls down in both directions at once, insuperposition. If you could perform this thought experi-ment, you would undoubtedly find that classical physicswas wrong and the card fell down. But you would alwayssee it fall down to the left or to the right, seemingly atrandom, never to the left and to the right simultaneouslyas the Schrodinger equation might have you believe. Thisapparent contradiction goes to the very heart of one ofthe original and most enduring mysteries of quantum me-chanics.

The Copenhagen Interpretation of quantum mechan-ics, which evolved from discussions between Bohr andHeisenberg in the late 1920s, addresses the mystery byasserting that observations, or measurements, are spe-cial. So long as the balanced card is unobserved, its

wave function evolves by obeying the Schrodinger equa-tion – a continuous and smooth evolution that is called“unitary” in mathematics and has several very attractiveproperties. Unitary evolution produces the superpositionwhere the card has fallen down both to the left and tothe right. The act of observing the card, however, trig-gers an abrupt change in its wave function, commonlycalled a “collapse”: the observer sees the card in one def-inite classical state (face up or face down) and from thenonward only that portion of the wave function survives.Nature supposedly decided which particular state to col-lapse into at random, with the probabilities determinedby the wave function.

Although this provided a strikingly successful calcu-lational recipe, there was a lingering feeling that thereought to be some equation describing when and how thiscollapse occurred. Many physicists took this to meanthat there is something fundamentally wrong with quan-tum mechanics, and that it would soon be replaced bysome even more fundamental theory that provided suchan equation. So rather than dwell on ontological impli-cations of the equations, most workers forged ahead towork out their many exciting applications and to tacklepressing unsolved problems of nuclear physics.

That pragmatic approach proved stunningly success-ful. Quantum mechanics was instrumental in predictingantimatter, understanding radioactivity (leading to nu-clear power), accounting for materials such as semicon-ductors, explaining superconductivity, and describing in-teractions such as those between light and matter (lead-ing to the invention of the laser) and of radio waves andnuclei (leading to magnetic resonance imaging). Manysuccesses of quantum mechanics involve its extension,quantum field theory, which forms the foundation of el-ementary particle physics all the way to the present-dayexperimental frontiers of neutrino oscillations and thesearch for the Higgs particle and supersymmetry.

MANY WORLDS OR MANY WORDS?

By the 1950’s, this ongoing parade of successes hadmade it abundantly clear that quantum theory was farmore than a short-lived temporary fix. And so, in themid 1950’s, a Princeton graduate student named HughEverett III decided to revisit the collapse postulate inhis Ph.D. thesis. Everett pushed the quantum idea to itsextreme by asking the following question: “What if thetime-evolution of the entire Universe is always unitary?”After all, if quantum mechanics suffices to describe theUniverse, then the present state of the Universe is de-scribed by a wave function (an extraordinarily compli-cated one). In Everett’s scenario, that wave functionwould always evolve in a deterministic way, leaving noroom for wave function collapse or God playing dice.

3

Instead of getting collapsed by measurements, seem-ingly innocent microscopic superpositions would rapidlyget amplified into most Byzantine macroscopic superpo-sitions. Our quantum card in Figure 1 would really bein two places at once. Moreover, a person looking at thecard would enter a superposition of two different men-tal states, each perceiving one of the two outcomes! Ifyou had bet money on the queen coming face up, youwould end up in a superposition of smiling and frown-ing. Everett’s brilliant insight was that the observersin such a crazy deterministic but schizophrenic quan-tum world could perceive the plain old reality that weare familiar with, as described in Figure 1. Most im-portantly, they would perceive an apparent randomnessobeying precisely the right probability rules, as the bot-tom panel of Figure 1 illustrates. The situation is morecomplicated, and still controversial, for the asymmetriccase when the probabilities for different outcomes are notequal.

Everett’s viewpoint became known as the “manyworlds” or, perhaps more appropriately, “many minds”interpretation of quantum mechanics because each ofone’s superposed mental states perceives its own world.This viewpoint simplifies the underlying theory by re-moving the collapse postulate, implying that there is nonew undiscovered physics that makes these superposi-tions go away. The price it pays for this theoretical sim-plicity is the conclusion that these parallel perceptions ofreality are all equally real, so in a sense it involves lesswords at the expense of more worlds.

EXPERIMENTAL VERDICT:THE WORLD IS WEIRD

Everett’s work was largely disregarded for about twodecades. The main objection was that it was too weird,demoting to mere approximations the familiar classicalconcepts upon which the Copenhagen interpretation wasfounded. Many physicists hoped that a deeper theorywould be discovered, showing that the world was in somesense classical after all, free from oddities like large ob-jects being in two places at once. However, such hopeswere largely shattered by a series of new experiments.

Could the apparent quantum randomness be replacedby some kind of unknown quantity carried about insideparticles, so-called “hidden variables”? CERN theoristJohn Bell showed that in this case, quantities that couldbe measured in certain difficult experiments would in-evitably disagree with the standard quantum predictions.After many years, technology allowed researchers to con-duct these experiments and eliminate hidden variables asa possibility.

A “delayed choice” experiment proposed by the secondauthor in 1978 (see Figure 2) was successfully carried outby Carroll Alley, Oleg Jakubowics and William Wickes

in 1984, showing that not only can a photon be in twoplaces at once, but we can decide whether it should actschizophrenically or classically seemingly after the fact!

The simple double slit interference experiment, hailedby Feynman as the mother of all quantum effects, wassuccessfully repeated for ever larger objects: atoms, smallmolecules and most recently a carbon-60 “Buckey Ball”.After this last feat, Anton Zeilinger’s group in Viennahas even started discussing doing it with a virus. Ifwe imagine, as a Gedanken experiment, that this virushas some primitive kind of consciousness, then the manyworlds/many minds interpretation seems unavoidable, ashas been emphasized by Dieter Zeh. An extrapolation tosuperpositions involving other sentient beings such as hu-mans would then be merely a quantitative rather than aqualitative one.

In short, the experimental verdict is in: the weird-ness of the quantum world is real, whether we like it ornot. There are in fact good reasons to like it: this veryweirdness may offer useful new technologies. Accordingto a recent estimate, about 30% of the U.S. gross na-tional product is now based on inventions made possibleby quantum mechanics. Moreover, if physics really isunitary (if the wave function never collapses), quantumcomputers can in principle be built that take advantageof such superpositions to make certain calculations muchfaster than conventional algorithms would allow. For ex-ample, Peter Shor and Lov Grover have shown that onecould factor large numbers and search long lists fasterthis way. Such machines would be the ultimate parallelcomputers, in a sense running many calculations in su-perposition. As David Deutsch has emphasized, it willbe hard to deny the reality of all these parallel states ifsuch computers are actually built.

QUANTUM CENSORSHIP: DECOHERENCE

The above-mentioned experimental progress of the lastfew decades was paralleled by a new breakthrough in the-oretical understanding. Everett’s work had left two cru-cial question unanswered: first of all, if the world actuallycontains bizarre macrosuperpositions, then why don’t weperceive them?

The answer came in 1970 with a seminal paper by Di-eter Zeh of the University of Heidelberg, who showedthat the Schrodinger equation itself gives rise to a typeof censorship. This effect became known as decoherence,because an ideal pristine superposition is said to be co-herent. Decoherence was worked out in great detail byLos Alamos scientist Wojciech Zurek, Zeh and others overthe following decades. They found that coherent quan-tum superpositions persist only as long as they remainsecret from the rest of the world. Our fallen quantumcard in Figure 1 is constantly bumped by snooping airmolecules, photons, etc., which thereby find out whether

4

1stbasemirror

3rdbasemirror

Half-silveredmirror

Half-silveredmirror

Left fieldphotoncatcher(detector)

Right fieldphotoncatcher(detector)

Photonpitcher(laser)

FIG. 2. The delayed choice experiment. The figure showsa so-called Mach-Zender interferometer in the guise of a base-ball diamond. The half-silvered mirror on home plate reflectshalf the light that strikes it towards 3rd base and lets therest through towards 1st base. Two ordinary mirrors then re-flect this light towards 2nd base, where the two beams strikeanother half-silvered mirror. The setup is such that the twobeams headed for left field will cancel each other through de-structive interference, i.e., all photons fired from home platewill be detected in right field, none in left field. This impliesthat each photon took both the 1st and 3rd base routes in su-perposition. If we remove the half-silvered mirror at secondbase, we detect half of the photons in left field and half inright field, and we know which baselines each photon traveledalong. We can therefore choose whether the individual pho-tons should act schizophrenically or not. Indeed, we can delaythis choice until seemingly after the fact! Let us turn on thelight source for only a billionth of a second, during which timeit emits, say, 1000 photons. At the speed of light, the photonstravel about a foot during this time. Let us therefore wait aleisurely 10 or 20 billionths of a second after the light source isturned off before we decide which experiment we want to do.The two photon convoys headed for 1st and 3rd base will beseparated by many meters by then, unable to communicatewith each other. If we want to demonstrate that each photonfollowed both routes at once, we need only wait and note thatno photons make it to left field. If we want to find out whichway each photon went, we swiftly remove the 2nd base mirrorbefore the photons have had time to reach it.

it has fallen to the left or to the right, destroying (“deco-hering”) the superposition and making it unobservable.This is somewhat analogous to the way in which inter-ference effects in classical optics would get destroyed ifperturbations along the light path messed up the phases.

The most convenient way to understand decoherenceis by looking at a generalization of the wave functioncalled the density matrix. For every wave function, thereis a corresponding density matrix, and there is a cor-responding Schrodinger’s equation for density matrices.For example, the density matrix of the quantum cardfallen down in a superposition would look like this:

density matrix =

(a cc∗ b

).

The numbers a and b are the probabilities of finding thecard face up or face down respectively, and would bothequal one half in our case. Indeed, a density matrix hav-ing the form

density matrix =

(a 00 b

)

would represent a familiar classical situation — a cardthat had fallen one way or the other, but we didn’t knowwhich. The off-diagonal numbers in the matrix (c in oursimple example) thus represent the difference betweenthe quantum uncertainty of superpositions and the clas-sical uncertainty (mere ignorance).

A remarkable achievement of decoherence theory is toexplain how interactions between an object and its en-vironment push the off-diagonal numbers essentially tozero, for all practical purposes replacing the quantumsuperposition by pure classical ignorance.

If your friend observed the card without telling you theoutcome, she would according to the Copenhagen inter-pretation collapse the superposition into classical igno-rance (on your part), replacing c by zero. Loosely speak-ing, decoherence calculations show that you don’t need ahuman observer to get this effect — even an air moleculewill suffice.

Decoherence explains why we do not routinely seequantum superpositions in the world around us. It isnot because quantum mechanics intrinsically stops work-ing for objects larger than some magic size. Instead,macroscopic objects such as cats and cards are almostimpossible to keep isolated to the extent needed to pre-vent decoherence. Microscopic objects, in contrast, aremore easily isolated from their surroundings so that theyretain their quantum secrets and quantum behavior.

The second unanswered question in the Everett picturewas more subtle but equally important: what physicalmechanism picks out the classical states — face up andface down for the card — as special? The problem wasthat from a mathematical point of view, quantum stateslike “face up plus face down” (let’s call this “state alpha”)

5

or “face up minus face down” (“state beta”, say) are justas valid as the classical states “face up” or “face down”.So just as our fallen card in state alpha can collapse intothe face up or face down states, a card that is definitelyface up — which equals (alpha + beta)/2 — should beable to collapse back into the alpha or beta states, or anyof an infinity of other states into which “face up” can bedecomposed. Why don’t we see this happen?

Decoherence answered this question as well. The cal-culations showed that classical states could by definedand identified as simply those states that were most ro-bust against decoherence. In other words, decoherencedoes more than just make off-diagonal matrix elementsgo away. If fact, if the alpha and beta states of our cardwere taken as the fundamental basis, the density matrixfor our fallen card would be diagonal to start with, of thesimple form

density matrix =

(1 00 0

),

since the card is definitely in state alpha. However, de-coherence would almost instantaneously change the stateto

density matrix =

(1/2 00 1/2

),

so if we could measure whether the card was in the al-pha or beta-states, we would get a random outcome. Incontrast, if we put the card in the state “face up”, itwould stay “face up” in spite of decoherence. Decoher-ence therefore provides what Zurek has termed a “pre-dictability sieve”, selecting out those states that displaysome permanence and in terms of which physics has pre-dictive power.

SHIFTING VIEWS

The discovery of decoherence, combined with the evermore elaborate experimental demonstrations of quantumweirdness, has caused a noticeable shift in the views ofphysicists. The main motivations for introducing the no-tions of randomness and wave function collapse in thefirst place had been to explain why we perceived proba-bilities and not strange macrosuperpositions. After Ev-erett had shown that things would appear random any-way and decoherence had been found to explain why wenever perceived anything strange, much of this motiva-tion was gone. Moreover, it was embarrassing that no-body had managed to provide a testable deterministicequation specifying precisely when this mysterious col-lapse was supposed to occur. Even though the wave func-tion technically never collapses in the Everett view, it isgenerally agreed that decoherence produces an effect thatlooks like a collapse and smells like a collapse.

An informal poll taken at a conference on quantumcomputation at the Isaac Newton Institute in Cambridgein July 1999 gave the following results:

1. Do you believe that new physics violating theSchrodinger equation will make large quantum com-puters impossible? 1 yes, 71 no, 24 undecided

2. Do you believe that all isolated systems obey theSchrodinger equation (evolve unitarily)? 59 yes, 6no, 31 undecided

3. Which interpretation of quantum mechanics is clos-est to your own?

(a) Copenhagen or consistent histories (includingpostulate of explicit collapse): 4

(b) Modified dynamics (Schrodinger equationmodified to give explicit collapse): 4

(c) Many worlds/consistent histories (no col-lapse): 30

(d) Bohm (an ontological interpretation where anauxiliary “pilot wave” allows particles to havewell-defined positions and velocities): 2

(e) None of the above/undecided: 50

The reader is warned of rampant linguistic confusionin this area. It is not uncommon that two physicistswho say that they subscribe to the Copenhagen inter-pretation find themselves disagreeing about what theymean by this. Similarly, some view the “consistent his-tories” interpretation (in which the fundamental objectsare consistent sets of classical histories) as a fundamen-tally random theory where God plays dice (as in the re-cent Physics Today article by Omnes & Griffith), whereasothers view it more as a way of identifying what is classi-cal within the deterministic “many worlds” context. Suchissues undoubtedly contributed to the large “undecided”vote on the last question.

This said, the poll clearly suggests that it is time toupdate the quantum textbooks: although these infalli-bly list explicit non-unitary collapse as a fundamentalpostulate in one of the early chapters, the poll indicatesthat many physicists — at least in the burgeoning fieldof quantum computation — no longer take this seriously.The notion of collapse will undoubtedly retain great util-ity as a calculational recipe, but an added caveat clar-ifying that it is probably an not a fundamental processviolating the Schrodinger equation could save astute stu-dents many hours of frustrated confusion.

The Austrian animal behaviorist Konrad Lorenzmused that important scientific discoveries go thoughthree phases: first they are completely ignored, then theyare violently attacked, and finally they are brushed asideas well-known. Although more quantitative experimen-tal study of decoherence is clearly needed, it is safe to

6

SUBJECT OBJECT

ENVIRONMENT

Object decoherenceSubject

decoherence,

finalizing

decisions

Measurem

ent,observation,"w

avefuntion collapse",w

illful action

FIG. 3. An observer conveniently decomposes the worldinto three subsystems: the degrees of freedom correspondingto her subjective perceptions (the subject), the degrees offreedom being studied (the obj ect), and everything else (theenvironment). As indicated, the interactions between thesethree subsystems can cause qualitatively very different effects,which is why it is often useful to study them separately.

say that decoherence has now reached the third phaseamong quantum physicists — indeed, a large part of cur-rent quantum computing research is about finding waysto minimize decoherence. The poll suggests that af-ter spending the sixties in phase 1, Everett’s idea thatphysics is unitary (that there is no wave function col-lapse) is now shifting from phase 2 to phase 3, replacingthe collapse interpretation as the dominant paradigm.

HOW DOES IT FIT TOGETHER?

If unitarity and decoherence are taken seriously, thenit is instructive to split the Universe into three partsas illustrated in Figure 3. As emphasized by Feynman,quantum statistical mechanics splits the Universe (or, inphysics jargon, its “degrees of freedom”) into two sub-systems: the object under consideration and everythingelse (referred to as the environment). To understand pro-cesses such as measurement, we need to include a thirdsubsystem as well: the subject, the mental state of theobserver. A useful standard technique is to split theSchrodinger equation that governs the time evolution ofthe Universe as a whole into terms that describe the in-ternal dynamics of each of these subsystems and termsthat describe interactions between them. These differentterms have qualitatively very different effects.

The term giving the object dynamics is normally themost important one, so to figure out what the object willdo, all the other terms can usually be ignored. Considerthe quantum card example in Figure 1, with the “ob-ject” being the (position of) the card. In this case, theobject dynamics is such that the card will fall left andright in superposition. When our observer looks at thecard, this subject-object interaction will make her men-tal state enter a superposition of joy and disappointmentover winning/losing her bet. However, she can never beaware of her schizophrenic state of mind, since interac-tions between the object and the environment (in thiscase air molecules and photons bouncing off of the card)cause rapid decoherence that makes this superpositioncompletely unobservable.∗ It would be virtually impossi-ble for her to eliminate this decoherence in practice sincethe card is so large, but even if she could (say by repeat-ing the experiment in a dark cold room with no air), itwouldn’t make any difference: at least one neuron in heroptical nerves would enter a superposition of firing andnot firing while she looked at the card, and this superpo-sition would decohere in about 10−20 seconds accordingto recent calculations.

There could still be trouble, since thought processes(the internal dynamics of the subject system) could cre-ate superpositions of mental states that we do not in factperceive. Indeed, Roger Penrose and others have sug-gested that such effects could let our brains act as quan-tum computers. However, the fact that neurons decoheremuch faster than they can process information (it takesthem about 10−3 seconds to fire) means that if the com-plex neuron firing patterns in our brains have anythingto do with consciousness, then decoherence in the brainwill prevent us from perceiving weird superpositions.

As mentioned above, we perceive only those aspectsof the world that are most robust against decoherence.Decoherence therefore selects what Zurek has termed a“pointer basis”, basically the familiar quantities of clas-sical physics, as special. Since all our observations aretransmitted through neurons from our sensory organs,the fact that neurons decohere so fast makes them theultimate pointer basis. As Zeh has stressed, this justifiesusing the textbook wave function collapse postulate asa useful “shut-up-and-calculate” recipe: compute proba-bilities as if the wave function collapses when we observethe object. Strictly speaking, we constantly keep entering

∗Although the processes of measurement and decoherencemay appear different, there is a symmetry between the object-subject and object-environment interactions, involving thelack of information about the object (entropy): loosely speak-ing, the entropy of an object decreases while you look at itand increases while you don’t. Decoherence is essentially ameasurement that you don’t know the outcome of.

7

FIG. 4. Theories can be crudely organized into a familytree where each might, at least in principle, be derivable frommore fundamental ones above it. For example, classical me-chanics can be obtained from special relativity in the approxi-mation that the speed of light c is infinite, and hydrodynamicswith its concepts such as density and pressure can be derivedfrom statistical mechanics. However, these cases where thearrows are well understood form a minority. Although chem-istry in principle should be derivable from quantum mechan-ics, the properties of some molecules are so complicated tocompute in practice that a more empirical approach is taken.Deriving biology from chemistry or psychology from biologywould be even more hopeless in practice.

into superpositions of different mental states, but deco-herence prevents us from noticing this — subjectively, we(all superposed versions of us) just perceive this as theslight randomness that disturbed Einstein so much.

A basic question of course remains: can quantum me-chanics be understood in terms of some deeper underly-ing principle? How come the quantum?

LOOKING AHEAD

After 100 years of the quantum, let us take a stepback and make some general remarks about what maylie ahead. Although basic issues about ontology and theultimate nature of reality often crop up in discussionsabout how to interpret quantum mechanics, this is prob-

ably just a piece in a larger puzzle. As illustrated inFigure 4, theories can be crudely organized in a familytree where each might, at least in principle, be derivablefrom more fundamental ones above it.

All these theories have two components: mathematicalequations and words that explain how they are connectedto what we observe. Quantum mechanics as usually pre-sented in textbooks has both components: some equa-tions as well as three fundamental postulates written outin plain English. At each level in the hierarchy of the-ories, new concepts (e.g., protons, atoms, cells, organ-isms, cultures) are introduced because they are conve-nient, capturing the essence of what is going on withoutrecourse to the more fundamental theory above it. It isimportant to remember, however, that it is we humanswho introduce these concepts and the words for them: inprinciple, everything could have been derived from thefundamental theory at the top of the tree, although suchan extreme reductionist approach would of course be use-less in practice. Crudely speaking, the ratio of equationsto words decreases as we move down the tree, droppingnear zero for highly applied fields such as medicine andsociology. In contrast, theories near the top are highlymathematical, and physicists are still struggling to un-derstand the concepts, if any, in terms of which we canunderstand them.

The Holy Grail of physics is to find what is jocularlyreferred to as a “Theory of Everything”, or TOE, fromwhich all else can be derived. If such a theory exists atall, it should replace the big question mark at the topof the theory tree. Everybody knows that something ismissing here, since we lack a consistent theory unifyinggravity with quantum mechanics. To avoid the problemof infinite regress, where each set of concepts is explainedin terms of more fundamental ones that in turn must beexplained, a TOE would probably have to contain noconcepts at all. In other words, it would have to bea purely mathematical theory, with no explanations or“postulates” as in quantum textbooks (recall that math-ematicians are perfectly capable of — and often pridethemselves of — studying abstract mathematical struc-tures that lack any intrinsic meaning or connection withphysical concepts). Rather, an infinitely intelligent math-ematician should be able to derive the entire theory treefrom these equations alone, by deriving the propertiesof the Universe that they describe, the properties of itsinhabitants and their perceptions of the world.

The first 100 years of the quantum have provided pow-erful new technologies and answered many questions.However, physics has raised new questions just as impor-tant as those outstanding at the time of Maxwell’s inau-gural speech; questions regarding both quantum gravityand the ultimate nature of reality. If history is anythingto go by, the coming century should be full of excitingsurprises.

8

The authors: MAX TEGMARK and JOHNARCHIBALD WHEELER discussed quantum mechanicsextensively during Tegmark’s three and a half years as apostdoc at the Institute for Advanced Study in Prince-ton, N.J. Max Tegmark is now an assistant professorof physics at the University of Pennsylvania. Wheeleris professor emeritus of physics at Princeton, where hisgraduate students included Richard Feynman and HughEverett III (inventor of the many-worlds interpretation).He received the 1997 Wolf Prize in physics for his work onnuclear reactions, quantum mechanics and black holes.

The authors wish to thank Emily Bennett and KenFord for help with an earlier manuscript on this topic,and Graham Collins, Jeff Klein, George Musser, DieterZeh and Wojciech Zurek for helpful suggestions.

Scientific American Website: www.sciam.com

9