The Theor Quantum y an d Reality The doctrine that the world is made up of objects whose existence is independent of human consciousness turns out to be in conflict

with quantum mechanics and with facts establishedby experiment

by Bernard d 'Espagnat

}ty successful theory in the physical nomena (the observed pO Si tI On of the tic theories of nature. An argument de­ sciences is expected to make ac­ pointer) and not with any underlying rived from these premises leads to an curate predictions. Given some physical state (the real position of the explicit prediction for the results of a well-defined experiment, the theory electron). certain class of experiments in the phys­ should correctly specify the outcome or ics of elementary particles. The rules should at least assign the correct prob­ t now turns out that even this renun­ of quantum mechanics can also be em­ abilities to all the possible outcomes. I ciation is no t entirely satisfactory. ployed to calculate the results of these From this point of view quantum me­ Even if quantum mechanics is consid­ experiments. Significantly, the two pre­ chanics must be judged highly success­ ered to be no more than a set of rules, dictions differ, and so either the local ful. As the fundamental modern theory it is st ill in conflict with a view of realistic theories or quantum mechanics of atoms, of molecules, of elementary the world many people would consider must be wrong. particles, of electromagnetic radiation obvious or natural. This world view is The experiments in question were first and of the solid stat e it supplies meth­ based on three assumptions, or premises proposed as "thought experiments," in­ ods for calculating the results of experi­ that must be accepted without proof. tended for the imagination only. In the ments in all these realms. One is realism,th e do ctrine that regular­ past few years, however, several ver­ Apart from experimental confirma­ ities in observed phenomena are caused sions of them have been carried out with tion, however, something more is gener­ by some physical reality whose exis ­ real apparatus. Although not all the ally demanded of a theory. It is expected tence is independent of human observ­ findings are consistent with one another, not only to determine the results of an ers. The second premise holds that in­ most of them support the predictions of experiment but also to provide some un­ ductive inference is a valid mode of quantum mechanics, and it now seems derstanding of the physical events that reasoning and can be applied freely, so that unless some extraordinary coinci­ are presumed to underlie the observed that legitimateconclusions can be drawn dence has distorted the results the quan­ results. In other words, the theory from consistent observations. The third tum-mechanical predictions will be con­ should not only give the position of a premise is called Einstein separability or firmed. It follows that the local realistic pointer on a dial but also explain why Einstein locality, and it states that no theories are almost certainly in error. the pointer takes up that position. When influence of any kind can propagate The three premises on which those theo­ one seeks information of this kind in the fasterth an the speed of light. The three ries are founded are essential to a com­ quantum theory, certain conceptual dif­ premises, which are often assumed to mon-sense interpretation of the world, ficulties arise. For example, in quantum have the status of well-established and most people would give them up mechanics an elem entary particle such truths, or even self-evident truths, form only with reluctance; nevertheless, it ap­ as an electron is represented by the the basis of what I shall call local realis- pears that at least one of them will have mathematical expression called a wave function, which often describes the elec­ tron as if it were smeared out over a large region of space. CORRELATIONS BETWEEN DISTANT EVENTS can form the hasis of conclusions about This representation is not in conflict the structure of the world. Suppose a physicist sets up an experiment in which subatomic par­ with experiment; on the contrary, the ticles such as protons are fired one at a time into an instrument that can give only two possible wave function yields an accurate esti­ readings, plus and minus (a). He finds that for some protons the reading is plus and for others it is minus, but he cannot tell whether the instrument measures some real property of the pro­ mate of the probability that the electron tons or merely records random fluctuations. The physicist then arranges two identical instru­ will be found in any given place. When ments with a source that emits two protons simultaneously (b). He observes a strict negative the electron is actually detected, how­ correlation: whenever one instrument reads plus, the other reads minus. On the basis of this cor­ ever, it is never smeared out but always relation the physicist concludes that a real property of protons is responsible for the readings has a definit e position. Hence it is not and that its value is determined before the protons leave the source. If the sample of particles entirely clear what physical interpreta­ measured meets certain statistical tests, he can go on to infer that every pair of protons emitted tion should be given to the wave func­ by the source consists of one proton with the property plus and one with the property minus, tion or what picture of the electron one even if neither proton is submitted to a measurement (c). The conclusions are reasonable if e should keep in mind. Because of ambi­ thre premises are accepted as valid: that at least some properties of the world have an existence guities such as this many physicists find independent of human observers, that inductive inference can be applied freely and that a mea­ surement made with one instrument cannot influence the result of a measurement made with it most sensible to regard quantum me­ the other instrument. A more restrictive form of the last premise forbids such influences only chanics as merely a set of rules that pre­ if the two measurements are so nearly simultaneous that the influence would have to propagate scribe the outcome of experiments. Ac­ faster than light. The premises can be identified as realism, the free use of induction and sep­ cording to this view the quantum theory arability; the more restrictive version of the separability premise is called Einstain separabil­ is concerned only with observable phe- ity or Einstein locality. Any theory that incorporates them is called a local realistic theory.

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© 1979 SCIENTIFIC AMERICAN, INC to be abandoned or modified or in some nation is called for. It would make no have a common cause. Until such a link way constrained. difference if the measured values were has been discovered the mind cannot The experiments are concerned with always opposite instead of the same; the rest satisfied. Moreover, it cannot do so correlations between distant events and correlation would then be a negative even if empirical rules for predicting fu­ with the causes of those correlations. one, but its magnitude would be ju st as ture correlations are already known. A For example, suppose two particles a great, and it would be just as unlikely to correlation between the tides and the few meters apart are found to have iden­ arise by chance. motion of the moon was observed in an­ tical values of some property, such as Whenever a consistent correlation be­ tiquity, and rules were formulated for electric charge. If this result is obtained tween such events is said to be under­ predicting future tides on the basis of once or a few times, it might be di s­ stood, or to have nothing mysterious past experience. The tides could not be missed as coincidence, but if the corre­ about it, the explanation offered always said to be understood, however, until lation is detected consistently in many cites some link of causality. Ei ther one Newton introduced his theory of univer­ measurements, a more systematic expla- event causes the other or bot h events sal gravitation. The need to explain observed corre­ lations is so strong that a common cause is sometimes postulated even when there is no evidence for it beyond the correlation itself. Whether or not ? REALISM this procedure can always be justified is a central issue in the conflict between quantum mechanics and local realistic theories. The correlations in question are between observations of subatomic particles, where a quantum-mechanical description, with its attendant episte­ mological hazards, is indispensable. The predictions of local realistic theories, however, can be illustrated by consider­ ' ing how correlations between distant events are explained in a more famil­ iar context, where qua ntum mechanics need not be introduced.

magine th at a psychologist has de­ I vised a simple test, which a subject must either pass or fail, so that there (/) w can be no ambiguity in the results. The LOCAL REALISTIC a: QUANTUM MECHANICS psychologist finds that some people THEORIES o w pass and some fail, but he does not I f- know what distinguishes the two groups other than their performance on the test itself. In other words, he cannot tell whether the test measures some real ap­ \I titude or attribute of· the subjects or (/) z whether the results are haphazard. o BELL INEQUALITY i= BELL INEQUALITY It seems there is no general solution to () IS VALID o IS SOMETIMES INVALID this problem, but in a special case it w might be solved. Suppose the test is ad­ a: [L ministered not to a series of individuals but to a series of married couples and that a strong correlation is detecred in their answers. The procedure might con­ sist in separating the husbands from the t wives before the test and then giving the test to each of them in isolation. When th e results are analyzed, it is found again that part of the popula tion has passed EXPERIMENTAL and part has failed, but in the case of TEST each couple where the husband passed so did the wife; similarly, whenever the husband failed so did the wife. If this correlation persists after many couples are tested, the psychologist is almost sure to conclude that the re­ sponse of each subject is not determined randomly at th e time of testing. On the RESULT contrary, the test must reveal some real property or attribute of the subjects. LOCAL REALISTIC THEORIES and quantum mechanics make conflicting predictions for The property must already be present certain experiments in which distant events are correlated. In particular, local realistic theories in the subjects before they are tested, predict that a relation called the Bell inequality will be obeyed, whereas quantum mechanics and indeed before they are separated. predictsa violation of the inequality. There is strong experimental evidence that the inequality is violated in the way predicted by quantum mechanics. Local realistic theories therefore seem Chance may have had some influence to be untenable, and at least one of the premises underlying those theories must be in error. on the development of th e property,

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BELL INEQUALITY, formulated by John S. Bell of the European Organization for Nuclear Research (CERN), can be proved in two stages. The inequality applies to experiments with particles that have three stable properties, A, Band C, each of which can have the values plus and minus. Thus tbere are 23, or 8, possible classes of particles, corresponding to the eight regions of the diagrams shown here. If a particle has been found to have the properties A + and B -, then it must be a member either of theclass A +B-C+ or of the class A+B-C-. Hence if N(A+B-) represents the number of such particles, it must be equal to the sum N(A +B-C+) + N(A +B-C-). In a similar way it can be shown that N(A+C-) is equal to N(A+B+C-) + N(A+B-C-), from which it follows that N(A+C-) is greater than or at least equal to N(A + B -C-). The same reasoning leads to the conclusion that N(B -C+ ) must be greater than or equal to N(A+B-C+). These three relations can now be combined to yield a further inequality, wbich asserts that the number of A+B- particles cannot exceed the sum of the A+C­ particles and the B-C+ particles. The same relation holds if all signs "7 are reversed to give the inequality N(A-B+) � N(A-C+) + N(B+C-). The last two inequalities can be added to yield a relation among all individual particles for which two propertieshave opposite values.

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© 1979 SCIENTIFIC AMERICAN, INC since not all the couples possess it, but that influence must have been exerted at some time before the husbands and the wives were separated. It was only then, while the husbands and the wives were still united, that they could have ac­ quired any traits that would in duce them to respond consistently the same way. Thus the correlation is explained by attributing it to a common cause an­ tecedent to the test. One other explanation that must be excluded in deriving this conclusion is the possibility that husbands and wives could communicate with each other while they were taking the test. If some means of communication were avail ­ able, there would be no need for any tested attribute to exist beforehand. Whichever spouse' was given the test first could choose a response at random and send instructions to the other, there­ by creating the observed correlation. In giving a psychological test it would not be hard to guard against subterfuge of this kind. In the extreme case the tests could be made so nearly simultaneous, or husbands and wives could be tested at sites so far apart, that a signal moving no faster than light could not arrive in time to be of any value.

nce having decided that the test measures some real property of in­ dividuals,O the psychologist can take a further step and make an inductive in ­ ference. If the couples already tested constitute an unbiased sample of some population of couples, and if the sample meets certain statistical standards, the psychologist can infer that any couple taken from the same population will be made up of a husband and a wife who either both possess or both do not pos­ sess the property measured by the test. By the same principle he can conclude that in any large, unbiased sample of couples who have not yet been tested some of the couples will have the prop­ erty and some will not. The confidence of these assertions approaches certain­ ty as the size of the sample increases. Hence both the correlation within cou­ ples and the existence of differences be­ tween couples are inferred to exist even in the segment of the population that has not been submi tted to any test. These concl usions rest on the same three premises that form the basis of lo­ cal realistic theories. Realism is a neces­ sary assumption if one is to beli eve at least some tests measure stable proper­ ties that exist independently of the ex ­ perimenter. It was necessary to assume the validity of inductive inference in or­ der to extrapo late from the observed data to the segment of the population that had not yet been tested. Separabili­ ty was incorporated in the assumption that husbands an d wives being tested cannot communicate with each other. If the tests are given simultaneously, so that any signal passing between hus-

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© 1979 SCIENTIFIC AMERICAN, INC THEB_528i. A CAR THAT _ITS THEDBIANDSOFTHE80� WITHOUT VIOLATING THE CONCEPTO F A Conventional automotive wis­ 528i's fuel-injected, six-cylinder, And, while the 528i provides dom has it that any increase in a car's overhead cam engine responds in a as longBMW. a list of lUxury items as one environmental control paraphernalia manner that can only be described could sanely require-AM/FM must inevitably result in a corre­ as exhilarating. stereo cassette, full-power acces­ sponding decrease in performance. And yet, the 528i (with stan­ sories, air conditioning, etc.-its lux­ Indeed, many serious automo­ dard transmission) delivers an ury is purposefully engineered to tive writers have warned that pollu­ impressive Dll EPA estimated mpg, help prevent driver fatigue. tion systems and fuel efficiency 26 estimated highway mileage and, Vital controls are within easy regulations have all but sounded the based on these figures an esti­ reach; the tachometer, speedom­ death knell for high-performance mated mpg range ofl2791 miles and eter and ancillary instruments are automobiles. a highway range of 426 miles. well-marked and easy to read. These gloomy predictions, (Naturally our fuel efficiency Its front seats are designed to however, do not take into consider­ figures are for comparison purposes hold their occupants firmly in place, ation the determination of the engi­ only. Your actual mileage and range and are so thoroughly adjustable neers at the Bavarian Motor Works may vary, depending on speed, that it is all but impossible not to to build extraordinary automobiles. weather and trip length. Your actual find a comfortable seating position. Against all odds, the BMW highway mileage and highway If you'd care to judge the ex­ 528i not only meets the demands of range will most likely be lower.) traordinary performance of the society, it also provides the kind of Its four-speed manual trans­ 528; for yourself, phone exhilarating driving experience that mission (automatic is available) runs your nearest BMW deal- '� most people have all but given up smoothly and precisely up through er and he will arrange for lost in today's lUXUry automobiles. the gears. a thorough test drive at AMIDST INCREASING MEDIOC­ Its suspension system-indepen­ your convenience. & RITY, BMW GETS EVEN BEDER. dent on all four wheels-provides the THE ULTIMATE DRIVINGMACHINE. Press the accelerator and the driver with an uncanny feel of the road. Bavarian Motor Works, Munich, Germany. © 1979 BMW of North America. Inc. The BMW trademark and logo are registered trademarks of Bayerische Motoren Werke, A.G.

© 1979 SCIENTIFIC AMERICAN, INC bands and wives would have to propa­ an argument th at was somewhat similar erty of th e protons or merely observing gate faster th an th e speed of light, th e to th e one I have attributed to th e psy­ random fluctuations in his apparatus. assumption is eq uivalent to Einstein ch ologist. In 1935 Einstein pub lished a He th erefore tries applying the test not separability. paper with two young colleagues, Boris to individual protons but to pairs of At firstth e conclusions drawn from Podolsky and Nathan Rosen, in wh ich th em. Th e protons th at make up each thishy pothetical experiment in psychol­ he stated his objections explicitly. He pair are initially in close proxim ity, ogy seem to follow quite obviously from did not maintain th at th e quantum th eo­ having been broug ht together by some the data. An epistemologist might none­ ry is wrong; on th e contrary, he assumed well-defined procedure th at is th e same theless maintain th at th e conclusions are that at least some of its predictions must for all th e pairs. The protons are th en uncertain. In particula r an epistemolo­ be correct. Wh at he proposed was th at allowed to separate, and wh en th ey gist trained in th e foundations of quan­ the quantum-mechanical description of have moved some macroscopic distance tum mechanics mightargue th at th ere is nature is incomplete or approximate. apart, th ey are tested, simultaneously no logical necessity for accepting th e Th e motion of a particle must be de­ for some pairs and with an interval be­ three premises of the psychologist's ar­ scribed in terms of probabilities, he ar­ tween th e tests for th e remaining pairs. gument; hence neither would it be neces­ gued, only because some of the parame­ The ph ysicist discovers a strict negative sary to conclude th at a correlation exist­ ters that determine th e motion have not correlation: wh enever one proton in a ed between th e husbands and wives be­ yet been specified. If th e values of th ese pair passes th e test, th e other proton in­ fore they were tested, or th at di fferen­ hypothetical "h idden parameters" were variably fails. ces existed between the couples before known, a fully deterministic trajectory Th e situation of th e ph ysicist has ob­ any tests were given. The psychologist is could be defined. vious similarities to that of th e psychol­ likely to findth ese objections laughable, A number of counterarguments to ogist giving a test to married couples, an expression of misplaced doubt or of a Einstein's proposalha ve been formulat­ and the same reasoning might be ap­ very unscientific adherence to paradox. ed. For now I sh all mention only one of plied to th e results of th e ph ysical exper­ In th e literature of quantum mechanics, th em, wh ich is based on th e criterion of iment. If realism, th e free use of induc­ however, th ere are numerous arguments utility. It is immaterial, the argument tion and Einstein separability are all ac­ similar or equivalent in form to th is one, states, wh ether or not hidden parame­ cepted as premises, then th e ph ysicist is all purporting to sh ow th at correlations ters exist, or whether differences be­ justified in concluding th at his test does and differences need not exist until th ey tween married couples exist in th e ab­ measure some real property of protons. are measured. sence of a test. Even if th ey do exist, th ey For th e correlation to be explained th e A singular fe ature of quantum me­ sh ould not be incorporated into any th e­ property must exist before th e protons ch anics is th at its predictions generally ory devised to explain th e observations, in each pair are separated, and it must give only th e probability of an event, not and so th ey can be said to have no sci­ have some definite value from th en until a deterministic statement that the event entific existence. Th e exclusion of the th e measurement is made. Furthermore, will happen or that it will not. The wave hidden parameters is justified by th e if additional pairs of protons are pre­ function employed to de scribe th e mo­ conjunction of three facts. First, th e pared by th e same method, the physicist tion of an elementary particle is often mathematical formalism of th e th eory knows th at in each case one proton will interpreted probabilistically: the proba­ is simpler if any hidden parameters are have th e property and one will not, even bility of finding the particle at any given ignored. Second, th is simple formalism if neither proton is actually tested. point is proportional to th e square of predicts results that are confirmed by Is th ere any real test th at can be car­ the wave function at th at point. As I experiment. Third, adding th e hidden ried out on subatomic particles with re­ mentioned above, a wave function can parameters to th e th eory would give rise sults like th ese? There is. It is a measure­ sometimes be spread out over a large to no supplementary predictions th at ment of any one component, defined region, wh ich implies th at the probabili­ could be verified. Th us th e assertion that along some arbitrary axis, of th e spin of ty can also be broadly distributed. Of hidden parameters exist is beyond th e a particle. Th e spin attributed to a suba­ course, wh en a measurement is actually reach of experiment and is a proposition tomic particle is analogous only in some made at some ch osen point, th e particle not of ph ysics but of metaphysics. respects to th e spin angular momentum must either be detected or not be detect­ Th is defense of th e conventional in­ of a macroscopic body such as th e earth. ed; the wave function is th en said to col­ terpretation of quantum mechanics dis­ For th e purposes of this discussion, lapse. Suppose th e particle is detected. misses any hidden parameters as being however, th ere is no need to introduce Th e question of epistemological interest superfluous and ultimately, perhaps, the details of how spin is treated in is th en: Did th e particle have th at defi­ meaningless. Recent th eoretical devel­ quantum mechanics. It will suffice to nite position all along, even before th e opments have sh own that th eir actual note th at th e spin of a particle is repre­ measurement was made? status is quite different. Th e hypothesis sented by a vector, or arrow, th at can be Th e conclusi ons of th e psychologist, th at hidden parameters exist does in fact imagined as being attached to th e parti­ if th ey could be transferred to this con­ lead to experi mental pred ictions di ffer­ cle. A projection of th is vector onto any text, would imply that the position of ing from th ose of quantum mec hanics. axis in th ree-dimensional space is th e the particle was well defined from th e Hidden-parameter theories, and local cO l1l ponent of th e spin along that axis. A start, just as th e att ribute di scovered in realistic th eories in general, place a lim­ well-established but nonetheless sur ­ some members of th e population was it on th e extent to wh ich certain dis­ prising property of protons (and many deduced toha ve existed before any tests tant events can be correlated; quantum other particles) is th at no matter wh at were given. According to th is argument mechanics, in contradistinction, predicts axis is chosen for a measurement of a the position of th e particle was never th at under some circumstances th e limit spin component th e result can take on indeterminate but was merely unknown will be exceeded. Hence it should be only one of two values, whic h I sh all to th e experimenter. possible, at least in principle, to devise designate plus and minus. (A measure­ an experimental test that will discrimi­ ment of a component of th e eart h's spin ost authorities on th e quantum th e­ nate between th e two th eories. would give very different results; de­ M ory would disagree. One excep­ pending on th e direction of th e compo­ tion among ph ysicists was Einstein, wh o uppose a ph ysicist has devised a test nent, it could have any value fr om zero throughouthi s life remained dissatisfied that can be carried out on subatomic up to th e total angular momentum of with the probabilistic nature of th e in­ particlesS such as protons. After many th e earth.) terpretations generally given to quan­ trialshe finds th at some protons pass th e A strict negative correlation between tum mechanics. He based his most inci­ test and others fail, but he does not know spin components is observed wh en any sive criticism of th ose interpretations on wh etherhe is measuring some real prop- two protons are brought together in

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© 1979 SCIENTIFIC AMERICAN, INC the quantum-mechanical configuration of a particle is defined by components longer have the same spincomponents it called the si nglet state. In other words,if along three axes in space, which need had when it entered the first instrument. two protons in the si nglet state are al­ not necessarily be at ri ght angles to one Although noin strument can measure lowed to separate and the same compo­ another. For a vector associated wi th a more than one spin component at a nent of spi n is subsequently measured macroscopic objectin everyday li fe, one ti me, a device can be built that is capa­ on both particles, it will always be plus would assume as a matter of course, ble of being adjusted to measure the spin for one proton and minus for the other. and with good reason, that all three component along any one of three ar­ There is no known means of predicting components have definite values at all bi trarily chosen axes. I shall designate which particle wi ll have the plus compo­ times; the value of a component mi ght these axes A, Band C and note the re­ nent and which the mi nus component, be unknown, butit cannot be undefined. sults of experiments as follows. If the but the negative correlation is well es­ When this assumption is applied to the spin component along axis A is found to tablished. It makes no difference what spin vector of a particle, however, it be plus, it is labeled A+ ; if the compo­ component of the spin the experimenter becomes highly suspect, and indeed in nent along axis B is minus, it is given as chooses to measure, provided the same the conventionalin terpretation of quan­ B-, and so on. The physicist can now component isme asured for both parti­ tum mechanics itis di smi ssed as an in­ prepare a large batch of protons in the cles. It alsoma kes no difference how far stance of a hidden-parameter theory. singlet state. He finds thatif he measures the protons travel before the measure­ The problem is that no experiment can component A for both protons in each ment isma de. as long as there are no be devised, evenin pr inciple, that would pair, some protons are A+ and others are perturbing influences,such as other par­ provide information about the sim ulta­ A-, but whenever one member of a pair ti cles or radiation, along their paths. neous values of all three components. A isA+ , the other member is always A-. If single instrument can measure only one he decides instead to measure compo­ n this si mple measu rement there is spin component, and in doing so it gen­ nent B, he observes the same negative I no conflict between the predictions erally alters the values of the com po­ correlation: whenever one proton is B+, of quantum mechanics and those of nents. Hence in order to learn the val­ its si nglet partner is B-. Similarly, a C+ local realistic theories. A conflict can ues of three components threeme asure­ proton isin variably accompanied by a arise, however, when the experiment is ments would have to be madein succes ­ C-one. These results hold no matter made somewhat more complicated. si on. By the tim e the particle em erged how the axes A, Band C are oriented. The vector that represents the spin from the third instrument it would no It isim portant to emphasize that in these experiments no proton is submit­ ted to a measurement of more than PAIRS OF NEGATIVELY one spinco mponent. Nevertheless,if the CORRELATED physici st accepts the three premises of PARTICLES local realistic theories, he can draw con­ clusions fro m these findings about the values of all three components, follow­ ing an argument much like that of the

TEST RESULTS hypothetical psychologist. Considering a fresh batch of proton pairs in the sin­ glet state on which no spinme asurement has yet been made (and perhaps on which no such measurement wi ll ever be DEDUCED PROPERTIES made), he can infer that in every pair one proton has the property A + and the other has the property A -. Similarly, he NUMBER OF can conclude that in every pair one pro­ TEST RESULTS ton has the property B+ and one B-and NUMBER OF PARTICLES one has the property C+ and one C-. WITH DEDUCED PROPERTIES hese conclusions require a subtle INEQUALITY Tbutim portant extension of the mean­ N(A+B-) + N (A-B+) .;;N(A +C-) + N (A-C+) + N(B +C-) + N( B-C+) DEMONSTRATED ing assigned to a notation such as A +. PREVIO USLY Whereas previously A+ was merely one THEREFORE possible outcome of a measurement

BELL INEQUALITY made on a particle, itis converted by this argument into an attribute of the SECOND STAGE OF THE PROOF extrapolates from tbe case of single particles for wbicb particle itself. To be explicit, if some two properties are known to tbat of pairs of particles, each particle of which is tested for one unmeasured proton has the property property. The pairs are created in sucb a way that there is always a strict negative correlation that a measurement along the axis A for any property considered separately, that is, if one particle in a pair has the property A +, would give the definite result A+ , then the otber must bave tbe property -. Because of this correlation, if one particlein a pair is A that proton is said to have the property found to be and the otber is found to be B+, it is possible to deduce both properties of both A + A +. In other words, the ph ysicist has particles. The doubly positive test result can arise only if one particle has the two properties been led to the concl us ion that both pro­ A + B-and the other has tbe properties -B+. Hence the number of sucb doubly positive test A tonsin each pair have definite spin com­ results, which can be designated n[A + B+ 1, must be proportional to the total number of parti­ cles with the properties A + B-and A -B+. Similar proportionalities can be derived for the num­ ponents at all times. The components ber of doubly positive results observed when pairs of particles are tested for properties Aand C may be unknown, si nce the physicist and for properties Band C; these are tbe quantities n[A +c+ 1 and n[B +C+ 1. Tbe constant of cannot say which proton in a pair has proportionality depends only on tbe number of pairs submitted to eacb set of tests and on the the property A+ and which has th e prop­ total number of pairs, and so tbe constant is the same in all three cases. It follows that the tbree erty A -until a measurement along axis ratios of the number of doubly positive test results to tbe number of individual particles tbat A has been made, but he can argue from can give rise to tbose results must also be equal. A relation has already been demonstrated the premises of local realistic theories between tbe numbers of individual particles with tbe indicated properties; it is tbe inequali­ ty proved in the illustration on page 162. If that inequality is to hold, there must be a simi­ that the values are quite definite even in lar inequality between tbe numbers of doubly positive test results. This is the Bell inequality. the absence of any measurements. This Tbe proof is valid only if tbe tbree premises of local realistic theories are assumed to be valid. view is contrary to the co nventional in-

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THOUGHT EXPERIMENT would test the Bell inequality by mea­ suitable pair of protons bad bee n emitted. Each proton would then suring tbe components of tbe spin of protons or otber elementary par­ enter an analyzer, wbere it would be deflected to one of two detectors ticles. A spin component is a projection along some axis of tbe pro­ depending on tbe value of its spin component along tbe axis defined ton's intrinsic angular momentum; eacb component can bave only by tbe analyzer. If tbe analyzers were set to measure the spin compo­ two possible values, wbicb can be designated plus and minus. Tbe nents along tbe same axis, a strict negative correlation would be ob­ experiment, wbicb assumes tbe availability of perfect instruments, served. If one amllyzer were rotated, so that they measured different would bave a source wbere pairs of protons are brought together in a components, local realistic tbeories predict that the correlation ob­ quantum-mecbanical configuration called tbe singlet state. Tbe pairs served would be no greater tban tbat allowed by the Bell inequality would tben be broken up, and the protons would fly apart in opposite regardless of wbat tbe angle between the analyzers was. Quantum directions. "Event-ready" detectors would issue a signal wbenever a mecbanics predicts a violation of the Bell inequality for some angles.

terpretation of quant um mechanics, bu t In 1964 Jo hn S. Bell of the Europe ­ gle particle. Su pp ose this impossible in ­ it is not contradicted by any fact that has an Organization for Nuclear Research strument has revealed th at a part icular yet been introduced. (CERN) discovered such a relation. For proton has th e sp in components At and The strict negative correlation for any large sample of singlet proton pairs B-. The third component, C, ha s not protons in th e singlet state is expected Bell showed that the tenets of local real­ been measured, bu t it can have only one only wh en th e same sp in component is istic th eories impose a limit on th e ex­ of two values, plus or minus; hence th e measured on both protons. What hap­ tent of correlation that can be ex pect­ measured proton mu st be a member of pens wh en th e instruments are set to ed when different spin components are one of tw o sets ofpr otons, ei ther the se t measure different components? To be measured. The limit is expressed in th e with sp in components A+ B-C I or the precise, consider th e following ex peri­ form of an inequality, which is now set with components A r B-C . There ment. Pairs of protons are brought to­ called th e Bell inequality. Given the ex­ are no ot her possibilities. gether in th e singlet st at e by th e same perimental conditions described above, If manypr ot ons with th e sp in compo­ method employed in th e earlier experi­ it states that the nu mber of A+B+ pairs nents A+ B-are detec ted, one can wri te ments and are allowed to separateun der cannot exceed th e su m ofth e nu mber of an equat ion about thei r nu mber: exactly th e same conditi ons. Each pro­ A+C+ pairs and th e nu mber of B+C+ ton is th en tested for ju st one sp in com­ pairs. Th e inequality can be expressed in N(A+ B-)=N(At B-C+)+N(A" B-C-). ponent, A, B or C,bu t wh ich one of th e symbols as components is measured in each case is In order to avoid conf usion th e symbol determined entirely at random. Some­ I/[A+ B+].s I/[A+C+] + I/[B+C+] . N(A+ B-) has been em ployed to rep re­ times by coincidence the same compo­ sent th e numb er of individual prot ons nent will be measured on both protons Many similar inequalities could be con­ wit h the two sp in com ponents A rand in a pair; th ose results are discarded, structed with the various symbols trans­ B-; th e symboll/[A+ B-] gives the nu m­ since theypr ovide no new information. posed or with the signs reversed. Be­ ber ofpr ot onpa irs in wh ich onepa rt icle The remaining pairs mu st then be made cause th e directions along wh ich the has th e component A t an d th e oth erha s up of either one proton tested along axis sp in components are defined were ch o­ th e component B-. Th e eq uat ion st ates A and one tested along axis B, or one sen arbitrarily, all su ch formulations th e obvious fact that wh en a set ofpa rt i­ tested along axis A and one along axis C, are interchangeable, and I sh all discuss cles is divided intotw o su bsets, th e total or one along axis B and one along axis e. only th is one. number of part icles in th e original se t For th e sake of brevity I sh all refer to mu st be eq ual toth e su m of the num ­ the pairs in each of th ese th ree popu la­ he Bell ine quality can be proved, bers in the su bsets. tions as AB, AC and Be. A pair th at on with in th e context of local realis tic Th e prot ons foun d toha ve the sp in testing yields th e results A+ for one pro­ Tth eories, throu gh a st raightforward ar­ components At C-can be analy ze d ex ­ ton and B+ for th e other can be labeled gu ment in th e mathematical theory of actly th e same way. Every su ch proton an A+B+ pa ir. The nu mber of su ch pairs sets. It is convenient to begin with an mu st be a member eith er of th e se t observed can be represented by th e no­ assumption contrary to fact: th at some At B+C-or ofth e set AT B-C-, and th e n[A total nu mber N(A+C-) mus t be eq ual tation + B+].Can any relation among means exist for independently measur­ these quanti ties be ex pected? ing two comp onents of th e sp in of a sin- toth e su m N(A +B+C-) + N(A+B-C-).

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© 1979 SCIENTIFIC AMERICAN, INC SCIENTIFIC AMERICAN Medicine is You can wait years for new the clinician's answer to the dif­ fuseness of the periodicals and developments to appear in the prepublication obsolescence of the textbooks. standard texts. spend Because its authors update

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© 1979 SCIENTIFIC AMERICAN, INC A further step can now be taken. If number of such doubly positive pairs, the number of protons N(A +C-) is equal must be proportional to N(A+ B-), the to N(A + B+C-) + N(A + B-C-), then it number of individual protons with the must be greater than or at least equal to spin components A+ B-. In the same N(A + B-C-). (The two sets will be equal way n[A+C+] must be proportional to if the B components of all the particles' N(A +C-) and n[B+C+] must be propor­ spins happen to be minus, so that the tional to N(B-C+). The constant of pro­ subset (A+ B+ C-) is empty; otherwise portionality in all three cases is the N(A +C-) will be larger. In other words, same. For single protons each of which a part of the whole cannot be greater is subjected to an imaginary double than the whole.) The same reasoning measurement an inequality has already can be applied once again to prove that been proved, showing that N(A + B-) can the number of protons with spin compo­ be no greater than the sum of two terms: nents B-C+ mu st be equal to the sum N(A +C-) N(B-C+). It is now possible +' N(A+B-C+) + N(A-B-C+) and hence to replace each of these unmeasurable that N(B-C+) must be greater than or quantities by the corresponding num­ Establishing eq ual to N(A + B-C+). bers of doubly positive proton pairs. Consider again the first equation de­ The resulting expression is A Vineyard rived above: . '. ' To produce wine grapes of n[A+B+] � n[A+C+ ] + n[B+C+ ]. : . • "1 a truly premium nature, N(A + B-)= N(A + B-C+)+ N(A + B-C-). " :. 0: : you mus't begin with a This is the Bell inequality. .: ,.; properly established vineyard. We recently It has just been demonstrated that Of course the inequality is proved by addedm··· acres to our Sonoma Valley 80 N(B-C+) is greater than or at least equal this argument only if the three premises N(A + B-C+), vineyard, a project that involved many to which is the first term of local realistic theories are considered steps over several months. on the right side of the equation. It has valid. Indeed, it is here that the premises We first clearedand contoured the also been shown that N(A +C�) is greater have their most important application land. Next we "ripped" or loosened the than or equal to N(A + B-C-), which is and ultimately their most questionable soil to a depth of 5 feet wi th a tractor and the second term on the right side of the one. If the premises are granted, at least deep-toothed ripper. We equation. It is therefore permissible to for the sake of argument, it should be smoothed the surface by make the appropriate substitutions in clear that the Bell inequality must be discing and then dragging a heavy weight over the soil. the equation, changing the equals sign to satisfied. Moreover, the orientation of one signifying "less than or equal to." the axes A, Ba nd C has nowhere been The result is the inequality specified, so that the inequality should be valid regardless of what axes are cho­ N(A + B-) � N(A +C-) + N(B-C+). sen. The only possible violation of the inequality would result from a statisti­ Although this inequality is hereby cal fluke, where many particles with the A surveyor laid out a grid of 96 foot formally derived, it cannot be tested di­ spin components A+ and B+ happened squares and working within one square at a rime, we laid out a row every feet rectly by experiment because no instru­ to appear through random coincidence. 12 with vines spaced 8 feet apart. Vine loca­ ment can independently measure two The probability of such a coincidence tions were marked with chalk and a stake approaches zero as the number of parti­ spin components of a single proton. The driven at each. experiments under consideration, how­ cles tested increases. Vines were planted by hand, the roots ever, are carried out not on individual The Bell inequality constitutes an ex­ carefully spread and watered before cover­ protons but on correlated pairs of them, plicit prediction of the outcome of an ing. The entire vine was then covered by a and there is no need to make such im­ experiment. The rules of quantum me­ mound of loose soil to prevent sun dam­ possible measurements. Suppose one chanics can be employed to predict the age while young. Trellis wires were strung proton in a pair is submitted to a mea­ results of the same experiment. I shall throughout the vineyard to support fu ture growth and surement of its spin component along not give the details of how the predic­ finally we installed a drip the A axis and is found to have the value tion is derived from the mathematical irrigation system, a major A+. No other measurements are carried formalism of the quantum theory; it can project involving construc­ out on this particle, but its singlet part­ be stated, however, that the procedure is tion of a new reservoir. ner is tested for the component along the completely explicit and is object ive in A new vineyard such as B axis and the result is found to be B+. the sense that anyone applying the rules oursis a lot of work, but if The latter measurement, which might be correctly will get the same result. Sur­ you're serious about consis­ made at a distant site after the protons prisingly, the predictions of quantum tent grapequality, it's have been moving apart for some time, mechanics differ from those of the lo­ worth the effort. you 'd enjoy hearing conveys additional information about cal realistic theories. In particular, quan­ If more from the wine coun­ the state of the firstproton. To be ex­ tum mechanics predicts that for some try, pleasewrite for our free choices of the axes A, Ba nd C the Bell plicit, the existence of a strict negative monthly newsletter. correlation implies that the firstproton, inequality is violated, so that there are Sam]. Sebastiani which is already known by direct mea­ more A+ B+ pairs of protons than there surement to have the spin component are A+C+ and B+ C+ pairs combined. A+, must also have the component B-. Thus local realistic theories and quan­ �/��, tum mechanics are in direct conflict. Sebastiani y this means the observation of a pair The conflict raises two questions. B of protons one of which has the spin First, what are the experimental facts of component A+ and the other the compo­ the situation? Is the Bell inequality satis­ VINEYARDS nent B+ can be employed as a signal fied or is it violated? Whatever the out­ EST. 1825 indicating the existence of a single pro­ come of an experimental test there must P.O. Box AA Sonoma CA 95476 ton with the components A+ B-. Fu r­ be a flaw of some kind either in the rules thermore, it can be demonstrated by a of quantum mechanics or in local realis­ statistical argument that n[A + B+], the tic theories. The second question there-

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© 1979 SCIENTIFIC AMERICAN, INC fore is: What premise underlying the re­ number of photons that pass through atomic ones, but the apparatus required futed theory is at fault? the filter. Neither of these components is quite different. In general detectors The thought experiment proposed in is perfect, so that the failure to register are more efficient for high-energy pho­ 1935 by Einstein, Podolsky and Ro­ a photon does not necessarily mean that tons, but polarization filters are more sen called for measurements of the posi­ it had the wrong polarization. efficient for low-energy ones. tion and momentum of particles. The Experiments have also been done on One experiment has measured the experiment on spin components of pro­ the polarization of gamma rays, which correlations of spin components of pro­ tons was first discussed in 19 52 by Da­ are high-energy photons. The gamma tons and therefore closely resembles the vid Bohm of Birkbeck College in Lon­ rays were created by the mutual anni­ original thought experiment. The pairs don, but still in the context of a thought hilation of electrons and the ir antipar­ of protons are created by injecting pro­ experiment. It was not until 1969, after ticles, positrons. Su ch an annihilation tons of comparatively low energy into a Bell had introduced his inequality, that gives rise to two gamma rays, which are target made up partly of hydrogen at­ real experiments exploring the se ques­ emitted in opposite directions and have oms. The nucleus of a hydrogen atom tions were contemplated. The feasibility opposite polarization. The experiments consists of a single proton. When an in­ of such experiments was discussed by are therefore formally equivalent to the cident proton strikes a hydrogen nucle- John F. Clauser of the University of California at Berkeley, R. A. Holt of the University of Western Ontario and Mi­ EXPERIMENT DATE PARTICLES STUDIED RESULTS chael A. Horne and Abner Shimony of Boston University. They found that for In agreement with a practical experiment the Bell inequali­ Stuart J. Freedman and John F. Clauser, Low-energy photons emitted University of California at Berkeley during transitions in quantum mechanics. ty would have to be generalized some­ calcium atoms. what, but a meaningful test of the alter­ native theories would still be possible. 1972 The technical difficulty of the experi­ ments should not pass unmentioned. In a thought experiment both protons of R. A. Holt and F. M. Pipkin, Low-energy photons emitted In agreement with every pair always reach the instruments Harvard University during transitions Bell inequality. in atoms of mercury19 8. and the instruments themselves always yield an unambiguous measurement of the spin component along the chosen 1973 axis. Real apparatus cannot reproduce these results. The detectors are never John F. Clauser, Low-energy photons emitted In agreement with perfectly efficient: many protons are University of California at Berkeley during transitions in atoms quantum mechanics. simply not registered at all. Because of of mercury202 . the imperfections of the instruments the number of protons counted in each cate­ 1976 gory cannot be interprete d directly; in­ stead an allowance must be made for the In agreement with inefficiency of the detectors, which adds Edward S. Fry and Randall C. Thompson, Low-energy photons emitted Texas A. & M. University during transitions in atoms quantum mechanics. to the uncertainty of the results. of mercury 200.

f seven experiments reported since 1976 1971, six have not concerned mea­ surementsO of the spin components of protons but have instead measured the G. Faraci, S. Gutkowski, S. Notarrigo High-energy photons (gamma In agreement with polarization of photons: the quanta of and A. R. Pennisi, rays) from annihilation Bell inequality. electromagnetic radiation. Polarization University of Catania of electrons and positrons. is the property of a photon that corre­ sponds to the spin of a material particle. 1974 In one series of experiments atoms of a particular element and isotope were l. Kasday, J. Ullman and C. S. Wu, High-energy photons (gamma In agreement with raised to an excited state by the absorp­ Columbia University rays) from annihilation of quantum mechanics. tion of laser light and then allowed to electrons and positrons. return to their original energy level in two steps. At each step a photon with a 1975 characteristic energy or wavelength was emitted. The photons moved off in op­ In agreement with posite directions, and they had opposite M. Lamehi-Rachti and W. Mit tig, Pairs of protons in the Saclay Nuclear Research Center singlet state. quantum mechanics. polarizations. In other words, if the po­ larization of both ·photons was mea­ 1976 sured along any single direction, a strict negative correlation was observed. The differences between ideal instru­ REAL TESTS OF THE BELL INEQUALITY have been carried out by seven groups of in­ ments and real ones are quite plain in vestigators. Only one of the experiments measured the spin components of protons; the others these experiments. There is no single de­ studied the polarization of photons, or quanta of electromagnetic radiation. In four experi­ vice that can intercept a photon and re­ ments pairs of low-energy photons with opposite polarization were emitted by atoms that had port directly on its polarization. Instead been raised to an excited state. Pairs of oppositely polarized ga mma rays, or high-energy pho­ tons, were created in two other experiments by the mutual annihilation of electrons and their two devices are necessary, a filter and a antiparticles, positrons. In the remaining experiment protons from a particle accelerator struck detector. The filter is designed to allow a target made up partly of hydrogen; the accelerated protons and the hydrogen nuclei formed the passage of those photons that have pairs in the singlet state. Five of th e experiments gave results in violation of the Bell inequality the selected polarization and to stop or and in agreement with quantum mechanics. That the Bell inequality is violated is now generally deflect all others; the detector counts the accepted. The cause of the discrepancy in the results of the otber two experiments is uncertain.

172

© 1979 SCIENTIFIC AMERICAN, INC us, the two protons interact briefly and Regardless of what particles are being A and C and further data are recorded. enter the singlet st a te. Both then leave studied, the experiment consists of three Finally the filters are reoriented again to the target, sharing the momentum ofseries the of double measurements. Three axes Band C. The coincidences record­ incident proton, but if they are undis­ axes, A, Ba nd C, are selected; in general ed in each configuration are counted and turbed, they remain in the singlet state. the angles between them are set to the corrections are made for the inefficiency Preliminary measurements of the same values where the maximum discrepancy of the apparatus. It is then a matter of spin component on both protons give between quantum mechanics and local simple addition to compare the results opposite results. realistic theories is expected. One filter is with the Bell inequality. The instruments for an experiment then set.to admit particles with the po­ Of the seven completed experiments with proton pairs again consist of filters larization or spin component A+ and the five endorse the predictions of quantum and detectors. In the one experiment other is set to pass particles with the mechanics, that is, they indicate a vio­ that has been completed the filter was a component B+ . After a large enough lation of the Bell inequality for some carbon foil, which scattered each proton sample of particles has been recorded in choices of the axes A, Band C. The other into one of two detectors depending on this configuration the filters are rotated two give correlations no greater than the value of the measured component. to measure the components along axes those allowed by the Bell inequality and

BEAM OF ATOMS

DETECTOR DETECTOR

LENS POLARIZATION FILTER LENS POLARIZATION FILTER LENS

LlJ DETECTOR

ELECTRONS

./ POLARIZATION ANALYZER " " < j? :> HIGH-ENERGY PHOTON

POLARIZATION ANALYZER ./� ././ POSITRONS

DETECTOR

PROTON :>

PROTON ACCELERATOR

DETECTORS

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© 1979 SCIENTIFIC AMERICAN, INC therefore support local realistic theo­ one. A great variety of systematic flaws tent results, that the issue has already ries. The score is thus five to two in fa­ in the design of an experiment could de­ been decided. For 'some choices of the vor of quantum mechanics. Actually the stroy the evidence of a real correlation, axes A. Ba nd C the Bell inequality is support for quantum mechanics is much yielding results within the limit set by violated in nature, and local realistic stronger than this ratio would seem to the Bell inequality. On the other hand, it theories are therefore false. imply. One reason for attributing great­ is hard to imagine an experimental error er credibility to the five experiments that that could create a false correlation in f it can be considered as having been violate the Bell inequality is that they five independent experiments. What is I demonstrated that local realistic the­ represent a larger sample of data and more, the result s of those experiments ories are in error, which of the three are therefore statistically more signifi­ not only violate the Bell inequality but premises underlying those the ories is cant. Some of those experiments were also violate it precisely as quantum me­ to blame? A first step in answering this done after the two anom alous results chanics predicts. For the results of the question should be to make sure no ad­ were reported and included refinements five experiments to be produced by ran­ ditional assumptions were made in for­ in the instrumentation designed explicit­ dom coincidence would require an ex­ mulating the experimental test. ly to avoid any biases that might ac­ traordinary statistical fluke that is not As it happens, at least one subsidiary count for the two di screpant results. credible given the nu mber of particles assumption was needed. Because of the Clauser and Shimony have pointed out that have now been detected. limitations of practical instruments, it that there is also an epistemological jus­ Further tests of the Bell ineq uality are was necessary to generalize the Bell ine­ tification for disregarding the two exper­ under consideration, and at least one ad­ quality slightly, and that general ization iments that are in disagreement with the ditional experiment is already in prepa­ must be assumed to be valid; it cannot majority. Quantum mechanics predicts ration. Most physicists concerned with be proved. It seems most unlikely, how­ a larger correlation between events and these problems, however, have subs tan­ ever, that this circumstance could alter local realistic theories predict a smaller tial confidence, based on the five consis- the phenomena in such a way that the results of the experiments not only would violate the Bell inequality but also would be consistent with the predic­ tions of quantum mechanics. In any case it is possible more refined experiments o will test the inequality without the gen­ eralization. Because the subsidiary as­ sumption is susceptible to an experi­ mental test it seems less fundamental than the other three, and so it will not be considered further here. Another area that might be scruti­ nized for unacknowledged assumptions -.25 is the proof of the Bell inequality. In­ deed, it seems the proof does depend on the assumed validity of ordinary, two­ z o valued logic, where a proposition must be either true or false and a spin compo­ nent must be either plus or rriinus. Some �w a: interpretations of quantum mechanics a: have introduced the idea of a many­ 8 -.5 valued logic, but those. proposals have nothing to do with the reasoning applied in this proof. Indeed, in the context of \ the proof it is difficult even to conceive QUANTUM MECHANICS of an alternative to two-valued logic. Unless such a system is formulated it seems best to pass over the problem. -.75 The entire series of experiments founded on the ideas of Einstein, Podol­ sky and Rosen is sometimes regarded as merely a test of hidden-parameter theo­ ries. The experiments do indeed test those theories, but it should be empha­ sized that the existence of hidden pa­ rameters is not an additional premise of -1 local realistic theories. On the contrary, o 15 30 45 60 75 90 the existence of parameters specifying ANGLE BETWEEN ANALYZERS (DEGREES) the deterministic properties of a particle RESULTS OF AN EXPERIMENTAL TEST of the Bell inequality show that it is clearly vio­ was derived from the three original as­ lated. The experiment is the one that employed pairs of protons in the singlet state, which was sumptions. Remember that the psychol­ carried out by M. Lamehi-Rachti and W. Mittig of the Saclay Nuclear Research Center in ogist did not assume that his invented France. The negative correlation between the values of differentspin components is given as a test measured any real attribute of the function of the angle between the settings of the two analyzers. A correlation of -1 would indi­ tested subjects; instead he deduced the cate that the components invariably had opposite values. The Bell inequality states that the cor­ existence of such an attribute after ob­ relation at any angle must be on or above the colored line. The observed correlations at 30, 45 serving a strict correlation. In the same and 60 degrees are below the line. The results not only violate the Bell inequality but also are in good agreement with the predictions of quantum me chanics, which fact adds to their credibili­ way the existence of hidden parameters ty. The violation of the Bell inequality implies that at least one of the three premises of local was derived from the negative correla­ realistic theories must be false; Einstein separability is considered the most plausible candidate. tion detected when a single spin compo-

174

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© 1979 SCIENTIFIC AMERICAN, INC . MYERS'SMAKES IT BETTER. Ta ste how Myers's improves on cola. soda. tonic. fruit juice. Free Rec ipe Book : Myers's Rum, P. O. Box 1 622. FDR Station, New Yo rk. N. Y. 10022. Offer expires December 31. 1980.

© 1979 SCIENTIFIC AMERICAN, INC nent was measured on pairs of protons cal positivists have had an appreciable, ing the free use of ind uction. It is in­ in the singlet state. if indirect, influence on the thinking of duction that enabled the physicist to It is probably not possible to prove theoretical physicists. extrapolate from a series of observed rigorously that no other supplemen­ The sense of paradox induced by the negative correlations to the conclusion tary assumptions enter into the argu­ finding that the Bell inequality is violat­ that any two protons in the singlet state meht supporting the local realistic the­ ed can certainly be alleviated by adopt­ have opposite values of any single spin ories. The chain of reasoning is simple ing a positivist attitude, and such a component, even if none of the compo­ enough, however, that if other assump­ course of action was first proposed long nents is measured. The extrapolation tions are implicit in it, they should be ago. When all the consequences of aban­ was an essential step in the proof of the easily recognized. None has yet been doning realism are considered, however, Bell inequality, but it is clearly insup­ pointed out. It therefore seems that at­ it is too great a renunciation to have portable if the concept of unmeasured tention must be focused on the three much appeal. In the context of this ex­ properties has no meaning. premises of realism, the free use of in­ periment positivism asserts that it would This use of induction might be regard­ duction and Einstein separability. be meaningless to attribute anything re­ ed by some as a weak link in the chain of

Of the three premises realism is the sembling a definite spin component to a argument. Shortly after the paper by most fundamental. Realism can be stat­ particle before the component is mea­ Einstein, Podolsky and Rosen appeared, ed formally as the belief that a mere sured; that the only quantity with any Niels Bohr published a reply in which he description of data is not all that should verifiable reality is the observation it­ defended the completeness of the quan­ be required of a theory. Even an empiri­ self, the sensory impression; and that the tum-mechanical descr iption of nature; cal rule for predicting the patterns of psychologist's demand for an objective the basis of his criticism was that Ein­ future measurements is not enough. The explanation of the remarkable correla­ stein's use of induction was unwarrant­ mind demands something more: not tion he observes should ultimately be ed. Bohr's reply is a central document necessarily determinism-there is noth­ rejected. If this refusal to seek underly­ in what has come to be known as the ing intrinsically irrational about ran­ ing causes of observed regularities is ap­ Copenhagen interpretation of quantum domness-but at least objective expla­ plied consistently, it trivializes the entire mechanics. His reasoning amounts to an nations of observed regularities, or in scientific enterprise. Sci ence is red uced argument that a particle and an instru­ other words causes. Underlying this de­ to a set of recipes for predicting future ment adjusted to make a spec ific mea­ mand is the intuitive notion that the observations from a knowledge of past surement on it constitute in some re­ world outside the self is real and has at ones. Any notion . of science as "the spects a single system, which would be least some properties that exist indepen­ study of nature" is impossible; nature is altered in an essential way if the setting dently of human consciousness. a phantom. One can imagine a physics of the instrument were changed. For this A number of philosophers, who can grounded on positivist principles that reason it is not allowable to make any collectively be called positivists, have would predict all possible correlations inferences about the state of a particle rejected the reali stic viewpoint. The po­ of events and still leave the world total­ without specifying at the same time the sitivists do not assert that the world ex­ ly incomprehensible. Given the extreme settings of the instruments that will in­ ternal to the mind does not exist; they consequences of abolishing realism, one teract with the particle. merely dismiss as meaningless any state­ is inclined to cling to this firstpremise. Bohr's views have been widely influ­ ment about an external reality that does Realism enters the argument support­ ential, and in a sense rightly so; after all, not refer directly to sensory impres­ ing local realistic theories at another the recent work under discussion here �sions. In the 20t h century some radi- point: it is the justification for postulat- has shown that in these matters he was CTORS �

UJI

/B POLARIZATION ANALYZERS POLARIZATION ANALYZERScG i ii I �\\ I <

SOURCE OF LOW-ENERGY PHOTONS

EINSTEIN SEPARABILITY will be tested rigorously in an experi­ not pass from one detector to the other in time to influencethe result ment now being prepared by Alain Aspect of the Optics Institute of of the second measurement. In Aspect's experiment, which will mea­ the University of Paris. Earlier experiments tested only the less re­ sure the polarization of low-energy photons, this condition will be strictive separability principle: the settings of the analyzers were de­ met. Two sets of analyzers and detectors will be provided for each termined well in advance, so that some influence of one measurement photon, and the analyzers will measure different components. A fast could be communicated (by an unknown mechanism) to the other optical switch will determine which analyzer the photon enters only measurement at a speed well below the velocity of light. This possi­ when it is too late for the decision to influence the other measurement ble explanation of the observed correlation is extremely unlikely, but (assuming that the hypothetical influencepropagates no faster than it would be excluded entirely if the settings of the analyzers were light). The switch is shown as a moving mirror; actually the switching changed so quickly that a signal moving no faster than light could will be accomplished by ultrasonic waves on the surface of a crystal.

177 © 1979 SCIENTIFIC AMERICAN, INC closer to the truth than Einstein was. Save on Calculators Nevertheless, when Bohr's ideas are considered in their essence, they are sub­ ject to objections much like those that HEWLETT-PACKA RD were raised against a retreat to positiv­ Model Youreost HP-41C Scient $244.95 ism. Because realism provides the ulti­ Card Reader/41C 159.95 Printer/41C 289.95 mate rationale for the free use of induc­ HP·34C Scient 124.95 Hp·38C Bus. 124.95 tion, it can be argued that Bohr was not a HP-38E Bus, 99.95 HP-33C Scient 99.95 realist, or at least not a consistent one. HP-33E Scient 74.95 HP-37E Bus. prog 62.95 Any explanation of the di stant-correla­ HP-32E Adv. Scient 58.95 HP-31E Scient 42.95 tion experiments that relies on Bohr's HP-67 Scient Prog 299.95 Hp·97 Scient Print 594.95 reply to Einstein, Podolsky and Rosen HP-29C Scient elm 139.95 HP-IO HH Print 139.95 may turn out to be inconsistent with Hp·92 Bus, Print 399.95 even a moderate version of realism.

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As I have Ol'lmPIC SALE S COmPAn'l Inc. . shown, this assumption must now be re­ Box 428 S, Sausalito, California 94965 216 South Oxlord Ave ' POBox 74545 Los Anyeles, CA 90004 . (213)381 391 1 • T elex 67 3477 garded as highly questionable. Before considering the consequences ---Mail Ad. No Letter Needed -- - of this conclusion it should be pointed Mystery out that none of the experiments com­ pleted so far has rigorously tested the Electronic Top -�II-==- assumption of Einstein separability. In Spins For Days On those experiments the settings of the in; Invisible struments were determined well in ad­ "­ Power! Makes vance (on the time scale of particle phys­ Unique Gift! ics). Therefore the setting of one instru­ What Makes It Go On and On and On at ment could conceivably affectevents 2500 r.p.m. with no apparent energy source? BAFFLING BRAIN BUSTER that the BRIGHT· observed at the other instrument, or it EST. Demonstrated at science fairs and conventions. 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This limited edition will be issued only done by Alain Aspect of the Optics In­ during the centennial year, so order now! Turns on lights, bells, horns, sirens, alarms, tape re­ r------· stitute of the University of Paris. corders, wireless mikes, etc. Operates by voice, whistle Yes, Rush me my Einstein Centennial poster. : Hundreds of fun • 0 Quite apart from the question of how practicalor any sound uses. Dofrom mysterious across room.tricks stunts. Great for& , I enclose a check or money order for S ___, & : for---POster(s) at $10 each. Size 18"X21'" fast a hypothetical influence could trav­ experiments, electronic bugs. NOT A KIT. Completely : assembled, wired. Includes sensitive switch which re­ : (N .Y. STA TE RESIDENTS ADD 8% SALES TAX). 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© 1979 SCIENTIFIC AMERICAN, INC planation and to assume, pending the results of Aspect's experiment, that if ordinary separabil ity is violated, Ein­ stein separability will be violated too. I have discussed a pair of protons as Did you miss these if they were independent entities that come together in the target and then move apart again. They can also be re­ two highly-acclaimed garded as the elements of a single physi­ D£ DAL US? cal system that is created during the first interaction and becomes progressively more extended in space until it is dis­ issues of rupted by the first measurement. With respect to separability these descriptions Wo uld you like are equivalent. In each case a violation of Einstein separability req uires instan­ to receive them taneous action at a distance, either be­ tween independent systems or within a both ...FREE? single extended system. Must the principle of the finite prop­ agation of signals therefore be aban­ Do you find it difficult to keep up with doned? To that question no rash answer fields distant from your own? Do you should be given. The principle was in­ find yourself getting fragments of in­ troduced as a premise of the theory of formation about what is happening DISCOVERIES AND INTERPRETATIONS: relativity, which cannot be made consis­ in those fields-but seldom a coher­ Studies in Contemporary Scholarship. tent without it. Moreover, signals that outrace light give rise to bizarre para­ ent picture of what is happening? These two issues on a single theme are doxes of causality in which observers in yours FREE with your introductory sub­ A subscription to Daedalus can help. scription to Dae dalus. The issues show some frames of reference find that one Each quarterly issue examines a sin­ how traditional bound aries ha ve shifted, event is "cause d" by another that has gle theme from a variety of perspec­ and why research priorities today are sub­ not yet happened. It turns out, however, stantially different from what the y were tives, wit h contributions from many that the instantaneous influences that even a decade ago. Distinguished con­ of the leading thinkers of our time. tributors include: seem to be at work in the distant-corre­ You gain an appreciation of the lation experiments do not req uire such a Sidney D. Drell on elementary par ticle changes, the challenges, the contro­ physics drastic revision of accepted ideas. It versies in a given field. D. W. Sciama on black holes seems quite certain these influences D. P. McKenzie on plate tectonics could not be employed to transmit any Steven Weinberg on quantum field theory How far-ranging is Daedalus? About "useful" information, such as orders or as far-ranging in its intellectual curi­ Bruno Rossi on X-ray astronomy Lewis Thomas on biomedical science and instructions. No event that causes an­ osity as you are! Recent issues, for human health other event can be linked to it through example, have explo red the future of Edward O. Wilson on biology and the so­ this mechanism; the instantaneous influ­ cial sciences. Europe .•• Rousseau after 200 years ences can pass only between events that Stephen Toulmin on history and philoso­ .•.the family in modern society ••• phy of science are related by a common cause. Hence ethical and social limits on scientific the concept of a signal could be rede­ Also, Gerald Holton on the unity of sci­ research. Studies in progress include fined in such a way that only those ence ... M. I. Finley on historiography .•. U.S. defense policies in the 1980s and Svetlana Alpers on art history . . . Stanley means of communication that transmit the problem of scientific literacy. Hoffmann on international relations .•. useful information would be called sig­ Victor Turner on anthropology ... Gordon nals. The principle of the finiteveloc ity Each issue of Daedalus is printed and R. Willey on archaeology .. . Shmuel N. of signals would then be preserved. bound like a fine book, a permanent Eisenstadt on sociological theory . . . Lester C. Thurow on eco nomics ... Jean Even this solution impairs scientific addition to your library. Starobinski on criticism and autho rity . .. realism to some extent. The basic law Jonathan Culler on signs and meaning To start your subscription-and re­ that signals cannot travel faster than . . . George A. Miller on problems of light is demoted from a property of ex­ ceive your two FREE issues-simply communication ... Emmanuel B. LeRoy return the form below. Ladurie on recent historical "discoveries." ternal reality to a feature of mere com­ municable human experience. Although Mail to : this represents a step toward philosophi­ DAEDALUS, cal positivism, the concept of an inde­ Subscription Dept. pendent or external reality can still be 165 Allandale Street retained as a possible explanation of ob­ Ii Boston, Mass. 02130 served regularities in experiments. It is YES ... pl ease start my introductory subscription to Daedalus. I prefer: necessary, however, that the violation of o 1 year (4 issue s) for $14.00 0 2 years (8 issues) for $24.00 Einstein separability be included as a property, albeit a well-hidden and coun­

Please check appropriate boxes : terintuitive property, of that indepen­ I wish to receive my two free issues ri ght dent reality. It should be noted in pass­ away. ing that Boh r's refutation of Einstein's o Payment enclosed $, ______, Name______argument for hidden parameters intro­ o Charge my cr edit card: o Master Charge 0 VISA duces an implicit violation of separabil­ Address ______ity. It is founded on a strange indivisi­ Card Number Expiration Date bility of the system of particles and the o Please bill me later. (Your free spec ial City State ___Zip ___ instruments of observation. double issue will be sent upon receipt of payment.) (Add $2.00 for foreign subscriptions) The argument that proceeds from an Daedalus is published by the American Academy of Arts and Sciences. ------

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© 1979 SCIENTIFIC AMERICAN, INC observed correlation to the Bell in­ equality to the violation of Einstein sep­ arability is not particula rly complicat­ ed, but it is indirect. Could the same re­ sult have been obtained in some more straightforward way? As it happens, it could not have been demonstrated with­ out the Bell inequality, but it could have been suspected, and in fact it was. The suspicion arose from the fact that the wave function for a system of two or more particles is generally a nonlocal entity, which is considered to collapse suddenly or even instantaneously when a measurement is made. If the wave function is regarded as a kind of bizarre real jelly, the instantaneous collapse ob­ viously violates Einstein separability. This naive argument was never taken very seriously, however, because the conventional interpretation of quantum mechanics does not identify the wave function of a system with whatever is meant by the reality of the system. Bohr, for example, considered the wave func­ tion a mere tool for doing calculations. Besides, the wave function for a sys­ tem of several particles describes them only in an approximation that ignores the theory of relativity, and so its struc­ ture hardly seems a reliable argument against Einstein separability. For these reasons it was possible until a few years ago to believe in an independent, exter­ nal reality and simultaneously to regard Einstein separability as a completely general law bearing on that reality.

ne conceivable response to the dis­ tant-correlation experiments is that theirO outcome is inconsequential. The experiments themselves might represent a rare and therefore interesting test of quantum-mechanical phenomena ob­ served at long range, but the results are merely what was expected. They show that the theory is in agreement with ex­ periment and so provide no new infor­ mation. Such a reaction would be highly superficial. It is indeed true that the ex­ periments, now that they have been completed, have turned out to have little to do with quantum mechanics. That does not make them trivial; rather, it indicates that their real bearing is else­ where. A discovery that discredits a ba­ sic assumption about the structure of the world, an assumption long held and seldom questioned, is anything but trivi­ al. It is a welcome illumination. Most particles or aggregates of parti­ cles that are ordinarily regarded as sepa­ rate objects have interacted at some time in the past with other objects. The Help the U.S. Ski Teambri ng home the Gold. violation of separability seems to imply that in some sense all these objects con­ There's one thing standing between the U. S. Ski Team and a Gold Medal stitute an indivisible whole. Perhaps in at the Olympics: money. such a world the concept of an indepen­ Our Alpine and Nordic teams are not subsidized by the government. dently existing reality can retain some Team members invest years of their lives training to win. Now they need meaning, but it will be an altered mean­ your help. Ple ase send your tax-deductible donations to the U.S. Ski Ll/S ing and one remote from everyday expe­ Educational Foundation, Box 100 M, Park City, Utah 84060. rience. Thanks. �-'l iE.IA M, f, I

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© 1979 SCIENTIFIC AMERICAN, INC