The Wave-Particle Duality Teaching via a Visual Metaphor

J. Bemstein and S. S. Shaik Ben-Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105, Israel

The microsconic world of the quantum mechanical atom looks baffling and foreign to heg&ing chemistry students. Concepts such as the Heisenherg uncertainty principle and the wave-particle duality pose, hence, a real teaching chal- lenae. One method of meeting this challenge is to seek mac- roscopic metaphors that illustrate the behavior in the micro- scopic world of electrons and photons. An example that employs an overhead projector to demonstrate the uncer- tainty principle has appeared recently in this Journal1. Af- ter a number of vears of teaching general chemistrv to hoth - chemistry majors and engineering and science students, we have found a visual metanhor that renders vivid the concept of the wave-particle duaiity. This paper describes the use bf this metaphor.

The crux of the duality concept2,3 is that an electron, for instance, exhibits both particlelike and wavelike behaviors. These two "faces" of the electron are mutually exclusive and in no single experiment does one observe hoth particlelike and wavelike hehaviors4. The electron exhibits then a Jekyl- Hyde character, sometimes behaving like one, sometimes like the other, hut never like hoth at the same time. Despite

Figure 1. Young lady and old witch. The nose and left eye of the old witch are, res~ectivelv. the chin and left ear of the vouno iadv. A necklace on the vouna , . . - . . - lady is formed by the mouth ofthe old witch. This cartoon was created by M. E. Hill and was originally published in Pock in 1915 over the caption, "My Wife and Mother-in-Law"

Figure 2. The image of the goblet is formed by the facial profiles facing each other. Reproduced, by permission, from Scientific American (see ref 5).

these two "faces", the electron cannot he formally defined as heine half wavelike and half narticlelike. The electron has a - "oneness", while its wave or particle "faces" are the results of our ex~eriments to nrohe this "oneness". Thus. hv ohserv- ing the electron we interact with it and thereby split the "oneness" into two different exneriences, neither of which reveals the true nature of the elekron. WL thus observe and perturb, and the result of our interference with the nature of things is the wave-particle duality.

For students this new way of thinking about the behavior and properties of matter is very difficult to digest. There- fore, we sought some metaphorical means of visualizing the duality concept with a macroscopic model that would mimic the microscopic reality. The method we chose involves the use of a series of pictures, shown in Figures 1-5, that are based on some well-known optical illusions. This set of fig- ures has been resented nreviouslv as a eroun hv the osv- chologist Fred kttneave in a discussion ofihe kuitistab:lliiy of human perceptions. We have found that this effect of

I Peckham, G. 6. J. Chem. Educ. 1984, 61,868; Cosser, R. C. J. Chern. Educ. 1982,59, 300.

2The historical and philosophical background of the duality con- cept is described in Jammer, M. The Conceptual Development of Ouanturn Mechanics: McGraw-Hill: New York. For a poetic elucida- tion of this and other concepts of modern atomic theory see Hoff- mann. B. The Strange Worldof the Ouanturn; Dover: New York. 1959.

The concept is described in most standard general chemistry texts, for example. Dickerson. R. E.; Gray, H. 6.: Darensbourg, M. Y.; Darensbourg, D. J. Chemical Principles, 4th ed.; BenjaminICum- mings: Menlo Park, CA, 1984; p 273.

'The Thomson experiment to determine rnte demonstrates some of the particielike properties of the electron, while the Davisson- Germer experiment, in which electrons are diffracted in a manner identical to X-rays, demonstrates some of the wavelike behavior.

Anneave, F. Sci. Am. 1971, (12). 63; original sources for each of the figures are given in the captions.

Volume 65 Number 4 April 1988 339

Figure 3. A duck facing ien; a rabbit facing right. The psycho Janrow first used Mis figure in 1900 to demonshate the riv ambiguity.

Figure 5. A pomn of the painting by Salvador Daii entitled "Slave Market with the Disamearina Bust of Voitaire", oil on canvas. 1940. The bust of Voitaire is

Figure 4. By a series of relatively slight alterations in the shapes of some lines the image may be changed from the face of a man to a sitting nude. There is usuaily no question about the interpretation of the upper iefl and lower right figures, which, by analogy, may be said to represent macroscopic situations. With one, and only one, description. The figures in between may be said lo represent the microscopic world in varying degrees, where the ultimate description depends on the characteristics the observer wishes to ascribe to the figure. Repraduced by permission of the American J m l o f Psychoicgy.

perception multistability rather dramatically conveys the concept of the quantum duality to students. The figures are usually shown to the class in a series, immediately after presedtation of the formal material in which the~conse- quences of the wave-particle duality are first encountered. in addition to demonsirating the concept visually, the inclu- sion of the short slide show provides some relief for the students from the somewhat taxing intellectual challenge of these new ideas.

Each of these fieures can be intermeted in two wavs. For instance, in Figure 1, the perception is divided between the old witch and the vouna ladv. The crucial feature of this figure (and the othkrs) that the two images are not two halves contained in one drawing. Either image encompasses by itself the entire drawing. The drawing in Figure 1 is then a oneness, and it is by the vision-perception interaction that we observe two images out of this oneness. The class is involved in the discussion, and in our experience the class is

bes Perce re0 from a dslance Reprw-ced 0, perm s s m at lne Satmoor 0.3 M.se.m S' Pelersb.rG F orroa

usually split between the two interpretations, as if they were mutually exclusive. Lively (indeed sometimes heated) discussions develop as one group tries to demon- strate its internretation to the other eroup. Similar effects. in varying degrees, are obtained with ;he iictures in Figures 2-5. The repetition of this effect with a number of fiaures helps to drive home the point that every one of them is a "onenessn-a single drawing or painting, just as the electron is a single entity. Accepting this unity, the students begin to understand that in the process of observing and interpreting the figures-the visimn-perception interaction-this "one- ness" is split into two different and mutually exclusive im- ages. The analogy to the particle-wave duality and the na- ture of the electron becomes more lucid. A fundamental concept of contemporary physical sciences then becomes clear: namely that the results of the experiments are the results of perturbing the object under observation rather than the true revelations of the object2. Yet, knowing the result of every possible observation is equivalent in a way to understanding the nature of the object.

Acknowledgment We are grateful to Diane Powers of the New York Public

Library for background information on the figures present- ed here.

340 Journal of Chemical Education