Revista Brasileira de Ensino de Física, vol. 42, e20190134 (2020)www.scielo.br/rbefDOI: http://dx.doi.org/10.1590/1806-9126-RBEF-2019-0134Produtos e Materiais DidáticoscbLicença Creative CommonsLouis de Broglie’s wave-particle duality: from textbooks’blackboxes to a chain of reference presentationNathan Willig Lima*1, Matheus Monteiro Nascimento1, Cláudio Cavalcanti1, FernandaOstermann11Universidade Federal do Rio Grande do Sul, Instituto de Física, Porto Alegre, RS, Brasil.Received on June 07, 2019. Revised on October 31, 2019. Accepted on October 31, 2019We discuss the proposition of wave-particle duality made by Louis de Broglie in the period of 1922-1924 as wellas the narratives of undergraduate Physics textbooks that introduce this topic. After a brief discussion on thenature of scientific reality, we point out the main theories, assumptions and techniques adopted by de Broglie toachieve the relation between momentum and wavelength. We use these elements as analytical categories, observingwhich of them are still present in four popular undergraduate introductory textbooks. Our results show that noneof the textbooks used de Broglie’s original strategy (mathematical derivation), treating his ideas as postulates.Moreover, we show that only few elements of de Broglie’s original presentation are still commented by textbooks,which treat de Broglie’s ideas as purely speculative, reinforcing the “genius myth”. In the sequence, we proposea didactic alternative, which we call a “chain of reference presentation”. In this strategy, we highlight that allscientific knowledge is supported by previous theories and it works as the ground of future scientific improvements.With this perspective, we perform a didactic derivation of de Broglie’s momentum-wavelength relation (based onthe original papers and on the specialized literature) and we introduce empirical and theoretical works that maybe studied from it.Keyword:Quantum Mechanics, Textbooks, Epistemology.1. IntroductionPhysicists consider Quantum Physics (QP) the mostcomplete theory to explain the structure of matter, de-livering a high degree of precision in its experimentalpredictions. During the 20th century, its developmentled to the formation of new areas of Physics such asQuantum Field Theory [1], [2], Quantum Optics [3], [4]Quantum Information [5], Quantum Thermodynamics[6], Quantum Gravitation [7], among others, as well as tothe development of different technological applicationsin the aforementioned areas, such as Nuclear Engineer-ing and Semiconductor Physics, but also in Medicine [8]and much of nanosciences [9]. In addition, the quantummysticism movement has broadly spread QP terminologythrough idealistic interpretations of reality [10] – makingits elements part of non-scientist vocabulary.In general, one can think that QP refers to two ma-jor movements in Physics: the first involves studies onthe nature of radiation and the structure of matter inthe first half of the 20th century, culminating in theproposition of Schrödinger’s Equation and Heisenberg’smatrix physics; and the second involves the isolationof individual quantum objects, quantum entanglement,and Quantum Information Theory, which were developedin the second half of the twentieth century and in thetwenty-first century [11].*Correspondence email address: nathan.lima@ufrgs.brIn the context of the first movement, the propositionof wave-particle duality can be thought of as a centraltheme, or even as the only mystery of QP [12]. A firstsuggestion about it appears in an article by Einstein in1909 about the quantum [13] with a different concep-tion of his seminal paper on the theme [14], but it wasjust formalized and generalized by de Broglie in the be-ginning of the twenties1[15]. Along the development ofQuantum Physics, however the meaning of wave-particleduality has substantially varied – attributing differentontological natures to the particle and to the wave in thedual phenomena [16]–[19]. Schrödinger [20], for instance,proposed that radiation should be considered as a realmaterial wave propagating in the phase space, while itsparticle-like behavior should be attributed as a conse-quence of the quantized atom (a vision shared by Planck),1In his first papers about the nature of light, Einstein defendedthat radiation should be constituted by localized quanta in spacein opposition to its description as continuous wave [14]. In 1909,however, he computed the statistical fluctuations of energy inthe black-body radiation, achieving a term corresponding to acontinuous radiation and a term corresponding to a quantizedradiation. Einstein concluded that “I more or less imagine eachsuch singular point as being surrounded by a field of force whichhas essentially the character of a plane wave and whose amplitudedecreases with the distance from the singular point.” [13]. Despite ofthis suggestion, Einstein has not achieved any formalized theory fordual radiation. That is why there is a historiographic controversyabout considering de Broglie or Einstein as the “founder” of waveparticle duality [15] .Copyright by Sociedade Brasileira de Física. Printed in Brazil.
e20190134-2Louis de Broglie’s wave-particle duality: from textbooks’ blackboxes to a chain of reference presentationeven contesting Compton’s explanation on the collisionbetween photons and electrons [21]. Born [22], in theother hand, considered that the “wave” is not somethingmaterial, in nature, but merely an epistemic tool, aninstrument that informs us about our own knowledge,while the particle is what is real. Almost at the sametime, Bohr [23] proposed the Complementarity Principle,stating that wave-like and particle-like phenomena arecomplementary aspects of the same entity, not beingable to be observed mutually. In this proposition, theexperimental set up is what determines the appearanceof one or another aspect.A possible way to escape this ontological controversyin QP Education would be to follow the suggestion madeby some researchers of relativistic quantum mechanics:there are no particles, only fields [24], [25]. However, thewave-particle duality is still a major theme in contem-porary Quantum Physics historiography [15], [26] andits historical and conceptual relevance also motivatescontemporary research in Quantum Physics Teaching[27]–[29], besides of being a common subject in QuantumPhysics courses in undergraduate and high-school levels[18], [30]. We highlight that this topic may be approachedin different trends of Quantum Physics Teaching such asthe development of didactic experiments [31]–[36], theuse of metaphors [37], [38], production of tutorials [29],[39], [40], the use of computational simulations [41]–[46],the analysis of didactic textbooks [47], [48], and so on .In the Brazilian context, as in many other countries,the research on Quantum Physics textbooks and on theproduction of didactic material is especially importantsince future physicists and teachers of Physics are usu-ally introduced to this concept in basic Physics courses(commonly in the fourth semester of the undergraduatecourse) or in disciplines like Introduction to QuantumPhysics (or Modern Physics), in which the studies on ra-diation of the first two decades of the twentieth centuryare presented through textbooks and not the originalpapers.Textbooks, in this sense, are understood as a materialelement of the so calledScience Education Culture. [49],[50], being amediator(or atranslator) between the sci-entific gender (original papers) and scientists and scienceteachers in training. This is whytextbooksare not onlyimportant to the pedagogic context but to Science itself,as it was recognized by Thomas Kuhn inThe Structureof Scientific Revolution[51]. According to Kuhn, text-books are responsible for structuring scientific disciplinesand determining the methods and problems that futurescientists should be circumscribed to. This implies, in thekuhnian description, that textbooks perpetuate scientificknowledge by representing it as a collection of evidenttruths [52]. In the other hand, Kuhn also pointed outthat textbooks authors tend to erase controversy, crisis,historical contingency and so on, which demotivated theresearch on textbooks under a historiographical approach[53].According to Badino and Navarro [50], however, theinterest about the role of textbooks in science history haveincreased since the late nineties. The authors mention, forinstance the Science Education special topic on textbookin the scientific periphery [54] and David Kaiser’s workon scientific pedagogy [55]. Moreover, the authors arguethat the analysis of textbooks written in the period ofscientific crisis, such as the quantum revolution, hasshown that they cannot be seen as a “mausoleum ofscientific truths” (as Kuhn would describe it), but thatthey contributed actively to the scientific development.Furthermore, the narrative of undergraduate textbookssometimes is so relevant that is more diffused than theoriginal paper narrative [18].In this scenario, we have two goals. The first one is tocontribute to the analysis of contemporary undergradu-ate textbooks that introduce de Broglie’s particle-waveduality by evaluating how they dialogue with de Broglie’soriginal papers. The second one is to propose a differentdidactic strategy, which stresses the original techniques,theories and assumptions that de Broglie used to articu-late his proposition as well as the empirical and theoret-ical improvements that were allowed from it, based onde Broglie original papers and the specialized literature.More specifically, in the first part of the paper we pro-pose to answer three questions a) What is the meaningattributed to wave-particle duality by Louis de Brogliein the period of 1922-1924? b) Which tools, techniquesand theories did he use to support his proposition? c)How do introductory undergraduate textbooks describeLouis de Broglie’s proposition and which elements (tools,techniques and theories) they mention to support it?To answer questions “a” and “b”, we analyzed deBroglie’s three original papers written from 1922 to 1924[56]–[58] and interpretations offered by secondary sources[15], [59], [60]. To answer question “c”, we analyzed fourcontemporary higher education textbooks used in theBrazilian Physics introductory disciplines [61]–[64].In order to present the results of our analysis we struc-tured the paper in the following sequence. In section 2,we present the theoretical background that supported ouranalysis of the textbooks and we introduce the adoptedmethodological trajectory. In section 3, we introduce themains aspects of de Broglie’s original articulation and usethem as analytical categories to perform textbook anal-ysis. In section 4, we propose a didactic narrative thathighlights de Broglie’s theoretical backgrounds, assump-tions and techniques. By doing so, we show a possibleway to derive his famous relation between momentumand wavelength, in dialogue with de Broglie original con-ceptions and with secondary literature, and we discusshow de Broglie’s proposition allows the formation of newempirical and theoretical works.2. Theoretical Framework: ScienceDialectic Movements and ScientificRealityThe conception about what science is and how it worksis source of a profound and complex debate in the areaRevista Brasileira de Ensino de Física, vol. 42, e20190134, 2020DOI: http://dx.doi.org/10.1590/1806-9126-RBEF-2019-0134
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