Science & Education 7 : 245-260, L998.

@) 1998 Kluwer Academic Publishers. Printed in the Netherlands.

Theories as Models in Teachine Physics

NAHUM KIPNIS

The Bakken Library and Museum, 3537 Zenith Ave S, Minneapolis, MN 55416, USA

ABSTRACT. Discussing theories at length, including their origin, development, and replace-ment by other theories, can help students in understanding of both objective and subjectiveaspects of the scientific process. Presenting theories in the form of- models helps in thisundertaking, and the history of science provides a number of suitable models. The paperdescribes specific examples that have been used in in-service courses for science teachers.

INTRODUCTION

The history of science can be a valuable tool in teaching physics. I havealready discussed elsewhere the role of recreating historical experiments(Kipnis, 1996). However, experiments by themselves do not produce anynew knowledge: they are useful only if students learn how to put togetherexperiment and theory. This paper describes a way to deal with theoriesbased on a combination of historical readings with recreating historicalexperiments.

Physics courses usually do very little to explain the role of theories andtheir interaction with experiment, concentrating instead on their end-products: concepts and equations. The exceptions are few and they all areGrand Theories: molecular-atomic theory, kinetic theory of gases, thewave theory of light, and some others. And the nature of light is usuallythe only case where students learn something about competing theories.Traditionally, theories are introduced dogmatically, without much justifi-cation for their creation. The inductive component of scientific researchis omitted, and it appears that a theory results from an one-time mentaleffort of its author, coming up from his head in the same form as in thetextbook. Another implication is that experiment follows the theory,which justifies teachers' custom of first announcing a theory (or a law)and then illustrating it by demonstrations or'verifying' it in the laboratory.With this approach, students do not understand how and why theoriesemerge and replace their predecessors. As the result, the 'skeptics' amongstudents (usually, the brightest ones) may deny the relevance of studyingsomething which is a subject to change. Nor are the 'conformists' muchhappier: seeing only a few examples of theories, all of a very generalnature, they begin to believe that 'theorizing' is an activity reserved forgeniuses, such as Newton or Maxwell, and is certainly irrelevant to theirlives.

Recently, a new trend has emerged in science education, called 'con-

structivism' that aims at enhancing students role in the process of learning.Students experiment without knowing the'answer', and they are expected

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to produce from these experiments the relevant concepts and theories.Teachers guidance is reduced to a minimum. It appears that the maindrawback of the traditional approach is overcome, for students learn howscientists create theories by doing this themselves. In reality, teachers aremuch more preoccupied with involving students in this activity than withthe knowledge obtained through it. As the result, students leave theclassroom with a variety of results and not knowing which is correct, orwhat they have actually discovered. In their defense, these teachers referto the modern philosophy of science, which has supposedly proved thatthere is no objective truth in science, that the adoption of new theories isa purely social process, etc. (Collins, 1981; Collins & Shapin, 1983; Davis,L993; Roth, 1994). If so, then having a variety of results in the sameexperiment is normal, and students should negotiate among themselves,which of them is correct, as scientists supposedly do. Many students enjoythe process of doing something on their own, but the brightest amongthem sooner or later begin to doubt whether this activity truly imitatesscience: 'if proclaiming one result true and another false depends on theeloquence of their supporters, there cannot be any objective value inscience'.

We see that the two pedagogical methods reflect two major focuses inthe philosophy of science; on the objective and subjective components ofscience. Each of the two approaches exaggerates one aspect of science atthe expense of the other. The former concentrates on the best positiveknowledge available, which is within students'comprehension, while thelatter emphasizes the relativity of scientific theories and subjectivity intheir adoption. Neither turns out to be very productive on its own: oneteaches useful skills and facts but is boring and thus unsuitable for teachingphysics to a// students, while the other is quite stimulating but leaves nodefinite knowledge behind. combining the two would give a better pictureof scientific activity, enhance students' interest in science, and providethem with skills useful in daily life. I will discuss two examples of such acombination taken from in-service courses for teachers at the BakkenLibrary and Museum. The overall goal is to give students a more balancedview of science, that emphasizes both its subjective (human) side and itsobjective value. I find that treating theories as 'models' helps in such anundertaking.

since theory has multiple interpretations, I will define it for the purposeof this paper as a 'hypothesis that has already obtained a certain experi-mental support'. Theories differ by their degree of generality. physicalresearch begins with explaining a single phenomenon by means of ahypothesis. Then the hypothesis is applied to a few similar phenomena,and if confirmed, it becomes atheory. The next step is to test the theorywith other groups of phenomena, similar to the original one in anotherway. If they confirm the theory, its generality increases, and so on. Some_times the term model is used interchangeably with theory. There arevarious definitions of the model, and, in general, it is not clear how it

THEORIES AS MODELS IN TEACHING PHYSICS 247

Fig. 1.

differs from theory (Hesse, 1967). Perhaps, a more productive approach would be using different definitions for different purposes. In particular, in this paper, I will define model so as to make it useful in teaching: 'a model is a visual representation of a theory, usually based on an analogy with a known phenomenon, which has a capability for modifications'.

BUILDING A MODEL OF ELECTRICITY

The first example is based on the history of electricity. Let students start with reproducing a slightly modified experiment of Stephen Gray (1731). First, students observe that the declination of a single-thread electroscope produced by a charged rod decreases with the distance between them. Then the rod is placed at such a distance from the electroscope that the latter does not react. Next, we put between the rod and the electroscope a horizontal wire fixed to the top of a plastic cup (Fig. 1). Touching one end of the wire with a charged rod affects the electroscope at its other end. We may suppose that electricity somehow came close to the electroscope, probably through the wire, because removing it cancels the effect. Then we repeat the experiment using other objects instead of the wire and find that a similar phenomenon occurs with a wooden rod, a cardboard strip, and a cotton rope, but not with a plastic tube. We conclude that our hypothesis about electricity being capable of moving was correct and introduce the concept of conductors. Thus the construction of a mechan- ical model of electricity begins.

The next step is to find whether electricity moves like a solid body or a liquid. For this purpose, we attach a cotton rope horizontally to two insulating stands and set several electroscopes along its length. When one end of the rope is charged, the threads start moving towards the rope one after another and then retain their inclined positions for quite a while. Apparently, electricity retains its presence in the places it has passed, which resembles a flow of water in a pipe rather than a flight of a stone. Thus, we opt for a 'fluid model'.

Now, we are looking for the range of application of the new theory, or

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the circumstances at which electricity can move. Following Gray, we willchange not only the 'communicating line' per se but also its supports andfind that with some supports (paper, wood) electroscopes do not react.'Why does not electricity reach the end of the wire set on a wooden block?'To answer this question we invoke our model: is it possible that much ofwater in a long hose does not reach its end? Students answer withoutdifficulty that this can happen if there is a big hole in the hose. Whengoing back to electricity, we suppose that a conducting support plays therole of a hole in a hose, by diverting electricity from the other end of thewire into the table.

Thus, our model can provide clues for understanding Gray's phenome-non. If so, perhaps it can account for a difference in the speed with whichelectricity affects electroscopes when it travels through a cotton rope ora wire. Some students may point to a difference in water pressure or thefriction in a pipe, but since they are little familiar with hydrodynamics, itis advisable to conduct a few experiments with flowing water.

Observing a different speed of flow through tubes of a different diameteror through holes in a bucket of a different size may suggest that a flow ofwater experiences a certain resistance, which depends on the cross-sectionof the escape channel. To see if this concept is applicable to electricity ingeneral, we have to compare a few other objects, by setting them side byside, with the ends we touch with the charger contacting one another, andwatch the electroscopes at the other ends. We will see, for instance, thatthe electroscope placed against a thin wood rod reacts somewhat laterthen the one at the thick rod, and the one standing by a rope evenlater. Thus, it appears that different conductors do have a difference inresistance, which appears to depend on their material and dimensions.These may become the variables to be tested. (Henry cavendish estimatedthe speed of flow of electricity by the strength of a shock delivered froma Leydenjar through a given conductor. This technique is applicable afterstudying the Leyden jar, and it is particularly useful for differentiatingbetween the parameters both devices measure: potential and current.)

To increase the validity of this choice of variables, let us go to ourmodel and see if they are essential for liquids. By selecting two tubes ofthe same dimensions but of a different degree of inner smoothness we cannotice that the rate of flow through them is different. This suggests thata similar experiment can be performed with two conductors made ofdifferent materials but of the same dimensions: the results confirm thehypothesis that different materials differ in their resistance to a flow ofelectricity.

we can repeat a similar trick when determining the effect of dimensionsof a conductor on its resistance: instead of doing a purely empirical studyof different conductors made of the same material, we can first exploresuch an effect on liquids. A few experiments with glass or rubber tubesshow that water runs faster when the tube is wider or shorter. with thisfinding in mind, we return to electricity and observe that an electroscope

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reacts faster when a wooden dowel or a cotton rope are of a largerdiameter or of a shorter length. Similar results can be obtained withliquid conductors, such as salt water, filling a tube. The conclusion is thatelectrical resistance of a conductor increases with its length and decreaseswith its diameter (or cross-section).

Thus by using our model in both directions we not only learn moreabout electricity but increase our faith in the model itself, or, more exactly,expand its range of application. That limitations do exist becomes evidentfrom the fact that our experirnents have not yet determined whether the'friction' electricity travels, like water in a pipe, inside a conductor, oralong its surface. For this reason I use 'speed of flow', or the distancepassed by electricity along a conductor in a second, instead of'rate offlow', which usually means an amount of a fluid transferred through across-section per second.

Students can suggest that the speed of electricity may depend not onlyon the conductor but also on how long they rubbed their charger. Weturn their attention to the fact that in such a case the charger tested byan electroscope before the experiment showed a greater 'power'. Herewe can introduce the 'amount of electricity': if rubbing makes electricity,perhaps rubbing longer produces more electricity. If electricity is a fluid,a natural analog to the 'amount of electricity' may be the amount of water.We begin experimenting with water to determine if its amount affects itsflow. We see that when the same bucket has more water in it, waterescapes faster through the same hole. If students already know that movinga body in a resisting medium requires a certain moving force, they canconnect a higher level of water with a greater force. We may now presumethat electricity is also being moved by a force that was called an electric

force (Yolta called it tension).Experiments show, however, that tension depends not only on the

charge submitted to a conductor, but on the conductor itself. For instance,if we use an electrostatic generator to charge in turn two metal tubes ofthe same diameter but of a different length, that are insulated from thetable, the reaction of an electroscope will be stronger in the case of theshorter tube. The implication is that the same charge creates a greatertension in the smaller tube. Let us use our model to understand thisphenomenon. Can the same amount of water produce a greater force?When pouring the same amount of water into two vessels of a differentdiameter but with identical holes in the wall, students notice that waterruns out faster from a narrow vessel where the initial water level is higher.This leads them to a hypothesis that the moving force depends not onlyon the amount of water but also on the dimensions of the vessel, or on itscapacity. A few additional experiments will confirm that the flow increasestogether with the initial height of water, which, in turn, is inversely propor-tional to the vessels capacity. If we now make tension an equivalent ofthe height of water and characteize a larger conductor as the one of agreater electric capacitance, we can infer from our model the following

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law: the greater the capacitance, the smaller the tension created by thesame charge. Thus, tension acquires a meaning of electric height (level).

This concept will be somewhat corrected when students begin con-necting charged conductors to uncharged ones. An electroscope shows thesame deviation when being placed against any part of this system. If whatit measures is tension, then electricity moves until tension becomes equalin all connected conductors. However, if the physical meaning of tensionis a moving force, electricity must move until tension is zero. To removethis contradiction, let us seek help from our model. An equivalent ofconnected conductors is connected vessels. In such vessels water flowsuntil its level is the same in both. Although this level can be high, nomoving force exist after the flow stops. This force reappears and waterbegins to move only when the water levels become different. Thus, themoving force depends not on the level of liquid itself but on the differenceof two levels. For a case of a bucket with a hole in its wall, the other levelis that of the hole: when water reaches this level it stops running.

Returning to electricity, if we want to preserve the meaning of tensionas a moving force, we have to add another term potential, defined so thattension equals the difference of two potentials. Now we can say thatelectroscope measures a conductors potential, or, more exactly, a differ-ence of potentials between the conductor and electroscope itself. For acapacitor, we speak of a tension or a difference of potentials at the twosurfaces.

Our model will be also of a great help in deriving the laws for a singlecapacitor and for a connection of several capacitors. While charging aLeyden jar from an electrostatic generator, students notice that the largerthe jar, the longer it takes to reach the same tension. Since rubbing longermeans increasing the amount of charge, students will find a full justificationof their finding in the fluid model, because when filling several vessels tothe same level one needs the more water, the greater its capacity. More-over, the model predicts that as the same amount of water stays higherin a smaller vessel, so with the same number of turns (same charge) asmaller Leyden jar can be charged to a higher tension than the larger one.Experiments easily confirm this.

Students always wonder why after someone discharges a Leyden jarthrough his body, another person who grabs it feeling safe, can still receivea shock. Suggest to treat this case as a connection of two capacitors, oneof which is charged, and turn to the fluid model for a clue.

When a vessel full of water is connected to an empty one, water flowsuntil its level in both vessels is the same. It means that if the empty vesselis of a much greater capacity than the full one, most of the water will runout; however, if they are comparable in size, the amount of water leftmay be significant. For electricity it means that if the two conductors arecomparable in their capacitance, the remaining charge may be sufficientfor producing another shock.

Thus by using experiments and concepts introduced in the 18th century

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by Stephen Gray (1666-1736), Alessandro Volta (1745-1827), Henry Cav-endish (1731-1810), and others students can construct the fluid model ofelectricity, which helps not only in recreating some historical discoveriesbut also in understanding and practical usage of the laws and concepts ofstatic electricity. The same model turns out to be also very useful instudying the so-called 'current electricity'. If we retain with volta the ideaof tension as a moving force, whatever its origin (volta erred by attributingits cause to the contact of two different metals), we can extend our modelto a continuous flow of electricity. This was done in 1827 by Georg SimonOhm (1787-1854). While he claimed to build his theory on the basis ofPoisson's and Fouriers theories of heat transfer, it can be easier under-stood in terms of water flow, which anyway has some common featureswith the propagation of heat. Ohms revolutionary innovation was to applythe concept of tension to qny two points of a circuit (Volta used it onlyfor the point of the contact of different metals). Ohm described thecondition at each point by means of an electric force (now we use potential)and set the tension between any two points in a circuit to be equal to thedifference of respective electric forces. According to Ohm, currentthrough any conductor is proportional to the tension at its ends. Recallingthat in our model the electric force (or moving force) depends on the levelof water, Ohms law corresponds to the statement that the greater thedifference of water levels at two points, the faster the flow. The latter isfamiliar to those who observed mountain streams, and it can be easilyreproduced in a lab by changing the incline of a tube with running water.when looking at such a stream (or a tube), one realizes that indeed eachpoint of the river bed has a different level about the sea level. From thisperspective, Ohms innovation was fully justified.

However, if Ohm did have before his eyes an image of a stream, thereis one feature of water flow that he had to ignore. In his theory, a non-conductor made a part of a circuit stops electricity, which means zerocurrent, or zero difference of potentials at its ends, or the same potentialin all its points. when translated into hydrodynamic language, this meansthat if a part of a river bed is horizontal, the flow should stop. This is nottrue if the horizontal part is not very long, so that the kinetic energy ofwater is sufficient to overcome its resistance. on the other hand, ohmslaw refers to conditions that do create a current, thus he should not havebeen bothered by this exception.

BUILDING A MODEL OF DIFFRACTION

Unlike the previous case, here we are dealing with a number of models,and students have to rely not only on experiment but also on historicalreadings. we begin with a brief description of the discovery of diffractionby the Italian astronomer Francesco Maria Grimaldi (161g-1663). Heobserved that light entering a dark room through a pinhole produced a

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shadow exceeding the so-called 'geometric shadow', and also alternatingdark and white fringes, both inside and outside the shadow, some of whichwere colored. Grimaldi concluded that it was a new way of propagationof light unexplainable by either reflection or refraction. After this intro-duction, we reproduce Grimaldis phenomena either with sunlight (theway he did) or with an artificial light, using the early nineteenth-centurytechniques of Thomas Young and Augustin Fresnel (Kipnis, 1992). Thefollowing discussion of various historical models of diffraction is connectedwith these experiments.

Grimaldis book was little known in England, and Robert Hooke (1635-1703) thought that he made a discovery when he reported to the RoyalSociety in 1,675 about light bending into the shadow. Newton was quick toannounce at another meeting that Grimaldi observed similar phenomenonearlier: that was Newtons revenge for Hookes criticism of his theory oflight and colors. Newton also added that it cannot be a new way ofpropagation of light, because it could be reduced to a refraction in theaether. He assumed that if the density of the aether gradually changeswith the distance from the diffractor, rays passing by at different distancesfrom the body would curve differently, as in atmospheric refraction, andthus reach the screen at different locations. Newtons hypothesis was notpublished until 1757, and the French astronomer Jean-Jacques D'Ortousde Mairan (1,678-1771) reinvented it in 1738. ln 1768,Etienne-FrangoisDutour (1711-1784) modified the model, making the aether atmosphereof a constant radius and density, but supplementing refraction with reflec-tion at the body's surface. Even Thomas Young (1773-1829) played fora short while (in 1801) with this model trying to combine it with hisprinciple of interference. Another modification of the refraction modelreplaced the aether with air: the diffractor was heated by light, and inturn it warmed up the surrounding air creating in it layers of unequaldensity. However, experiments with an artificial heating of a diffractordid not show any changes in the fringes.

The 'refraction model' was eventually replaced by the 'interaction

model' again offered by Newton (in 1687). In this model, light passing inthe vicinity of a body deviates from its initial direction due to its interactionwith the diffractor. Newton assumed that the force of interaction rapidlydecreases when the distance from the body increases, so that only the rayscoming very close to the surface are affected. To explain the colorationof external fringes, Newton supposed that the force of interaction betweenlight and a body depends on the kind of light, so that for instance, red-making rays deviate more from their initial direction than the violet-making rays. In the beginning, on the basis of his observations of shadowsof wide objects, Newton assumed a deviation of light towards the body,which implied attraction. Later on, he deduced from his experiments witha hair that light rays bend only away from the body, which requiredrepulsion (Fig. 2). To explain several orders of colored fringes, RudjerBoskovic (1711-1787) modified this model so that the force changed its

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nature from attraction to repulsion and back at certain distances from thebody. In 1816, Jean-Baptiste Biot (1774-1862) combined the interactionmodel with Newtons concept of periodicity of light and supposed that themodifications of the force occur at periodical intervals from the surfaceso that they produce alternating condensations and rarefactions of light.

Fig. 3.

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He measured the distances between the diffraction fringes produced by aparallel slit and a circular opening and obtained a good agreement withhis theory.

In the models described above, each diffracted ray was a continuationof a specific incident ray, or, a light ray resembled a trajectory of a movingbody. For this reason, these models conformed to the corpuscular (oremission) hypothesis of light but not to the wave hypothesis. The firstwave model of diffraction, offered in 1802 by Thomas Young, also dealtwith rays but in a different fashion: here each incident ray produces amultitude of diffracted rays moving in all possible directions. Youngselected pairs of rays 'reflected' or'inflected'by the opposite edges of adiffractor in such directions, in which they cross after passing distancesdiffering by an even or an odd number of the half-wavelength: these pointsof the screen display, respectively, dark and bright fringes (Fig. 3). Thismodel became known as 'two-ray interference'. The drawing allows us topoint out an important distinction between a theory and a model. Whenreading about 'reflected' and 'inflected' rays, one can imagine that thetheory explains physical mechanisms that makes rays deviate from their

3m

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original directions. However, since the inflected ray is shown as passingthrough an opaque body, we understand that the model is geometricalrather than physical: Young was concerned only with finding certain inter-section points of rays coming from two centers but not with the physicalexistence of some of these rays. Likewise, when Young found a necessityto improve the agreement of his theory with experiment, he modified themodel by inverting the phase of the 'reflected' ray without discussing itsphysical mechanism.

Although Fresnel believed that he had refuted Newton's interactionmodel by qualitative experiments, the best argument in favor of lightwaves in his 1818 paper on diffraction was a confirmation of his theoryby exact measurements. The theory was a mathematical construction, inwhich the properties of secondary waves were adjusted so as to fit theexperimental data, and the diffractor was treated as a purely geometricalobstacle that has no physical effect on light. Incidentally, late in thenineteenth century Gouy found that for large angles of diffraction andvery close to the diffractor the character of fringes depends on the materialof the body. Thus, Newton's idea of an interaction between light andmatter made a comeback. It is worth noting, that Fresnel's theory includedYoung's theory as an extreme case, in which the contribution of secondarywaves of higher orders is neglected. One can see this much more clearlyfrom the geometrical model (Fig. a) than from Fresnels integrals. Andthe model itself played an important role in the creation of his mathema-tical theory. Like Young, Fresnel began with the interference of raystouching the opposite edges. Then he added another pair of rays passingslightly farther from the edges. And finally, he added an infinite numberof rays coming from all open parts of the wave front. The motive for allthese changes was the same: to obtain a better agreement with observa-tions. Eventually, Fresnel modified his model so as to determine positionsand relative intensity of the fringes using a simple geometrical constructioninstead of integrals. This model, known as the 'zone theory', became veryimportant in teaching physics.

SUBJECTIVE AND OBJECTIVE ELEMENTS IN SCIENCE

A discussion of these models can provide an insight into several aspectsof creating a physical theory and clear a few myths proliferating intextbooks and some other sources. One of the myths is that certain experi-ments by their very nature can support one theory against others. Inparticular, diffraction is proclaimed as an indisputable evidence for thewave theory. However, as noted above, until Young, diffraction wasconsidered the best argument against the wave theory. Moreover, eventoday, when the theories of light are discussed at the qualitative level, asin courses of'conceptual physics', diffraction does not help at all to decidebetween the two theories. Indeed, let us compare, for instance, Young's

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theory with that of Biot. The ordinary explanation of light and dark fringesis that they result from constructive or destructive interference of light,which conforms to the wave theory but not with the corpuscular theory.In fact, the latter did explain these alternations of light intensity but in adifferent way: by assuming that due to a diffractor's attraction or repulsionlight condenses or rarefies at certain distances from it.

In fact, the wave theory concurred with the corpuscular one aboutshifting light from one place to another, it only differed on its cause. Thus,at the qualitative level, the wave theory had no advantage over its rival.Its idvantages became apparent only when early in the nineteenth centurysome scientists began to feel that the time was ripe for rebuilding physicaloptics, including diffraction, on the quantitative basis. 'Some'is an impor-tant word here. When Young offered the first wave theory of diffractionin 1802, no one rushed to praise it. However, a very similar theory offeredby Fresnel in 1816 won an approval of Paris Academy of Science. It wasapproved not because it was a wave theory, but because it was a mathema-tical theory, and people like Laplace, Poisson, Amp6re, and Biot (all'corpuscularians') felt very strongly that the goal of physics was derivingmathematical laws of nature, regardless of the hypotheses they were basedon. And for the same reason, Fresnel's improved theory of diffractionwon the pize of the Academy in 1819. As the 'corpuscularians' Laplace,Poisson, and Biot, who were among the judges, saw it, Fresnel's theoryvindicated not the wave hypothesis but the principle of interference, whichthey viewed as a mathematical principle (Kipnis, 1991). Young could nothave such a support in London.

Incidentally, immediately after the presentation of Fresnel's 1816 paper,Young received full credit in Paris as the discoverer of the principle ofinterference. We must keep in mind, however, that the efforts to mathe-matize diffraction involved only a few physicists while the majority con-tinued to stick to qualitative models. The new trend spread only 15-20years later.

Another myth is that a new theory is offered when there is a need inexplaining phenomena unexplained in the old theory, or in improving itsagreement with experiment. This is not always true either for qualitativeor quantitative theories. The interaction model, for instance, did notexplain more phenomena than the refraction model. Both accounted for(equally vaguely) the expansion of the shadow and a possibility of coloredfringes. The actual reason for the new theory lay outside diffraction. In1675, Newton adopted the concept of the aether, and, accordingly, usedit to explain diffraction. However, upon completing his theory of gravi-tation in 1687 he had to abandon the aether in favor of action at a distance.With this he changed his explanation of optical phenomena, includingdiffraction, by introducing an interaction of light and a body.

For a new quantitative theory, a task of improving its precision com-pared to the previous one appears obvious, but this may not be the mainreason for its creation. For instance, in 1817, Fresnel, a beginning physicist

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seeking to make his reputation, faced a choice of continuing his study ofdiffraction or switching to polarization. The contest on diffraction an-nounced by Paris Academy of Science gave him an excellent opportunityto distinguish himself. As the result, Fresnel produced a mathematicaltheory of diffraction that was confirmed by experiment with great preci-sion. But was this improvement his original motivation? No, because noone complained about an insufficient precision of his first theory or of theexperiments supporting it, and the precision he achieved in 18L8 far ex-ceeded any contemporary needs. The real motive for this undertaking wasFresnel's dissatisfaction with his work in optics between 18L5 and L817:whatever he presented, he was told that it was already done by Young'Fresnel badly wanted to prove himself by creating something original,something that would supersede Young's theory, both mathematically andexperimentally. Of course, after he started his new research, the internalchallenges took over, and he was thinking more about overcoming aparticular obstacle in his theory or experiment than of the competitionwith Young.

One lesson from this is that passion and reason are intertwined inscience as in other human activities. Another lesson is that sometimes asuperior theory replaces its predecessor prematurely, before an actualneed in it develops. Incidentally, some physicists continued to use the firstwave theory of diffraction even after 1819, because it was simpler and yetsufficient. Thus, replacing one theory with another when viewed in theshort run, is not an automatic, impersonal process.

Concerning the response to a new theory, there is a myth that physicistsalways prefer a theory superior to its rivals. However, 'superiority' has adifferent meaning to different people. When one compares, for instance,two Newton's models of diffraction, one can easily find arguments againsteither. A certain preference for the interaction model in the L8th centurycame from it being a part of the general Newtonian framework in physics.Both models were very flexible: by adding extra hypotheses (such asreflection, or attraction changing to repulsion) one could increase thenumber of phenomena explained. For this reason, the very applicabilityof the dichotomy 'true/false' to such theories is questionable'

It appears that there cannot be any ambivalence about 'superior' forquantitative theories: the one that provides a closer agreement with mea-surements is superior to the rest. However, the history of diffractionresearch does not always support this contention. Fresnel's 1816 theoryof diffraction was no better that Young's 1802 theory, but Paris of L816was a more receptive place for such a theory than London of 1802. Whilea trend to quantification and mathematization of physics was then on therise, it was a mere chance that the wave theory of diffraction, whichopened the door to other waves theories, was approved in 1816 and notL0 or 20 years later. Had not mathematicians Laplace and Poisson havea strong interests in physics, had not their opinions were held in highesteem in the scientific world, the wave theory of light would have been

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adopted much later. Interestingly, after the publication of Fresnel's 181gprize-winning theory of diffraction, many physicists continued to useYoung's theory. Although less precise and less general, it was sufficientfor a variety of purposes and it was much simpler.

Thus, creating and adopting new theories of diffraction involved per-sonal decisions, which are subjective. To a large extent, an appearance ofa certain theory at a particular time was accidental, or subjective. onthe other hand, some trends in this research were objective, such asmathematizing diffraction. since early in the 19th century the wave theoryprovided better opportunities for such a mathematization than the cor-puscular theory, the eventual victory of the former was only a matter oftime, and thus it was objective. That the first wave theories of diffractionwere created by Young in 1802 and Fresnel in 1815 was a matter ofchance. However, that the two were practically identical was an objectivefactor: both physicists started with the simplest theories, and there is onlyone such based on the principle of interference. That Fresnel's theory wasadopted much faster than Young's, was a subjective result; however, thatsooner or later such a theory would have been accepted at the time, is anobjective conclusion.

Another objective feature of science is the retention of some results inone form or another. Some models, although discarded in favor of betterones, led to new fruitful experiments and theories and as such retain acertain lasting value in science. Even Newton's interaction model, whichnever received any experimental confirmation, deserves credit for stimulat-ing Fresnel's work. The fluid model of electricity helped to establish anumber of fundamental concepts and laws.

THE ROLE OF MODELS

we see from these examples several advantages of using the term modelin teaching physics. 'Theory'may imply something absolute or permanent,while 'model' is usually understood as temporary or tentative. Thus, toemphasize the process of change in the world of theories, ,model, may bea more adequate term. usefulness is another prerogative of a model, andit does not depend on the existence of subsequent improved theories. Forinstance, for one who is satisfied with the precision oi to-rsr in locatingdiffraction fringes, Young's model of diffraction is as useful today as iiwas at his time. The same is true about the fluid model applied, forinstance, to explain the law of a capacitor. Moreover, within iheir rangeof application these models can be even more usable than the modernones, because they are easier to operate and understand.

when a theory is used in a model form, it is easier to see its limits. Thefluid model explains how electricity moves, but not how it is created byfriction. The latter is explained in the electron theory. If so, to say thatthe necessity of a very close contact between two bodies for their mutual

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electrization falsifies the fluid theory, is unproductive. Instead of settingthem apart as 'true' or 'false', it is preferable to say that the fluid theoryis false in this case) or) in other words, that the case is outside its rangeof application. Instead of distinguishing these two theories as true andfalse, we can say that the electron theory is in some respect better thanthe fluid one, because it explains the production of electricity as well asits movement in some media (not in wood!). Such approach emphasizesthe fact that once true, a theory remains to be true forever when used forthe original phenomena and in a similar way (qualitatively or quantita-tively with the original precision) as at its inception. From this perspective,if properly used, Young's theory of diffraction is still true although it wassuperseded by Fresnel's theory. If so, since Young's theory is muchsimpler, it can be preferred even now in some cases of diffraction.

CONCLUSIONS

We expect teachers to infer from the examples presented here the follow-ing conclusions about science (or at least physics). First, no experimentalresearch, including the so-called 'empirical' research, can be fruitfullyconducted without involving a theory. Secondly, thinking of theories asmodels helps in their application and in obtaining an adequate view oftheir role in science. Thirdly, if even 'imperfect' theories have their valuein the advance of science, and any partial knowledge, if correct, is usable,'theorizing' may be an activity students can try on their own. Fourthly,like any other human enterprise, science is full of emotions and evenpassions, in particular, in selecting research topics or responding to thework of others. Finally, while being subjective on a personal or a grouplevel, when taken in its entirety, the scientific process reflects certainobjective features of the world itself and of the way people think.

REFERENCES

Collins, H.: 1981, 'Stages in the Empirical Program of Relativism', Social Studies of Science11, 3-10.

Collins, H. & Shapin, S.: 1983,'The Historical Role of Experiment', in F. Bevilacqua andP.J. Kennedy (eds.), Using History of Physics in Innovatory Physics Education. Pavia:The International Commission on Physics Education, pp.282-292.

Davis, N. et al.: 1993, Transitions from Objectivism to Constructivism in Science Education',International J ournal of Science E ducation 15(6), 627 -636.

Hesse, M.: 1.967, 'Models and Analogy in Science', in P. Edwards (ed.), The Encyclopediaof Philosophy, vol. 5, Macmillan Publishing Co. & The Free Press, New York.

Kipnis, N.: 1991, History of the Principle of Interference of Light, Birkhiiuser Verlag, Basel,Boston. Berlin.

Kipnis, N.: 1992, Rediscovering Optics, BENA Press, Minneapolis.

260 NAHUM KIPNIS

Kipnis, N.: 1996, 'The Historical-Investigative Approach to Teaching Science', Science and

Education 5,277-292.Roth, w.: 1994, .Experimenting in a constructivist High school Physics Laboratory' , Journal

of Research in Science Education 3l(2), 197-223.