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The Reality of the Quantum World Einstein held that quantum-mechanical descriptions of physical systems are incomplete. Laboratory tests show he was probably wrong; the bizarre nature of the quantum world must be accepted by Abner Shimony e live in a remarkable era in arrangement is specified. Finally, the quantum state of the photon is fixed which experimental results notion of indefiniteness is no longer if three quantities are known: the are beginning to elucidate confined to the atomic and subatom photon's direction, its frequency and philosophical questions. In no do ic domains. Investigators have found its linear polarization (the direction W main have the results been more dra that a macroscopic system can under of the electric field associated with matic than in quantum mechanics. some circumstances exist in a state the photon). A suitable apparatus for The theory has been confirmed mag in which a macroscopic observable measuring polarization is a sheet of nificently since the 1920's as its pre has an indefinite value. Each of these polarizing film. The film is idealized dictions of atomic, molecular, nu findings alters drastically the way we so that it transmits all light incident clear, perceive the world. on it at a right angle if the light is lin tion in the film called the transmis of these successes the bizarre and A n understanding of these exper J-\. iments and their philosophical sion axis. The film blocks all light in counterintuitive character of quan implications requires some familiar cident on it at a right angle if the light tum mechanics has led some investi ity with the basic ideas of quantum gators, including Einstein, to believe mechanics. Essential to any discus is linearly polarized perpendicular to the transmission axis. quantum-mechanical descriptions of sion of the theory is the concept of Various experiments can be per physical systems are incomplete and the quantum state, or wave function. formed by rotating the; polarizing optical, solid-state mentary-particle and phenomena ele early polarized along a certain direc were shown to be accurate. Yet in spite in need of supplementation. Recent The quantum state specifies all the film in different ways. If the photon experiments show that this opinion quantities of a physical system to the is linearly polarized along the trans is very likely wrong. The experimen extent that it is possible to do so. The mission axis, there is a probability tal results reveal more clearly than caveat at the end of the preceding of 1 that it will be transmitted. If the ever that we live in a strange "quan tum world" that defies comfortable, sentence is crucial, because accord photon is linearly polarized perpen ing to quantum mechanics not all dicular to the transmission axis, the quantities of a system have simul probability that it will be transmitted taneously definite values. The famil is zero. A further implication of quan commonsense interpretation. Here are a few of the new, strange findings we must begin to accept. First, two entities separated by many iar Heisenberg uncertainty principle, tum mechanics, going beyond what which asserts that the position and has been said so far, is that if the pho ton is linearly polarized at some an meters and possessing no mecha the momentum of a particle cannot nism for communicating with each be simultaneously definite, is per gle to the transmission axis between other nonetheless can be haps the best-known instance of this zero and 90 degrees, the probability "entan gled": they can exhibit striking cor proposition. of transmission is a number between relations in their behavior, so that What the quantum state of a sys zero and 1 (specifically, the square of a measurement done on one of the tem does provide unequivocally is the cosine of that particular angle). If entities seems instantaneously to af the probability of each possible out the probability is, say, one-half, then fect the result of a measurement on come of every experiment that can out of 100 photons linearly polarized the other. The finding cannot be ex be done on the system. If the proba at the corresponding angle to the plained from a classical point of view, bility is I, the outcome is certain to transmission axis 50 will be transmit but it agrees completely with quan occur; if the probability is zero, the ted on the average. tum mechanics. Second, a photon, outcome is certain not to occur. If, Another basic idea of quantum me the fundamental unit of light, can be however, the probability is a number chanics is the superposition princi ple, which asserts that from any two have like either a particle or a wave, between zero and I, then it cannot be and it can exist in an ambiguous state said in any individual case what the quantum states of a system further until a measurement is made. If a par outcome will be. All that can be said states can be formed by superposing ticlelike property is measured, the is what, on the average, the out them. Physically the operation corre photon behaves like a particle, and if comes of a specified experiment car sponds to forming a new state that a wavelike property is measured, the ried out on a large number of replica "overlaps" each of the states from photon behaves like a wave. Wheth systems will be. which it was formed. The concept er the photon is wave- or particlelike Imagine, for instance, that meas can be illustrated by considering two is indefinite until the experimental urements are made on a photon. The quantum states of a photon in which 46 © 1987 SCIENTIFIC AMERICAN, INC zation in the first state is perpendic chance-not just a matter of chance in the sense of unpredictability by quantum state that contains equal amounts of the vertically polarized ular to the direction of the photon's the scientist. Finally, the probabil state and the horizontally polarized polarization Then ity of each possible outcome of the state. This new state will figure prom any number of states can be formed measurement is an objective proba inently in what follows, and so it will in which the photon's polarization points at some angle between the bility. Classical physics did not con be given a name, '1'0 (since the Greek flict with common sense in these fun letter psi is commonly used to rep two perpendicular directions. damental ways. the direction of the photon's polari in the second. resent a quantum state). The proper Even more startling implications ties of '1'0 are most peculiar indeed. rom these two basic ideas alone flow from quantum mechanics if the Imagine, for instance, inserting in the indefiniteness and the superposi system consists of two correlated paths of the photons polarizing films tion principle-it should be clear al parts. Suppose two photons fly apart with vertically oriented transmission ready that quantum mechanics con in opposite directions. One possible axes. flicts sharply with common sense. If quantum state of the pair of photons amounts of the vertically and hor the quantum state of a system is a is the state in which both photons izontally polarized states, there is complete description of the system, are linearly polarized along a vertical a probability of one-half that both then a quantity that has an indefi axis. Another possible state is the photons will be transmitted through nite value in that quantum state is one in which they are both linear their respective films and a probabil objectively F Because '1'0 contains its value is ly polarized along a horizontal axis. ity of one-half that not merely unknown by the scientist There is nothing particularly bizarre blocked. What cannot happen is that who seeks to describe the system. or surprising about either of these one photon will be transmitted and Furthermore, since the outcome of a two-photon quantum states, beyond the other will be blocked. In other indefinite; both equal will be measurement of an objectively indef the peculiarities of the Single-photon words, the outcomes of the linear inite quantity is not determined by states mentioned above. But if the su polarization experiments on the two the quantum state, and yet the quan perposition principle is brought into photons are strictly correlated. tum state is the complete bearer of in play, strange effects can occur. formation about the system, the out In particular, by using the super come is strictly a matter of objective position principle one can form a EXPERIMENTAL TESTS are now shedding light on topics in The results will be the same if the . polarizing films are oriented at an angle of 45 degrees with respect to (The photon is the fundamental unit of light.) The photons travel quantum mechanics that were once confined to the realm of in opposite directions through 6. 5 meters of pipe, and those that philosophical debate. In this experiment, which was done by pass through polarization analyzers impinge on photodetectors. Alain Aspect and his colleagues at the Institute of Optics of the Quantum mechanics predicts there should be delicate correla University of Paris, the lasers at each side of the picture excite tions in the polarizations of the oppositely directed photons; the individual calcium atoms in the vacuum chamber (center). Each correlation conflicts with classical theories called hidden-var atom returns to its unexcited state by emitting a pair of photons. iables models. The experiment confirmed quantum mechanics. 47 © 1987 SCIENTIFIC AMERICAN, INC ... ...... ............. � �..... ... ... - .... _, .. ... ... ... INDEFINITENESS of a quantum system is illustrated for a photon. A sheet of polarizing film transmits all light incident on it at a right angle if the light is linearly polarized along a certain direction in the film called the transmission axis (hatching). This polar· ization state of the photon is represented by the wavy colored line at the top. The film blocks all light incident on it at a right angle if the light is linearly polarized perpendic· ular to the transmission axis (wavy gray line at top). Now suppose a photon is linearly polarized at some angle to the transmission axis between zero and 90 degrees (bottom). Then whether or not the photon will be transmitted is indefinite; the probability of transmission is a number between zero and 1 (the square of the cosine of the angle). the horizontal: either both photons will be transmitted or both will be blocked. It simply cannot happen that one photon will be transmitted and the other will be blocked. In fact, it does not matter what the orienta tions of the films are as long as they match each other; the outcomes of the linear·polarization experiments are strictly correlated for an infinite family of possible experiments. (Of course, no more than one of the ex· periments can actually be carried out.) Somehow the second photon of the pair "knows" whether to pass through its polarizing film in order to agree with the passage or non passage of the first photon, even though the two photons are well sep arated and neither has a mechanism for informing the other of its behav ior. In this kind of situation, then, quantum mechaniCS challenges the relativistic concept of locality, which holds that an event cannot have ef fects that propagate faster than light (and, in particular, instantaneous ef fects at a distance). t must be emphasized that all the implications that have been drawn so far-objective indefi niteness, objective chance, objective probability and nonlocality-depend crucially on the premise that a sys tem's quantum state is a complete de- I peculiar 48 scription of that system. A number of theorists have maintained, however, that the quantum state merely de scribes an ensemble of systems pre pared in a uniform manner, and that this is why good predictions can be made about the statistical results of the same experiment performed on all members of the ensemble. At the same time, the argument goes, the in dividual members of the ensemble differ from one another in ways not mentioned by the quantum state, and this is the reason the outcomes of the individual experiments are different. The properties of individual systems that are not speCified by the quantum state are known as hidden variables. If hidden-variables theorists are correct, there is no objective indef initeness. There is only ignorance on the part of the scientist about the values of the hidden variables that characterize an individual system of interest. Moreover, there is no objec tive chance and there are no objec tive probabilities. Most important, the quantum correlations of well-sep arated systems are no more surpris ing than the concordance of two newspapers printed by the same press and mailed to different cities. In 1964 John S. Bell of CERN, the Eu ropean laboratory for particle phys ics, showed that the predictions of local hidden-variables models are © 1987 SCIENTIFIC AMERICAN, INC incompatible with the predictions of quantum mechanics. Reflection on some hidden-variables models of David Bohm of Birkbeck College London and Louis de Broglie led Bell to prove the important theorem that no model that is local (in a carefully speCified sense) can agree with all the statistical predictions of quantum mechanics. In other words, there are physical situations in which the pre dictions of quantum mechanics dis agree with those of every local hid den-variables model [see "The Quan tum Theory and Reality," by Bernard d'Espagnat; SCIENTIFIC AMERICAN, No vember, 1979]. The idea of Bell's theorem can be grasped, at least in part, by returning to consider the quantum state '1'0. As noted above, the results of linear-po larization experiments performed on a pair of photons in this state must be strictly correlated when the angle be tween the transmission axes of the two polarizing films is zero degrees (as it is when both axes are aligned vertically). It should not be surpris ing to learn, therefore, that for the state '1'0 there is always at least a partial correlation between the out comes, no matter what the angle between the transmission axes is. (SpeCifically, if one of the photons is transmitted through its polarizing film, then the probability that the other photon will be transmitted through its film is the square of the cosine of the angle between the two transmission axes.) Consequently a hidden-variables model that agrees with all the statisti cal predictions of quantum mechan ics must assign quantities to each pair of photons in the ensemble in a delicate way in order to guarantee the strict or partial correlations at ev ery angle between the axes. But the condition of locality requires that the quantities assigned to each photon in a pair must be independent of the orientation of the polarizing film on which the other photon impinges and independent of the other pho ton's passage or nonpassage. It is this locality condition that makes quite impossible the delicate adjustments that would be necessary for repro ducing all the correlations, strict and partial, implied by '1'0. ell's theorem shows that in prin B ciple one can determine experi mentally which is correct: quantum mechanics or the local hidden-vari ables models. It was important to do such a test because, in spite of the im mense body of confirming evidence C ORRELATIONS between the polarizations of two photons oc there is a 50 percent probability that both photons will be trans cur when the photons are in a special state called '1'0 (after the mitted through their respective films and a 50 percent probabil letter psi in the Greek alphabet)_ The state can be formed by su ity that both will be blocked. What cannot happen is that one perposing the state in which both photons are linearly polarized photon will be transmitted and the other will be blocked: the along a vertical axis with the state in which they are both linearly outcomes of the linear-polarization experiments are strictly polarized along a horizontal axis. The state'!'0 contains equal correlated. In fact, it does not matter what the orientations of the amounts of the vertically polarized state and the horizontally films are as long as they match each other; somehow the second polarized state. Now imagine that polarizing films with horizon photon of the pair "knows" whether to pass through its polar tally oriented transmission axes are inserted in the paths of the izing film in order to agree with the passage or nonpassage of photons. Since '1'0 contains equal amounts of the two states, the first photon, even though the photons are well separated. for quantum mechanics at the time Bell proved his theorem, the very points where quantum mechanics is without equivocation irreconcilable with common sense had not yet been probed. In 1969 John F. Clauser, then at Co lumbia University, Michael A. Horne of Boston University, Richard A. Holt, then at Harvard University, and I pro posed a design for the requisite test. Pairs of photons with correlated lin ear polarizations were to be obtained by exciting atoms to an appropriate initial state; the atoms would subse quently return to the unexcited state by emitting two photons. Filters and lenses would ensure that when the photons flew off in opposite or virtu ally opposite directions, one photon would impinge on a polarization ana lyzer and the other would impinge on another analyzer. By switching between two orientations of each an alyzer and recording the number of photon pairs transmitted in each of the four possible combinations of ori entations of the two analyzers, meas urements of correlations of transmis sions of the photons of a pair could be made. We suggested that either calcite crystals or piles of glass plates serve as the polarization analyzers, since each of them is much more effi cient than an actual polarizing film in blocking photons polarized per pendicular to the transmission axis. Photodetectors placed behind the analyzers would detect a fixed frac tion of the photons passing through the analyzers. If two photons, one at each detector, were registered within 20 nanoseconds (billionths of a sec ond) of each other, the probability would be quite high that they were emitted by the same atom. Since the lenses would collect the two photons over a finite angle, the quantum state would not be exactly the '1'0 state dis cussed above but a modified state 'I' [, which also leads to correlations that cannot be reproduced by any local hidden-variables model. The experiment was done by Stu art]. Freedman and Clauser at the University of California at Berkeley in 1972, by Edward S. Fry and Randall C. Thompson at Texas A. & M. Uni versity in 1975 and by other groups after that. Most of the experimental results agree with the correlation predictions of quantum mechanics and disagree with the hidden-vari ables models. Moreover, the reliabil ity of the dissenting experiments is suspect because of subtle weaknes ses in their design. Yet until very recently all the ex periments had a loophole that al lowed staunch defenders of hid den-variables models to maintain their hopes: the polarization analyz ers were kept in their respective ori entations for intervals of a minute or so, which is ample time for the ex change of information between the analyzers by some hypothetical mechanism. As a result the defenders could contend that the special theory of relativity does not imply the valid ity of Bell's locality condition in the physical situation of the experi ments. But then these experiments © 1987 SCIENTIFIC AMERICAN, INC would not serve as decisive tests be tween quantum mechanics and the local hidden-variables models. o block this loophole, Alain As Dalibard and Gerard Roger of the Institute of Optics of the University of Paris did a spectacular experiment in which the choice be tween the orientations of the 'polar ization analyzers is made by opti cal switches while the photons are in flight. In their experiment, which required eight years of work and was completed only in 1982, each switch is a small vial of water in which standing waves are periodi cally generated ultrasonically. The waves serve as diffraction gratings that can deflect an incident photon with high efficiency. If the standing waves are turned on, the photon will be deflected to an analyzer that is oriented one way; if the standing waves are turned off, the photon will travel straight to an analyzer that is oriented another way. The switching between the orien tations takes about 10 nanoseconds. The generators that power the two switches operate independently, al though (unfortunately for the com plete definitiveness of the experi ment) the operation is periodic rather than random. The distance between the analyzers is 13 meters, so that a signal moving at the speed of light (the highest speed allowed by the special theory of relativity) takes 40 nanoseconds to travel between them. Consequently the choice of orientation for the first polarization T pect, Jean 49 DETECTOR DETECTOR COINCIDENCE COUNTING SEARCH FOR CORRELATIONS between members of pairs of tons through their analyzers. even though the photons have no photons was carried out in the 1970's by a number of investiga apparent means of communicating with each other. The experi tors_ The photon pairs were emitted in energy-state transitions ments mainly confirmed quantum mechanics, but they had a of calcium and mercury atoms; each photon impinged on a po loophole: the orientations of the two analyzers were fixed before larization analyzer- Quantum mechanics predicts there must be the photons were emitted. Consequently it was possible that delicate correlations in the passage or nonpassage of the pho- information was somehow exchanged between the analyzers. analyzer ought not to influence the transmission of the second photon through the second analyzer, and the choice of orientation for the sec ond analyzer ought not to influence the transmission of the first pho ton through the first analyzer. The experimental arrangement is thus expected to satisfy Bell's locality condition. It follows that-according to Bell's theorem-there should be some violations of the quantum-me chanical predictions of correlations in the experimental outcome. In point of fact, however, the ex periment yielded just the opposite re sult. The correlation data agree with in experimental error with the quan tum-mechanical predictions that are calculated on the basis of the quan tum state '1',. Moreover, the data dis agree by more than five standard de viations with the extreme limits al lowed, according to Bell's theorem, by any of the local hidden-variables models. Even though the experiment of As pect and his colleagues is not com pletely definitive, most people be lieve the prospects of overthrow ing the results by future experiments are extremely small. It seems unlike ly that the family of local hidden variables models can be salvaged. The strange properties of the quan tum world-objective indefiniteness, objective chance. objective probabil ity and nonlocality-would appear to be permanently entrenched in phys ical theory. One of the strangest properties of 50 the quantum world i s nonlocality. Can the fact that under some circum stances a measurement on one pho ton apparently instantaneously af fects the result of a measurement on another photon be capitalized on to send a message faster than the speed of light? Fortunately for the special theory of relativity the answer to the question is no. An underlying as sumption of that theory-that no sig nal can travel faster than light-is preserved. ere is a brief argument that H shows why. Suppose two people want to communicate by means of a device similar to the one for testing local hidden-variables models. Be tween the observers a source emits pairs of correlated photons. Each ob server is provided with a polariza tion analyzer and a photodetector. The observers are free to orient the transmission axes of their analyzers any way they choose. Suppose the observers agree to align the transmission axes vertical ly. Then every time a pair of photons is emitted there will be a strict cor relation in the outcome: either both photons will pass through the ana lyzers or both will be blocked. But the strict correlation is of no value for each observer in isolation from the other. The first observer will note that half of the time photons pass through the first analyzer, on the average, and half of the time they are blocked. The second observer will note the same thing for the sec© 1987 SCIENTIFIC AMERICAN, INC ond analyzer. In other words. each observer in isolation sees only a random pattern of transmissions and blockages. Now imagine that the first observer tries to encode some information and send it to the second observer by changing the orientation of the first polarization analyzer. Depending on the orientation of that analyzer. there will be either a strict or a partial cor relation between the outcomes of the events at each detector. Once again. however, each observer will note that on the average half of the time photons pass through the analyzer and half of the time they are blocked. In general. no matter what the orien tations of the analyzers are, each ob server in isolation sees only a ran dom (and statistically identical) pat tern of transmissions and blockages. The quantum correlations between the photons can be checked only by comparing the data accumulated at the two detectors. Hence the attempt to exploit the quantum correlations to send messages faster than light cannot succeed. In this sense there is a peaceful coexistence between quantum me chanics and relativity theory. in spite of quantum-mechanical nonlocality. For this reason it would be mislead ing (and wrong) to say that nonlo cality in the quantum-mechanical sense is a reversion to action at a dis tance, as in the prerelativistic gravi tational theory of Newton. It is tempt ing to characterize quantum-me chanical nonlocality as "passion at a distance," not with any pretension to provide an explanation for the strange correlations, but only to em phasize that the correlations cannot be exploited to exert a controlled in fluence more rapidly than a light sig nal can be sent. Another test, called the delayed .t-\.choice experiment, which was proposed in 1978 by John Archibald Wheeler, then at Princeton Universi ty, also reveals the strangeness of the quantum world. The basic apparatus of the experiment is an interferom eter, in which a light beam can be split and recombined. A pulse of light from a laser is fired at the beam split ter, which is oriented in such a way that half of the light passes through the splitter and half is reflected at right angles to the direction of the in cident pulse. If the light from the two paths is subsequently recombined, an interference pattern can be detect ed, which demonstrates the wavelike quality of light. Now suppose the pulse of laser light is attenuated so severely that at any time there is only one photon in the interferometer. In this case two different questions can be asked about the photon. Does the photon take a definite route so that it is either transmitted or reflected by the beam splitter, thereby exhibiting a particle like property? Or is the photon in some sense simultaneously transmit ted and reflected so that it interferes with itself, thereby showing a wave like property? An answer was recently supplied by Carroll O. Alley, Oleg G. Ja kubowicz and William C. Wickes of the University of Maryland at College Park and independently by T. Hell muth, H. Walther and Arthur G. Za jonc of the University of Munich. Both grouP.S found that a photon be haves like a particle when particle like properties are measured and that it behaves like a wave when wavelike properties are measured. The remarkable novelty of the re sults is that the experiment was ar ranged so that the decision to meas ure particlelike or wavelike prop erties was made after each photon had interacted with the beam split ter. Consequently the photon could not have been "informed" at the cru cial moment of interaction with the beam splitter whether to behave like a particle and take a definite route or to behave like a wave and propagate along two routes. The length of both routes in the interferometer was about 4.3 me ters, which a photon can traverse in roughly 14.5 nanoseconds. Obvious ly this does not allow enough time for an ordinary mechanical device to switch between measuring particle and wavelike properties. The feat was made possible with a switch called a Pockels cell, which can be ac tuated in nine nanoseconds or less. A Pockels cell contains a crystal that becomes birefringent when a voltage is applied across it: light polarized along one axis of the crystal propa gates at a velocity different from that of light polarized along the perpen dicular direction. Given the proper choice of voltage and configurational geometry, light polarized in one di rection when it enters the cell will emerge polarized in the perpendicu lar direction. The Pockels cell was in serted in one of the two routes the photon could take after interacting with the beam splitter [see illustration on next page]. A piece of polarizing film was the .t-\.other essential element needed to switch between measurements of particlelike and wavelike properties. Light emerging from the Pockels cell impinged on the film. If the cell was "on," the polarization of the light was such that the polarizing film reflected the light into a photodetector, there by answering the question of which route and confirming the photon's particlelike properties. If the cell was "off," the polarization of the light was such that the polarizing film trans mitted the light, which then was com bined with the contribution coming from the other route; interference ef- DETECTOR DETECTOR DETECTOR DETECTOR COINCIDENCE COUNTING RAPID SWITCHING between orientations of polarization ana el between the analyzers was greater than the time required lyzers as photons flew was the hallmark of the experiment done to switch between orientations, so that the choice of orienta by Aspect and his colleagues (see illustration on page 47), which tion for each analyzer could not influence the observation made was completed in 1982. When a switch was "on," a photon was at the other analyzer. (Unfortunately for complete definitive deflected to an analyzer that was oriented one way; when the ness, however, the switching was periodic rather than random.) switch was "off," the photon traveled straight to an analyzer that The experiment confirmed quantum mechanics; it would appear was oriented another way. The time required for light to trav- that the strange implications of the theory must be accepted. 51 © 1987 SCIENTIFIC AMERICAN, INC er the cat is dead or alive until the box is opened. There would be nothing paradox ical in this state of affairs if. the passage of the photon through the mirror were objectively definite but merely unknown prior to obser vation. The passage of the photon is, however, objectively indefinite. Hence the breaking of the bottle is objectively indefinite, and so is the aliveness of the cat. In other words, the cat is suspended between life and death until it is observed. The con clusion is paradoxical, but at least it concerns only the results of a thought experiment. It is now more difficult to dis DELAYED-CHOICE EXPERIMENT is another test that reveals the strangeness of the miss the paradoxical nature of the quantum world_ A photon impinges on a beam splitter_ Two questions about the photon conclusion, because something sim can be asked_ Does the photon take a definite route so that it is either transmitted or re ilar to Schrodinger's thought experi flected by the beam splitter, thereby exhibiting a particlelike property? Or is the pho ton in some sense both transmitted and reflected so that it interferes with itself, exhib iting a wavelike property? To find out, a switch is positioned in one of the two paths the photon can take after interacting with the beam splitter (here, path A ). If the switch is on, the light is deflected into a photodetector (path B), thereby answering the question of which route and confirming the photon's particlelike properties. If the switch is off, the photon is free to interfere with itself (paths A and A') and produce an interference pattern, demonstrating the photon's wavelike properties. Results from the experiment show that a photon behaves like a wave when wavelike properties are measured and behaves like a particle when particlelike properties are measured. Remarkably, the ment has recently been achieved by a number of groups of investigators including Richard F. Voss and Rich ard A. Webb of the IBM Thomas ]. Watson Research Center in York town Heights, Lawrence D. Jackel of the AT&T Bell Laboratories, Michael H. Devoret of Berkeley and Daniel B. Schwartz of the State University switch was trigger�d after the photon had interacted with the beam splitter, so that the of New York at Stony Brook. Their photon could not have been "informed" whether to behave like a particle and take a work has relied to a certain extent on calculations that were done by definite route or to behave like a wave and propagate simultaneously along two routes. Anthony]. Leggett of the University of Illinois at Urbana-Champaign and fects confirmed the photon's wave photon, then that conclusion is not Sudip Chakravarty at Stony Brook, like aspect. Both groups of investigators have surprising, since in every quantum among other investigators. state there are properties that are The experimental apparatus con reported results that are in excellent indefinite. But the conclusion does sists of an almost closed supercon agreement with quantum mechan raise a further question: How and ducting ring. A thin slice of insulating ics. Their work shows that the choice when does an indefinite property be material (called a Josephson junc between the two questions can be come definite? Wheeler's answer is tion) interrupts the ring, but an elec tric current can circulate around the made after an individual photon has that "no elementary quantum phe interacted with the beam splitter of nomenon is a phenomenon until it is ring by "tunneling" through the insu an interferometer. a registered phenomenon." In other lator. The current generates a mag netic field. How are the results of the delayed words, the transition from indefinite choice experiment to be interpret ness to definiteness is not complete The quantity that is of interest ed? It is worthwhile first to disclaim until an "irreversible act of amplifica in the system is the magnetic flux one extravagant interpretation that tion" occurs, such as the blackening through the ring, which (when the has sometimes been advanced: that of a grain of photographic emulsion. field is uniform) is equal to the area of quantum mechanics allows a kind Students of the foundations of quan the ring multiplied by the component of "reaching into the past." Quan tum mechanics disagree about the of the magnetic field perpendicular tum mechanics does not cause some adequacy of Wheeler's answer, how to the plane of the ring. If the ring thing to happen that had not hap ever. The next experiment shows were uninterrupted, the flux would pened previously. SpeCifically, in the why the question is still open. mechanics does not cause the pho be trapped within the ring, but the in sulator allows the flux to slip from delayed-choice experiment quantum Erwin Schrodinger proposed one value to another. With modern magnetometers the flux can be meas later the photon impinges on a half-silvered ured with fantastic accuracy. The Pockels-cell switch is turned on, and mirror. The photon has a probabil fact that the flux arises from the it does not cause the photon to take ity of one-half of passing through motion both routes, in wavelike fashion, if the mirror and a probability of one zero if 12 nanoseconds I n 1935 a famous thought experiment. A ton to take a definite route at time of enormous numbers of half of being reflected. If the photon electrons (on the order of 1023) in the superconducting ring justifies A more natural interpretation is passes through the mirror, it is de speaking of the flux as a macroscop that the objective state of the photon tected, and the detection actuates a in the interferometer leaves many device that breaks a bottle of cya ic quantity. There is now good evi dence that states of the supercon properties indefinite. If the quantum state gives a complete account of the nide, which in turn kills a cat in a box. It cannot be determined wheth- which the flux does not have a def- the switch is off. 52 © 1987 SCIENTIFIC AMERICAN, INC ducting ring can be prepared in mite value-a quantum-mechanical mut Rauch and Anton Zeilinger of feature that had previously been es the Atomic Institute of the Austrian tablished only for observables of mi Universities, croscopic systems. To understand how this indefinite the University of Missouri at Colum Samuel A. Werner of bia and Clifford G. Shull of the Mas ness is demonstrated experimental sachusetts Institute of Technology ly, it is necessary to know that for each value of the flux the ring has a and their associates, the wave func tion of a neutron is split by a sheet certain potential energy. Ordinarily one would not expect that the flux of crystal and recombined by one or two other sheets. The interference through the ring could change spon effects exhibited in the recombina taneously from one value to another, tion demonstrate a number of re because a potential-energy barrier markable properties, including the separates adjacent values of the flux indefiniteness of the neutron's route from each other. Classical physics through the interferometer. forbids the transition between two Finally, R. G. Chambers of the Uni MACROSCOPIC SYSTEM can under some such values of the flux unless some versity of Bristol, G. M611enstedt of external source of energy, typical the University of Tilbingen and Akira ly thermal, is supplied to traverse Tonomura of Hitachi, Ltd., have con the barrier between them. In quan firmed by electron interferometry croscopic systems, such as the photon. The system shown here is a supercon circumstances exist in a state in which a macroscopic variable has an indefinite value; indefiniteness is not limited to mi tum mechanics, on the other hand, the remarkable Aharonov-Bohm ef the barrier can be tunneled through fect, in which an electron "feels" the ducting ring that does not quite bend without any external source of en presence of a magnetic field that is in back on itself. A thin slice of insulating ergy. The groups of investigators a region where there is zero probabil material separates the two ends of the mentioned above have shown that ity of finding the electron. This is a ring from each other, and an electric cur the flux does change between two striking demonstration of a kind of values, and that the change cannot nonlocality different from, although be entirely accounted for thermally; the observed tunneling must be at remotely related to, the nonlocality least partially quantum mechanical, A thorough understanding of the re particularly at very low tempera lation between the two kinds of non tures. But quantum-mechanical tun locality as well as the many other exhibited by correlated photon pairs. rent is made to circulate around the ring by "tunneling" through the insulator. The current generates a magnetic field. If the ring were continuous, the magnetic flux through the ring (the area of the ring mul tiplied by the component of the magnet ic field perpendicular to the plane of the ring) would be trapped at a fixed value, neling rests essentially on the indefi perplexing issues raised by exper niteness of the flux, which thus can iments probing the nature of the from one value to another. Surprisingly, not be localized definitely at or close quantum world awaits further work. the flux does not have a definite value. but the insulator allows the flux to slip to one value or another. The experimental demonstration of quantum indefiniteness in a mac roscopic variable does not ipso facto contradict the statement by Wheeler quoted above, but it does show that amplification from a microscopic to a macroscopic level does not in itself exorcise quantum-mechanical indefi niteness. The emphasis in Wheeler's statement about an "irreversible act of amplification" must be placed on the word "irreversible." The condi tions for the occurrence of an irre versible process are far from settled in contemporary theoretical physics. Some students of the subject (includ ing me) believe new physical princi ples must be discovered before we can understand the peculiar kind of irreversibility that occurs when an indefinite observable becomes defi nite in the course of a measurement. T he strangeness of the quantum world continues to be explored. Still other experiments have recent ly been performed or are now un der way; two classes of these exper iments should be mentioned here, INDEFINITENESS in the system shown at the top of the page is depicted schematically. Each value of the flux through the superconducting ring has a certain potential energy associated with it. Ordinarily one would not expect that the flux through the ring could spontaneously change from one value to another, because a potential-energy barrier separates the adjacent values of the flux from each other. The barriers can be thought of as hills, and the state the system is in can be represented as a ball residing in a valley among the hills. According to classical physics, a transition between two values sepa even though there is no room to dis rated by a barrier requires outside energy (to push the ball over the hill). Quantum me cuss them in detail. In the neutron chanically, however, the barrier can be tunneled through without any external source interferometer experiments of Hel- of energy. Tunneling is essentially a manifestation of the indefiniteness of the flux. © 1987 SCIENTIFIC AMERICAN, INC 53