Advantages and disadvantages of various interpretations of the quantumtheoryHenry Margenau

Citation: Physics Today 7, 10, 6 (1954); doi: 10.1063/1.3061432View online: https://doi.org/10.1063/1.3061432View Table of Contents: https://physicstoday.scitation.org/toc/pto/7/10Published by the American Institute of Physics

ARTICLES YOU MAY BE INTERESTED IN

A new theory for the great ice agesPhysics Today 7, 14 (1954); https://doi.org/10.1063/1.3061397

Math is FunPhysics Today 7, 18 (1954); https://doi.org/10.1063/1.3061398

Quantum mechanics and realityPhysics Today 23, 30 (1970); https://doi.org/10.1063/1.3022331

Quantum Theory—Interpretation, Formulation, InspirationPhysics Today 53, 11 (2000); https://doi.org/10.1063/1.1325219

Quantum Theory Needs No ‘Interpretation’Physics Today 53, 70 (2000); https://doi.org/10.1063/1.883004

Smyth Resigns as Atomic Energy CommissionerPhysics Today 7, 5 (1954); https://doi.org/10.1063/1.3061431

Advantages and Disadvantages of VariousInterpretations of the Quantum Theory

By Henry Margenau

JOSEPH HENRY'S genius was attracted primarilyto the great experimental problems of his age. Al-

though he was a professor of natural philosophy, adiscipline which a century ago combined the variousbranches of physical science, he is not known to haveindulged in the kind of formal considerations to whichthe title of this evening's discourse alludes. Yet I amconfident that my subject is not wholly inappropriateto the occasion of a lecture in honor of Joseph Henry.For his eminent biographer, Charles Greeley Abbot,describes him as "a man of varied culture, of largebreadth and liberality of views, of generous impulsesand of great gentleness and courtesy of manner".Hence, while the speculations on which I am about toembark can hardly aspire to honor his memory, wemay take comfort in supposing that he would grace-fully listen to them and accept them as a small tokenof respect.

Questions as to fundamental meanings have accom-panied the development of the quantum theory fromthe beginning. They appeared in the controversy overthe wave-particle dualism, in the problem of observ-ability posed by Heisenberg's matrix mechanics, in theearly pilot wave conjunctures of de Broglie, in the com-plementary principle of Bohr. They have been revivedby the recent publications of Bohm, de Broglie, Vigier,and Weizel. It is the attempts of these latter authorswhich I should like to appraise in simple philosophicterms.

Contrary to wide-spread belief, the problem in ques-tion is not difficult to conceive or to explain. I shallendeavor to present it in its basic features, shunningthe artifacts of mathematics which often serve to be-cloud the scene. The details, it is true, can hardly betreated without analysis. But the details are not indoubt; the controversy concerns their interpretation.It is therefore proper to select for study the simplestpossible instances of quantum mechanical reasoning andexamine their bearing upon the issues of the presentdebate.

The first example I propose is the motion of a fireflyin a dark summer night. To the eye, the motion of thisinsect is not continuous; what it presents is a succes-sion of bright spots or streaks at different places in ourfield of view. The judgment that this phenomenon rep-resents the uninterrupted passage of an object fromone point of space to another is based, strictly speak-ing, on an interpolation between the bursts of lumi-nosity that are actually perceived. Yet common sense,

and indeed scientific description, regard themselvesfully justified in performing that ideal supplementationof immediate perception which the interpretation ofthese sporadic darts as continuous motion demands.The chief reasons for this attitude are the following.

First, the hypothesis of continuous motion is testablethrough other experience. It is possible to watch thefirefly in the daytime, when its progression from pointto point becomes visible. This settles the issue in largepart, although it may not convince the inverteratesceptic who feels that, when unilluminated, the fireflybehaves like the angels to whom St. Thomas attributedthe ability of emerging at separate points without hav-ing to traverse the intervening distance. To answer thesceptic, we must demonstrate the simplicity and con-venience of the continuity hypothesis. Thus we add, tothe fact of partial testability, a second item of evidenceof a more rational sort, namely the simplicity of thegeometric curve on which the luminous dots are situ-ated. If the interpolated path were very irregular,showed unlikely curvatures and strange convolutions,doubts as to continuity might remain; the smoothnessof the plotted trajectory goes a long way toward re-moving them.

The validity of every scientific theory, even the sim-plest, rests ultimately on two kinds of evidence: (1)empirical verifiability of some of its consequences, and(2) rational coherence, economy of thought, or sim-plicity conveyed by the ideas composing the theory.

Atomic entities, like electrons, present phenomenawhich, on the purely empirical side, are not unlike thesporadic emergences of a lightning bug at night. To besure, the electron in an atom cannot be seen. Never-theless if the results of experiments and observationsusing the refined techniques of modern physics can betrusted, an electron in what is called a Bohr orbit re-veals its position as a random set of points locatedthroughout a region of space in the neighborhood ofthe classical orbit. More precisely, if a series of posi-tion measurements were made while the electron is inthe unvarying state known as the ground state of thehydrogen atom, the results would form a probabilityaggregate of known spatial distribution; the individualpositions thus established would dot this region in acurious manner, offering no immediate suggestion asto continuity of motion.

Henry Margenau, professor of physics and natural philosophy at YaleUniversity, presented this the 23rd Joseph Henry Lecture, before thePhilosophical Society of Washington on March 26th, 1954.

PHYSICS TODAY

Thus the question naturally arises: can we regularizethose emergences by the same principles which we em-ployed in concluding that the path of the lightning bugwas continuous? Or do we confront here a situationcalling for entirely different treatment?

Unfortunately, the road leading to empirical verifica-tion of the continuity hypothesis is blocked, not merelyby incidental obstacles arising from imperfections ofmeasurement or observation, hut by infelicities of afundamental kind. The electron is intrinsically toosmall to be seen: the act of vision, even if it were pos-sible, requires a time too long for a clear ascertainmentof instantaneous positions; last but not least importantis the fact that elementary particles are promiscuousentities with a perversity which prevents us from everbeing sure that we see the same individual in differentobservations. If these difficulties seem inessential, ifhope still remains that they may be overcome in thefuture, then we need to remember that their denialcontradicts the basic tenets of the quantum theory, theonly theory capable of explaining what can in fact beobserved about electrons. The conclusion is inescap-able: there is no daytime in which the electron's pathcould be watched.

Let us therefore examine the continuity interpreta-tion from the point of view of simplicity or economyof thought. Here we encounter another failure. A curvedrawn through the measured points becomes compli-cated and aimless, wandering in erratic fashion, withno preference for connecting neighbors, a curve inter-twining and crossing itself in obvious labor to accom-modate the positions of the particle. Certainly, nothingis gained in ease of conception, in plausibility, or inpower of prediction by this familiar artifact.

Thus it is seen that the physical microcosm, theatomic realm, confronts the physicist with a novel kindof problem in interpretation, with a challenge to sim-plify or rationalize perhaps in ways to which he is notaccustomed. And nature is not generous in providinghints for the solution of this methodological puzzle:the difficulties of direct verification we have alreadynoted are so great that theories cannot be readily ex-posed to test. The sphinx is noncommittal. The physi-cist has an embarrassing amount of freedom in makinghis interpretations.

And how happily would he welcome the logical ex-perts on "theory construction", the men who have putscientific procedure in pigeon holes, to whom the factssuggest inductively an hypothesis with computableprobability. Here is a place where the principles oftheory construction could be tried in vitro, with bene-fit for science itself. But nothing seems to be happen-ing to relieve the suspicion that there are no recipesfor constructing successful theories, that the creativeact in factual discovery as well as in theoretical inter-pretation refuses to be codified. Let us return, then, tothe physics of the situation and examine the proposalsin terms of which the antics of the electronic lightningbug have thus far been rationalized.

1. Thi Mechanistic Thesis

THERE are three distinguishable views with pos-sible gradations between them. The first of them,

which I have somewhat bluntly called mechanistic, is.1 continuation of time-honored procedures in classicalphysics or, in the eyes of its opponents, an obsoletehangover from an unenlightened past. It persists inportraying phenomena continuously in time and spacedespite the difficulties we have noted; it goes on usingvisual models where vision palpably fails. It reaffirmsthe convictions of a number of famous nineteenth cen-tury scientists (Maxwell, Kirchhoff) who saw the aimof all science in the discovery of models which allowan understanding of phenomena by their interactions intime and space. De Broglie, one of the foremost advo-cates of this school, identifies pictorability in time ,mdspace with "clartd Cart6sien".

The word "mechanistic" is literally applicable onlyto the simplest variety of space-time interpretations;others are more refined and complex, introduce non-mechanical agencies like fields, both three- and many-dimensional, but continue to avow the real existenceof specific world lines, of detailed trajectories in a con-tinuous space-time manifold. These latter formulations,which include the theories of de Broglie and Bohm.might be called quasi-mechanistic; in a deep philo-sophic sense however they are related to the othersand I shall not hesitate to deal with them as specialversions of the mechanistic thesis. Our attention mustthus be directed, under this heading, to two related at-tempts at explanation, one simple and the other morerefined.

The simple one sees the cause for the firefly be-havior of electrons in the havoc wrought by the meas-uring process. It holds that the electron has a perfectlydeterminate position at all times, but this position isdisturbed by the photon which, on being reflected, car-ries to the eye or to the measuring device the informa-tion where the electron was. The photon imparts to theelectron a recoil which in consequence makes the po-sition of the latter object uncertain. It will be recalledthat all early explanations of the uncertainty principleinvoked mechanical processes of this kind: transfer ofmomentum, or energy, scattering, lack of temporal pre-cision of the measuring act with consequent uncer-tainty in the position of the observed object. Further-more, if the particle aspect did not yield a convincingdemonstration of uncertainty, there was always thewave nature of electrons to be drawn upon for furtherevidence.

The inherent plausibility of this reasoning is strength-ened by the circumstance that it shows why atomicparticles are erratic and the objects of our daily livesare not. A single photon represents a negligible disturb-ance when it impinges on bodies of ordinary size, butis a very energetic and disarranging missile when firedupon the miniscule electron. And the quantum theoryshows that its energy cannot be made arbitrarily small,its amount being fixed at hv-

OCTOBER 1954

8

Why, then, does this simple explanation fail to com-mand universal acceptance? Its shortcomings are fairlyimpressive: In the first place there are unquantizedmissiles such as other particles, for which the last pre-ceding argument does not hold. Secondly, it is hard tosee why the measuring disturbance should destroy thestate before the measurement, why it should not con-vey information as to what the electron's position wasprior to the act of collision. An operation can effect asuccessful diagnosis of a disease even if it kills the pa-tient! Finally, to extend the criticism, it is possible toshow that the uncertainty principle, which we may lookupon as a quantitative expression of the erratic be-havior in question, is a consequence of the basic lawsof quantum mechanics and makes no direct referenceto the destructive effects of measurements.

None of these objections, however, is entirely con-clusive; they are merely irritating and can be removedby clever reasoning, chiefly by a skillful use of the so-called wave-particle dualism. But the major blow tothe simple mechanistic view comes from the realizationthat, even if it is adopted, it provides no opportunityfor calculating or predicting the mysterious disturb-ances that confuse the otherwise clean trajectories. Itasserts their presence and resigns. It forms an idle em-bellishment of the facts and yields, perhaps, esthetic.not scientific or philosophic, satisfaction.

The refined version of the mechanistic thesis promul-gated by de Broglie, Bohm and Vigier is largely im-mune to such elementary criticisms. It is far moreexplicit and does an analytically competent job ofinterpreting the fundamental equations of quantummechanics. It seizes upon a well-known connection be-tween the Hamilton-Jacobi equation of classical physicsand the Schrodinger equation, splits the latter into apair of real equations, one of which can be used todefine a path for the electron. This path is disturbed,not by interfering measurements, but by a nondassicalfield arising from the presence of the electron itself.When a measurement is actually performed, this some-what mysterious field, in conjunction with the measur-ing instrument, brings about the emergence of theparticle at the place of registration.

Admittedly, such reasoning is complicated and, be-cause of its appeal to an unorthodox and special kindof field, perhaps in need of treatment by Occam'srazor. But the formal structure of the theory is withoutflaws, and it is developing, chiefly through the work ofBohm, into an amazingly consistent formalism, deBroglie, it is true, takes exception to the latest formsof it, but on grounds of extra-scientific convictions andof the lack of plausibility of the quantum field. Briefly,his objections are these.

(a) According to Bohm's interpretation, an electronin an 5-state does not move, thus contradicting a notionfamiliar in physics since the days of the Bohr theory.

(b) The state function (t/0 cannot represent physicalreality because it is complex, and it extends in configura-tion space of many dimensions, not in ordinary space.(This argument can be met by supposing that the

forces conveyed by the nonclassical field are com-plicated many-body forces.)

(c) Finally, de Broglie points out, the physical actcalled measurement is turned into a mystery, for itinvolves a sudden, infinitely rapid collapse of thei/»-field, which before the measurement filled all space,upon the immediate locus of the electron.

This is not the place to examine the soundness ofthe foregoing strictures; some of them have plaguedquantum mechanics from its beginning and apply toother interpretations as well. The last point, whichadverts to the sudden disappearance of the i -field uponmeasurement, is often made and presents in my opinionan unsurmountable difficulty to every mechanistic in-terpretation of quantum mechanics. But more of thislater. Let it be noted for the present that the con-troversy involves no questions of empirical fact andthat the view here outlined is perfectly tenable in theface of what is now established scientific knowledge.

Before turning to another doctrine I should like tosay why I did not follow the custom of calling theinterpretation here under review a causal one. Thatadjective is correct but not discriminating, for thereis another type of description, outlined in section 3,which in a certain sense is causal too. What charac-terizes Bohm's ideas is a narrowly mechanistic form ofcausality, not causality in its widest scope.

2. The Formalistic Thesis

MANY a modern scientist will question the wisdomof indulging in considerations as speculative as

the preceding, may even doubt that they have meaning.He will ask: do we not have a formal theory satisfac-tory for making valid predictions about things thatmatter? Why bother about interpretations beyondnecessity? This positivistic attitude takes what is goodand useful in modern theory, systematizes it as well aspossible, and does not feel the pangs of conscience thatafflict the tenderhearted metaphysician. The view sym-pathetic to it may be sketched as follows.

It takes the vagaries of the electron as facts. Ifpressed, it regards them as symptoms of disturbances bymeasuring devices but grants that every attempt topredict them or to understand them in detail is uselessand in need of discouragement. Particles have positionsin space and time under all circumstances, but atomicnature is so constituted that we often cannot knowthem. Because of this, a single measurement of position—or in general of any observable attribute—cannotfunction as the basis of a precise and valid prediction

To make some sort of prediction possible the physicistintroduces his ^-functions, which are essentially meas-ures of information. Being incomplete as carriers ofinformation, these functions permit only statisticalpredictions concerning aggregates of future events. In-dividual events, though always embedded in continuoustemporal and spatial sequences, thus lose their effective-ness as causal agents in the physical world. To restorecausality in a statistical sense, another description is re-quired, a description in terms of i^-functions, which are

PHYSICS TODAY

often waves. The universe of happenings is thus dividedinto two separable strands of development, one con-sisting of events in space-time with real but unknow-able connections between them and devoid of causalnexus, the other a ghostlike space-time manifold ofcausally evolving states whose relation to observableevents is but statistical.

The square of \p in this interpretation, as in all others,represents a probability; but here a probability of arather special kind. As is well known, probabilities arcsometimes regarded as subjective measures of knowl-edge or belief, sometimes as objective frequencies (orlimits of frequencies). Subjective probabilities changediscontinuously with evidence, the others do not. Thus,for example, before a die is thrown, the subjectiveprobability of the appearance of a five is 1/6. Aftera throw it is either 0 or 1. The objective probability is1/6 at all times, for the frequency always refers to alarge aggregate of throws and is unaltered by a singleevent. The formalistic view, insofar as it has becomeexplicit on this issue, adopts the subjective meaning ofprobability. It assumes, for instance, that the ^-functionsuddenly collapses from a field-like distribution through-out space to a small, point-like residue at the instantof a measurement.

Bohr's authority stands impressively behind thisdoctrine. He speaks of it as the principle of comple-mentarity and regards it as the final form of physicalanalysis. The two modes of describing our experience,irreconcilable in man's mind, are the best we canachieve; the dualism they imply is here to stay. Itstands as a memento to the fundamental truth that, inexploring nature, we become disturbing (or, if you will,creative) agents and thereby alter what would otherwisehave been the case.

This view, appealing because of its candor and itsseeming modesty, is espoused in its essence by themajority of physicists. To acknowledge the dualismhas many soothing advantages, as every other form ofdualism does. It relieves its advocates of the need tobridge a chasm in understanding by declaring thatchasm to be unbridgeable and perennial; it legislates adifficulty into a norm. It is little wonder, therefore,that philosophers at times feel ill at ease when study-ing this solution of a dilemma, a solution which pays itsrespects to both horns. But the reward for this ac-complishment is quite considerable: it gives the physi-cist a powerful philosophic tool. Clearly, if the mostfundamental of all sciences has to accept comple-mentarity, is it not natural that bifurcation should alsopervade the lesser realms? Are not the mind-bodyproblem, the conflict between values and fact, betweenfreedom and necessity, mere manifestations of com-plementarity?

I fear that my own lack of sympathy with theseextrapolations of the formalistic thesis has been illconcealed. Bohr's own cautious formulation does notsuffer from such indiscretions. Yet it does commitphysics to a dualism which is neither simple nor il-luminating.

3. A Third Interpretation

F T is possible to avoid the dualism by an interpreta-•*• tion which is philosophically more radical and moreprofound, a view that asks for a surrender of certainfamiliar habits of thought and a few cherished concep-tions. To many, this price seems too high. I shall tryto make this thesis as reasonable as possible, for it isthe one which in view of all present evidence I findmost congenial.

Why not simply deny that the electron has a positionat all times? The real firefly partakes of "simple loca-tion", to use Whitehead's phrase, for the reasons wehave mentioned: its path can be directly inspected andthe use of continuous interpolation between unin-spected points leads to a simple and reasonable theo-retical account. Neither is true for the electroniclightning bug! Of course one feels, initially, that some-how the electron must have a position, that position isan essential property of real material things. But thisis clearly an example of accepting what Whitehead callsthe fallacy of simple location. As we learn more andmore about the world, we are asked to sacrifice in in-creasing measure the facile and picturesque presump-tions of what we call so ineptly "common sense". Itwas common sense that argued that all physical entities,to be real, must occupy space; must have color evenif they are smaller than a wavelength of visible light;must have definite shapes even if invisible; it wascommon sense that said the universe must be Euclidean,simultaneity must be absolute, and there must be anether. The present situation, it seems, demands thecourage and the modesty to disavow common sense;courage in the sense of D'Alembert's admonition, Allezen avant, la foi vous viendra!; and humility to grantthat knowledge in one domain does not render uswise enough to foretell another.

In the spirit of these injunctions we ought perhapsto admit that position—and with it many other ob-servables—is undergoing the fate that befell the ideaof color: it is not generally applicable to things thatare too small or too elusive to be seen. Nor is it properto ask whether such objects are particles or waves; thevery denial of the unrestricted meaningfulness of theconcepts position, size, etc., prevents it from beinganswered. Note, however, that this acknowledgementdoes not destroy our right to affirm the electron'spresence as an objective component of reality. For itmerely substitutes certain abstract qualities for thosewe deemed obvious and immediate; it substitutes mathe-matical models for mechanical ones. Logically, there isno reason why the character of an entity should bedescribed by a visual image rather than a Hamiltonian.

The view in question is the culmination of a philo-sophic development of long standing. Galileo introducedthe distinction between primary and secondary qualities,Locke and Descartes employed it significantly in theirown philosophies. Primary qualities are those which areresident within their object; they are inalienable fromit and make up its essence. Secondary qualities arise

OCTOBER 1954

10

in the act of perception, are subjective in the simplesense of that word and are therefore less certain. Tomany of us, size, mass, atomic structure are primaryqualities of a material body, whereas heaviness, color,temperature are secondary. But the very recital of suchspecific examples already tends to be embarrassing, andI for one would not care to defend the assertion thatmass is primary and temperature secondary. Yet inearly Greek philosophy, Anaxagoras thought it per-fectly plausible to assign to his "elements" (home-omerics) the intrinsic property of taste.

Even this superficial account suggests what has infact taken place throughout the history of naturalphilosophy. Primary qualities, first posited and affirmedwith innocence and scientific blissfulness, engaged in acontinual retreat before the onslaught of science. Oneafter another of them was converted into a secondaryquality, until today we are wondering whether perhapsthe distinction is illusory, whether perhaps all qualitiesare secondary.

To sharpen this issue, I propose a shift of attention.The distinction between primary and secondary qualitiesis indeed of lesser interest today and may be regardedas settled, as Jeans believes. But though it be dead, itsghost is still very much alive and amongst us. Thecontrast, or at any rate the difference, is now betweenwhat I have called elsewhere possessed and latentobservables. Possessed are those, like mass and chargeof an electron, whose values are "intrinsic", do notvary except in a continuous manner, as for example themass does with changing velocity. The others are quan-tized, have eigenvalues, are subject to the uncertaintyprinciple, manifest themselves as clearly present onlyupon measurement. I believe they are "not alwaysthere", that they take on values when an act of meas-urement, a perception, forces them out of indiscriminacyor latency. If this notion seems grotesque, let it beremembered that other sciences, indeed common sense,employ it widely. Happiness, equanimity are observablequalities of man, but they are latent qualities whichneed not be present at all times; they, too, can springinto being or be destroyed by an act of inquiry, apsychological measurement. The third interpretationregards the position of the electronic lightning bug asa latent observable.

It is less committal than the others. For clearly, ifthe electron did have a determinate position at alltimes and we could not possibly know it, this viewwould still stand aright. Likewise, it is compatible with,though again less committal than, the appeal to meas-urement as bringing about this latency. Perhaps it is aninstrumental disturbance that does it, perhaps—and Ishould favor this conjecture—there is an irreduciblehaziness in the very essence of perceived phenomenaof which Planck's constant h is the quantitative expres-sion. It may be that this latency affects even theidentity of an electron, that the electron is not thesame entity with equal intrinsic observables at differenttimes. The suggestiveness of the hypothesis is evident,and with it the danger of mysticism. When the view is

shorn of its extraneous implications, it avers that theelectron is where it is measured, that it may be nowherewhen it is not measured, that a measurement, properlycontrived, may cause it to appear somewhere. Theadvocate of this view is not entitled to speculate aboutreal trajectories, to follow his mechanistic propensity ofpicturing the motion of an atomic particle accurately inspace and time (except as an approximation). Wethereby cut off one horn of the complementaritydilemma and take as the only valid description ofreality the (//-function formulation. Before seeing whatthat entails, let me insert another word about thedifference between possessed and latent observables, aspeculative word.

I believe that this contrast, like that between primaryand secondary qualities, will ultimately be resolved infavor of the latent observables; that is, the representa-tion of physical observables in terms of operatorsrather than c-numbers is probably fundamental, and weshall perhaps find suitable operators for charges andmasses as we have for positions, momenta, energies,spins and all the rest. The fact that under certainconditions quantization, uncertainty and latency seemto be absent, as in the large-scale world, is guaranteedby Bohr's correspondence principle, which is not aspecial postulate but can be derived from the axiomsof quantum mechanics.

Now, in what sense can the shadowy (//-functions ofthe Schrodinger equation be real? Let us translate thequestion into the familiar terms of the lightning bugphenomenon. The (//-function, when squared, representsthe probability that a speck of luminosity will appear ina specified volume under scrutiny, or, still less tech-nically, the number of times I see a speck divided bythe number of times I have looked. There is nothingvague or tentative about such probabilities; they arenumbers obtainable by observations just like thosewhich describe all other physical fields. The only dif-ference is that a probability number requires numerousobservations in order to be established, whereas anelectric field strength can in principle be determinedby a single observation. In practice, however, thephysicist is able to perform his set of observations in asingle act because he has available a large number ofsimilar atomic systems. For example, a single illumina-tion of hydrogen atoms by an x-ray beam produces apattern on a photographic plate from which the proba-bilities of position for an electron can be inferred.Hence even the one methodological distinction betweena probability field and other fields is largely academic.

Yet physicists, mindful of earlier theories whichused probabilities only a, jaute de mieux, have come toassociate with them a flavor of ignorance, a mentalquality; they often regard them as subjective ap-praisals of a situation not completely understood, oras intrusions of metaphysics into the objective schemeof things. There are many signs on the horizons ofmodern science which belie this view, interesting newdevelopments in mathematics, statistical mechanics andinformation theory that lie beyond the scope of this

PHYSICS TODAY

11

account. Hence one may well regard the denial of realstatus and fundamental importance to probabilities,which is so characteristic of classical physics, as anoutmoded attitude. This leads me to suggest that wegrant consciously to probability the function which infact it already assumes: to serve as the basic de-terminant of experiences in a real world.

After all, there is nothing illogical in the seeminglygrotesque conception of probabilities Hying about inspace! Their relation to observational experience iscertainly no more remote than the connection betweena light wave and its visual manifestation, or indeedbetween the observed emission of a beta-ray and aneutrino field. Nor does it put any strain upon commonsense in the world at large, for the correspondenceprinciple converts all probabilities referring to ordinaryobjects into 8-functions (i.e. point-like concentrationsat the place where the object is conceived to be), andthere is no difference between probabilities flying throughspace in the form of 8-functions and classical objects!

This third interpretation is simple as a philosophicdoctrine, monistic by virtue of its rejection of detailedparticle trajectories, objective because it takes itsprobabilities as measurable fields and not as indexes ofknowledge or belief; unfortunately, however, it demandsa maximum departure from familiar lines of thought.I have chosen not to name this view because it isdifficult to label in a simple way. V. F. Lenzen(Causality in Natural Science, Charles C. Thomas,1954) calls it the objective view because it ascribes ob-jective reality to probabilities. This terminology seemsto me very appropriate.

On what grounds are we to judge these three inter-pretations? Is the final verdict as to their validity amatter of personal taste? The state of affairs here isquite different from what it ordinarily is in science, nocrucial experiment being available for discrimination.In such cases recourse can and must be taken to theprinciples of scientific methodology, for in the lastanalysis these provide the criteria which every goodscientific theory must satisfy. I shall therefore give abrief review of these principles.

4. Methodology of ScienceCCIENCE serves to make reasonable or understand-^ able as large as possible a portion of our experience.Certain parts of experience, like fleeting sensations, un-related perceptions and observations, are in themselvesdevoid of rational order. Science strives to make themcoherent, not so much in their direct setting, but bycarefully associating with them specific ideal structuressometimes called concepts or constructs, and by en-deavoring to reproduce among these meaningfully re-lated structures the perceptory sequence of immediatefacts. Permit me, to avoid circumlocutions, to statethe essence of scientific method in somewhat arbitrarybut pictorial terms (cf. The Nature of Physical Reality,McGraw-Hill, 1950).

The figure represents what one might call a sectionof our (cognitive) experience. Its limit is the f-plane

(P for "perception" or "protocol" [public record]), thelocus of immediate perceptions, observations, data oranything else we deem incontrovertible. It is in asense a boundary of our experience, because we do notgo beyond it to anything more ultimate in science assuch. To the left of the />-plane extends a vast domainpervaded, as it were, by rational texture. It is the fieldof concepts or constructs (C-field), populated by origi-nally ideal entities which habit, plausibility considera-tions or outright postulation has associated with thedata on the /'-plane. The linkages between the P-t\t-ments and the C-elements will be called rules ofcorrespondence.

Under certain conditions, to be outlined presently,the constructs take on scientific validity, assume anapproved status as real entities in the world or, as Ishall briefly say, become verifacts. In popular, onto-logical language, these verifacts "exist''.

It is clearly of prime importance to know the criteriaunder which the transformation from the tentative-character of a construct to the approved state of averifact takes place. These criteria may be found, notin speculative conjectures about first principles or rulesof thought, but through a study of the actual proceduresin historical science. Such a study, it seems to me,yields two classes of verifying conditions.

In the first place, the constructs employed in scien-tific explanation must satisfy certain vague formalrequirements which often go under the names ofcoherence, neatness, or economy of hypotheses. Sec-ondly, they must "agree" with the facts of the f-plane.Let us call these two requirements the metaphysicaland the empirical criteria. Each is, of course, in needof a more meticulous analysis than this brief surveycan undertake; their general features, however, can besketched.

The meaning of the second, the empirical set of re-

C-Fl£LQ

Constructs (designated by circles) are connected by formal relations(light lines) to one another; some are linked by rules oj corre-spondence, which usually are operational definitions, to the plane ofperception (/'-plane). Aletaphysical requirements regulate the C-field;verified sets 01 connected constructs, i.e., accepted theories, can betraversed by circuits of empirical confirmation, one of which isdrawn as E.

OCTOBER 1954

12

quirements, is illustrated by the line E, which startson the P-plane, moves via rules of correspondence tothe C-field and finally returns to P. It represents atypical circuit of empirical verification. Some observa-tions (like Newton's falling apple) suggest constructs(mass, acceleration, force of gravitation) which, whencombined in accordance with theoretical rules applyingto these constructs, allow a return to the P-plane atsome other place (motion of the moon). Thus, on thebasis of some initial facts, a prediction of other factshas been made. Circuits of this kind are extremelynumerous, and each can be traversed in both directions.When a given set of constructs, a theory, has beencrossed by a sufficient number of circuits like E, it issaid to be empirically valid.

The metaphysical requirements are of another sort,for they do not relate to specific matters on theP-plane. Rather, they constitute ideal devices by meansof which the a priori fitness of the constructs is ap-praised. No attempt will here be made to present themin their fullness. Let us rather discuss the three whichare of greatest relevance to the interpretations of thequantum theory.

In the first instance, the constructs of a theory mustbe so chosen and connected as to permit continuousand uniquely determinable sequences of states. Thisis often called the postulate of causality; it is alsoregarded by many as differentiating between the mecha-nistic thesis which is said to obey it, and the other twointerpretations which do not. The principle of causalityin what seems to me to be its simplest and clearestform requires only this: that physical systems bedescribed in terms of states which are self-unfoldingin a determinate manner; that the state of a systemat time / be sufficient for a prediction of the state (i.e.the values of the same crucial variables) at any othertime t'. The principle does not spell out what thesestates must be, leaving mechanics free to operate withpositions and momenta of particles, electrodynamics touse field variables, hydrodynamics to use pressures andvelocities at points. Nor does it discriminate againstthe use of i//-functions in quantum mechanics. Andthese ^-functions are elements of a causal descriptionwhether \p refers to an ensemble of trajectories as inBohm's interpretation; or whether it is the probabilityamplitude of a statistical ensemble. Only if the specialmechanistic version of causality, the version whichrequires that prediction be based on single observationsor individual events, is given unique and preeminentimportance, does the third interpretation become non-causal. However, this narrow insistence does violenceto a wider methodology of science and is difficult to

justify.Next among the three metaphysical requirements I

have chosen to offer for consideration is extensibility.A theory must be extensible to a large domain of facts.Science prefers that one among rival theories which isapplicable to the greatest number of phenomena. Fromthis point of view Newton's theory of dynamics waspreferable to Aristotle's, Maxwell's equations are pref-

erable to theories of Faraday and Ampere, Einstein'sgeneral theory of gravitation is preferable to Newton's,the quantum theory to classical dynamics. The principleof extensibility (or extensiveness) itself is vague inlogical contour; one cannot say in any given instancewhether a theory is sufficiently extensive or not. Itspower arises, as with all metaphysical principles, fromthe fact that the scientist is apparently always able toform an intuitive judgment with regard to sufficiency.Even more effectively can he use the principle indiscriminating between competing theories.

Finally, there is the requirement of simplicity. Again,I do not feel the need for defining the exact meaningof simplicity, nor do other scientists who use this ideain their appraisal of theories. In practice, and certainlyfor our present purposes, its intention is clear, I amsure. Galileo's description of free fall was simpler than,say, Tartaglia's; Newton's theory of motion simplerthan Aristotle's; Copernicus' astronomy simpler thanPtolemy's; the electromagnetic theory of light simplerthan the late ether theories; the 5-matrix approach innuclear theory is simpler than the use of different nu-clear potentials on different occasions, and so on. Theserequirements are felt in all disciplines given to carefulthought: even philosophers prefer monism to pluralismbecause of its better accord with the requirements ofextensibility and simplicity.

Having now come to the end of our sketch of themethodology of science, we are perhaps in better posi-tion to judge the advantages and disadvantages of theinterpretations of quantum mechanics described in sec-tions 1-3. It should be acknowledged, however, that thesituation under study differs from those normally metin science, and presents unusual difficulties, because ofthe paucity of decisive data on the P-plane. For curi-ously, the known facts are explained by all three inter-pretations, and unknown facts crucial to one thesis andnot to the others are extremely difficult to obtain. Itis evident, therefore, that we are forced to place anabnormal reliance on the metaphysical principles. Byand large, the circuits of empirical verification start atthe same points on the P-plane and end at the samepoints in the three different interpretations. And wherethe mechanistic thesis does suggest possible discrim-inating observations, experience is noncommittal.

As a case in point I refer to a paper by Weizel (Z.f. Phys.: 134, 264: 1953). This author takes the mech-anistic thesis seriously and considers what, in mechani-cal terms, Bohm's quantum mechanical field might be.He asks: what kind of physical entity, thus far undis-covered, could possibly interact with the invisible fire-fly in a manner producing its erratic appearances? Itmust be able to act on the firefly without suffering areaction itself, and this is a difficult assignment. ButWeizel does find a suitable mechanism which he calls a"zeron"; he visualizes it as a sort of jellyfish movingwith the speed of light, yet able to absorb an electronif given momentum and to spew it forth again withthe same momentum at another place. Needless to say,these zerons have not been found.

PHYSICS TODAY

13

5. Assessment of Merits and Demerits

E now bring the principles of method to bearupon the three interpretations, hoping to reach

some verdict. Let us make sure that all the evidencehas been heard. I have reason to think that many ofyou doubt this point and are disposed to say that Ihave packed the court against the interests of themechanistic view. For I have said nothing about pic-torability of constructs as a requirement for a goodtheory; I have placed an abstract notion, like entropy,field strength or probability, on a par with Rube Gold-berg devices. Nothing has been said in favor of visualmodels. Is this fair?

To be sure, most of us find pictorable models likebilliard balls or waves highly desirable and convenient;indeed we often use them in our reasoning when weknow we should not. They are suggestive, conduciveto clarity of thought. The reason is doubtless psycho-logical: our sensory experience is strongly colored byour visual sense; people learn most easily by seeing.But it is also true that science has carried us very farbeyond the range of vision, and to assume that picturesare useful where vision fails is wholly without logicalcogency. On the other hand, physics uses nonpictorialelements with great success, as in electrodynamics.This sometimes fails to be recognized because physi-cists gain familiarity with E and H through use andthen mistake what seems familiar for what is pictorable.

My own uneasiness about including pictorability inthe list of metaphysical requirements arises from theintolerable way in which it contradicts or curtails bothextensiveness and simplicity. If physics were to insiston it, its methods would not embrace the present pro-cedures of Gestaltism and behaviorism in psychology,of social theories and economics. For such constructsas Gestalt, drive, habit, supply and demand have verylittle in the way of mechanistic pictorialness. This ismy primary' reason for omitting the (pseudo-) postu-late in question.

A while ago I spoke of rendering a verdict; yet thisis hardly what the occasion demands. We have seenthat the scientific evidence is not complete and thatonly half the resources of scientific methodology,namely the metaphysical ones, can be drawn upon.Let us therefore temper our judgment with modestyand concede that part of it depends on taste. We aresomewhat in the position of a literary critic evaluatingthree poems and cannot expect finality or general ac-ceptance of our conclusions. Or, with greater optimism,we may consider ourselves in the position of a teacherwho grades three themes, themes which he does notfully understand.

Here are the marks I would assign. On the score ofcausality, the mechanistic thesis gets a perfect mark;but the third interpretation ranks equally, for we haveagreed not to discriminate unfairly between mechani-cal and statistical causation. The formalistic view re-nounces causality in its space-time description but re-tains it in the complementary i/<-neld. Hence it would

seem to merit half-credit on this score, i.e. five out often.

Extensibility seems equally great for the second andthird interpretations. Bohr's complementarity finds ap-plication in many realms of thought; it has been ac-claimed even by theologians as casting light on theirproblems (e.g., freedom of the will). The last view,which regards probabilities as irreducible and admitslatent qualities, is very close to the thinking of psy-chologists, social scientists and modern statisticians.It too is compatible with the possibility of freedomthough it provides no solution for it. The mechanisticthesis, on the other hand, is of use primarily in thephysical sciences. Furthermore, it makes a paradox ofhuman freedom. Hence a fair rating on the score ofextensibility would seem to be: Mechanistic view 2,formalistic view 8, third view 8.

Finally we come to simplicity. Here it appears thatthe formalistic thesis scores very low, since it resignsitself to a dualistic explanation of nature. I would rateit 20%. The mechanistic thesis does not do much bet-ter because it encumbers the conceptual scene withideas not needed in the third interpretation, which isthe simplest of the three. To these two views I wouldassign, respectively, the marks 50% and 80%. The sum-mary is given in Table I.

Table I

Score Based on MethodologicalRequirements of Theories

Principle InterpretationMechanistic Formalistic Third

Causality 10 5 10Extensibility 2 8 8

Simplicity 5 2 8Total Score 17 15 26

The outcome of this test will be radically changed infavor of the mechanistic thesis if one or more of sev-eral possible contingencies occur. If Vigier, de Broglie,or Bohm succeed in their present endeavor to derivethe equations for the quantum field from the principlesof general relativity, I should change the mark of 2 onextensibility for that theory to 9. A similar or evengreater improvement would result from success of themechanistic interpretation to explain the puzzling fea-tures of nuclear physics or other now mysterious effectsby reference to its novel field. Indeed, this would forcethe other theories to take on modifications and neces-sitate a rescoring in connection with simplicity as well.

Finally, and this seems most important, experimentsmight be performed which bring into evidence newphysical entities giving verified status to those featuresof the mechanistic view that count most against it.The likelihood of such evidence for Weizel's zerons islow, but there are surely alternative models. When suchdiscoveries are made the whole status of our problemis changed because advantage can then be taken of new-circuits of empirical verification, and a complete re-appraisal will be necessary.

OCTOBER 1954