- 2.1 Introduction
- 2.2 Göttingen 1887–1894: From the Optics of Ether to the Electromagnetic Equations
- 2.3 Leipzig 1894–1900: From Physik des Aethers to Lehrbuch der Optik
- 2.4 The Lehrbuch der Optik
- 2.5 Giessen 1900–Berlin 1906: Development of Lehrbuch der Optik’s Program up to the Second Edition
- 2.6 Epilogue: Following the Traces of Lehrbuch der Optik
- Abbreviations and Archives
My goal will be reached if these pages will strengthen in the reader the view that optics is not an old, worn-out domain of physics, but that also here a fresh life pulses, the contribution to whose further nourishment should be enticing for anyone.1 (Drude 1900a, vi)
With these stimulating words Paul Drude aimed at engaging physicists, in 1900, in the reading of his textbook Lehrbuch der Optik. More than one hundred years later, in this paper I will try to clarify historically these inspired words: In what sense could optics have been considered old? In which aspects did Drude’s new account of optics “pulse with fresh life”? How could the further “nourishment” of optics take place in Drude’s view? To what extent did Drude succeed in achieving his goal?
In fact, in 1985 Jed Z. Buchwald already spoke of Drude’s Lehrbuch der Optik in his thorough account on the complex and gradual transition between the macroscopic outlook of Maxwell’s electrodynamics and Drude’s microscopic approach to electromagnetic optics (Buchwald 1985). Lehrbuch der Optik was Buchwald’s finale. I share with Buchwald the viewpoint that Lehrbuch der Optik was the first encompassing work in which a microscopic approach to optics was established. For this reason, the book is a particularly interesting subject of study. However, in this paper, instead of analyzing Drude’s work against the background of the general history of electrodynamics, I will explore the articulation of the book with other contexts.
First, I understand Lehrbuch der Optik not only as a singular point in Drude’s career, but as the result of a long process, started in the early 1890s, through which he reflected upon and changed his understanding of what optics should be. Moreover, Lehrbuch der Optik not only had an impact on the physics community; the endeavor to write a comprehensive book on optics was also important for Drude as a way to organize his knowledge, strengthen his views on the field, and revamp his career. I will thus follow the story of Lehrbuch der Optik through the development of optics, and not electrodynamics. Second, to understand better the distinctiveness of Drude’s decisions for a redefinition, both ontological and epistemological, of optics, I will follow Drude in his conversation with his contemporaries, in particular his mentor and dissertation advisor
In the first section, I will follow Drude’s early career at the University of Göttingen, from 1887 until 1894, under
From 1894 to 1900, Drude served as full professor at the University of Leipzig, where he could develop in depth his own standpoint on optics, hinging completely upon the electromagnetic theory of light. In the years after 1894, Drude managed the incorporation of matter into the electromagnetic picture of light. By 1900 he envisioned a unified theoretical approach for a variety of optical phenomena stemming from different kinds of interactions between light and matter. In his second textbook, Lehrbuch der Optik, published in 1900, Drude displayed his own, programmatic view, which merged the electromagnetic theory of light with the dynamical action of the microstructure of matter. I will give an account of Drude’s development between 1894 and 1900 in the third section.
Lehrbuch der Optik was not a compendium of well-established knowledge in optics. New optical phenomena were explored experimentally at the end of the nineteenth century, which led to a revitalization of theoretical discussions about the interaction between light and matter. For this reason, many textbooks had become rapidly outdated. Drude’s Lehrbuch der Optik was very innovative in attempting to encompass both old and new phenomena, through his personal strategy of merging electromagnetism and matter. But Drude’s textbook was original also for other reasons. Most European textbooks on optics evinced a special concern for the nature of the ether, because light presumably amounted to the perturbation of that substance. In Lehrbuch der Optik, instead, Drude relinquished questions about the constitution of the ether, taking the electromagnetic equations of light as the starting point for his account of optical phenomena. Actually, Drude did not eschew mentioning the ether as the substratum for light, but in starting from the light equations, Drude completed a radical shift in the kind of questions textbooks had addressed so far: from the relation between the nature of the ether and its mathematical expression, to the relation between the microstructure of matter and the modification of the light equations that captured this new dimension of optical phenomena. I will describe the content, organization, and main points of Lehrbuch der Optik in the fourth section.
In the fifth section, I examine Drude’s work, between 1900 and 1906, concerning the relation between optical phenomena and the microstructure of matter. Important outcomes stemmed from the incorporation of the electron into the previous picture of optics, which allowed Drude to network optics with other fields in science, like chemistry. Such modifications were included in a second edition of his book in 1906.
All in all, Drude not only provided readers with explanations of new phenomena, but also with new questions to ask and a new methodological approach to optics. Advancing into almost virgin terrain, Drude’s claims in Lehrbuch der Optik had a strong impact, which I will analyze in the epilogue of the paper. Without criticizing directly previous works in optics, Drude redefined them as part of a past that should be overcome. He simply reorganized optical knowledge in such a way that these older traditions were not mentioned or were re-understood through “Drude’s lens.” Lehrbuch der Optik remained influential for years to come, in part through
2.2 Göttingen 1887–1894: From the Optics of Ether to the Electromagnetic Equations
2.2.1 On Voigt’s Footsteps
Paul Drude was born on 12 July 1863 in Braunschweig, where he lived until he completed his studies at the local Gymnasium in 1882 (Hoffmann 2006; Goldberg 1990). Thereafter, he studied mathematics, first at Göttingen and then at Freiburg and Berlin. In the sixth semester, he decided to return to Göttingen and devote himself to theoretical physics, under the guidance of Woldemar Voigt, director of the Physics Institute at Göttingen. Drude’s early research was very much influenced by Voigt in terms of subject matter, guidelines, and research procedures. Voigt, in turn, was a faithful heir of
Neumann, one of the founding fathers of German theoretical physics, was Privatdozent for physics and mineralogy starting in 1826 at the University of Königsberg. To supplement his lectures, in 1833, he inaugurated the German mathematical-physical seminar, through which he trained his students, including
In such a dualist scheme, Neumann pursued a very specific methodology, which Kathryn Olesko dubbed the “ethos of exactitude” (Olesko 1991). The key to
Voigt completed his dissertation in 1874, expanding upon one of the most frequently recurrent topics in optics tackled at the Königsberg seminar: the behavior of light reflected by or refracted through crystals. On the one hand,
Voigt brought the Königsberg tradition to the Göttingen Physics Institute in 1883 (Olesko 1991, 412–414). Four years later, Drude finished a dissertation in Göttingen that was a continuation of
2.2.2 Towards a New Way to Optical Knowledge: Practical Physics
In 1887–1888, in his laboratory in Karlsruhe,
Drude’s first open demonstration of a radical departure from Voigt’s standpoint was his provocative 1892 paper (Drude 1892a). There Drude addressed one of the most puzzling consequences of comparing electromagnetic and mechanical theories of light: the various sets of differential equations derived from considering the ether as an elastic substance were mathematically equivalent to
Since many different theories, which derive from very different basic assumptions, can account for scores of observable features in the same way without contradictions, the theoretical research on optical phenomena has been discredited to the extent that one tries to understand these phenomena through mathematical and almost philosophical speculations, from which new knowledge about the true properties of nature cannot be extracted, for the same properties are explained differently in the different theories. (Drude 1892a, 366)
What Drude described was an epistemological dilemma. The only criteria the ethos of exactitude offered to evaluate the validity of an optical theory was the precision of the numerical agreement between experimental data and theoretical predictions. Now, given the mathematical equivalence between mechanical and electromagnetic theories of light, it was clear that numerical exactitude could not be the only way to mediate between optical experiments and the physical properties of the ether. How to proceed in this situation? Drude’s way-out involved a twofold break with
First of all, Drude endorsed a more radical phenomenological standpoint: theories of light he reduced to just the differential equations and the imposed boundary conditions. He called the combination of these two ingredients an Erklärungssystem (explanatory system). The point of departure for optics was then the Erklärungssystem. Questions about the true nature of the ether became irrelevant for the mathematical construction of an optical theory, while the physical system to be studied was reduced to the mathematical parameters making up the Erklärungssystem. The choice of an optical theory was thus a choice of language: either density, elasticity, and velocity of ether perturbations, or magnetic permeability, dielectric constant, and magnetic field strength.
Secondly, since the ethos of exactitude had exhausted its potential for revealing new knowledge about the ether, Drude hinted at other possible criteria to help one choose among the different theories of light. More specifically, he claimed that
the adoption of the electromagnetic theory of light seems to be a significative step in the true understanding of nature, since the velocity of light in vacuum or through air derives directly from electromagnetic features. (Drude 1892a, 366)
In other words, Drude promoted a unification of optical and electromagnetic theories from below. Given that experiments proved that optical and electromagnetic waves propagated at the same velocity, one was inclined to extend this coincidence to the rest of the optical and electromagnetic features. Unification would then mean, according to his radical phenomenological move, the adoption of a single physical language to describe the mathematical equations accounting both for optical and electromagnetic phenomena.
Voigt was also aware of the mathematical equivalence between mechanical and electromagnetic theories. Nevertheless, for years he did not sympathize with this idea of unifying optics and electromagnetism from below. For him, the only way to strive for unification was the determination of the properties of a general ether, from which the equations of optical and electromagnetic phenomena could be derived. Thus, adopting an electromagnetic language would mean, for him, losing generality, and restricting oneself to only one possible nature for the ether. In fact,
The break with his master notwithstanding, Drude was not alone in his positivistic move, which he dubbed “practical physics.” As he mentioned in his 1892 paper, Drude found inspiration in
Despite Drude’s clear alignment with Hertz’s approach, he still pondered for some time the definitive adoption of the electromagnetic theory of light. The theory was troubled by one important difficulty: Maxwell’s equations accounted well for the phenomena of reflection and refraction of light, but not for those optical phenomena in which matter was assumed to contribute directly to the generation and absorption of light waves. Ever since the early 1870s, it had become clear to physicists that ether waves were not sufficient to describe optical phenomena, like optical dispersion. In these cases, differential equations referring to the ether had to be combined with differential equations accounting for the action of matter. While there were attempts to interweave the action of ether and matter in the framework of the mechanical theories of light,
2.2.3 Optical Dispersion and the “Practical Physics” at Work
Beginning in the seventeenth century, optical dispersion was understood as the continuous spread of white light into different colors when passing through a prismatic medium. The ensuing order of colors was always: red, orange, yellow, green, blue and violet, as observed in rainbows. One parametrized this phenomenon through , the index of refraction, which referred to the change in the direction of light propagation with respect to the initial beam. Each color corresponded to one frequency of light waves, thus optical dispersion amounted to the dependence of on the light frequency . The continuity of the analytical function stood for the observed order of colors mentioned above.
In the early 1870s, though, a series of circumstances changed radically the understanding of this phenomenon, both from the experimental and the theoretical perspective. On the one hand, it was found that when light passed through certain substances (actually, liquid dyes), the normal succession of colors appeared reversed. The reversal implied that the function was discontinuous with respect to at some point. More interestingly, it was acknowledged that the discontinuity in the behavior of took place around those colors of the spectrum whose frequency coincided with the frequency at which the liquid dyes typically absorbed light. That is to say, when interacting with these substances, one color component of the light was absorbed, while the others passed through and were dispersed into a spectrum. Absorption and dispersion of light became two complementary features of the same light-matter interaction. But if this was the case, matter should not just modify the properties of ether, but should play an active role in the production and absorption of light waves.6
On the other hand, almost simultaneous with these experimental findings, a radically new optical theory was put forward, in which both the action of matter and ether were taken into account.7 It was assumed that hypothetical microscopic matter particles vibrated around fixed positions under the action of elastic forces. When light interacted with them, the particles were set in Mitschwingungen (co-vibrations) with ether waves. Only when the frequency of light coincided with the proper frequency of the matter particles did these absorb the light, by resonance, in analogy with a tuning fork. For the other colors, light was transmitted through the material, but with a certain phase delay, whose empirical counterpart was the change of direction of light propagation, parametrized through the index of refraction . According to the Mitschwingungen model, the phase delay depended on the color of the light. Thus the new optical theory accounted for a dispersion of light over the whole spectrum, interrupted at resonance frequencies, which occured when the microscopic particles of matter were assumed to absorb light. If the experimentally determined points of color reversal coincided with the natural frequencies of the hypothetical particles of matter, the Mitschwingungen model would explain perfectly the phenomenon of optical dispersion, as complementary to the absorption of light.
Even after the adoption of the electromagnetic theory of light, the Mitschwingungen model was considered the most satisfactory account of this phenomenon, and generally, a paradigm for the way in which matter and light should interact at the microscopic level. Yet, the Mitschwingungen represented light as consisting of mechanical perturbations of the luminiferous ether and not of electromagnetic fields. How could one account for optical dispersion and for processes of light-matter interaction in general, on the basis of the electromagnetic theory of light? For several theoretical physicists in the early 1890s, most significantly Hermann von Helmholtz,
Von Helmholtz’s, Lorentz’s, and Drude’s approaches to optical dispersion were rather different. The first two physicists sought a mechanical foundation for
Drude’s analysis of optical dispersion in 1893 was different from von Helmholtz’s and
In his 1893 paper, Drude conducted a formal analysis, comparing the mathematical expression for
derived from the Mitschwingungen model with the definition of
according to Maxwell’s equations. Regarding this comparison, it was important that, in the case of the simplest phenomena of reflection and refraction, when the change of direction of light did not depend on the frequency, the mathematical equivalence of mechanical and electromagnetic theories of light entailed the equivalence of optical and electromagnetic parameters. As in both cases the differential equations referred solely to the behavior of the ether, either luminiferous or electromagnetic, that is
being the dielectric constant of the ether. Now, for optical dispersion and other phenomena involving the action of matter, the equality
only held in the limit of very low frequencies, i.e.
. Drude aimed at determining the differential terms of the Mitschwingungen model responsible for the difference between the dispersion formula
and its limit
. This would tell him how to complement mathematically
His reasoning developed through several steps. The starting point was the mechanical Erklärungssystem corresponding to the model of Mitschwingungen.11 By comparing it with Maxwell’s equations, Drude arrived at a very interesting conclusion: the difference between —derived from the Mitschwingungen Erklärungssystem—and its limit at very low frequencies corresponded to the ratio of the sum of the masses of all matter particles to the mass of ether contained in the same volume. Therefrom Drude surmised that amounted to the contribution of the hypothetical microparticles that composed matter. The problem was that, within the electromagnetic framework, the masses did not relate to the efficacy of those particles in interacting with the ether. To overcome this difficulty, Drude assigned to each particle an electrical polarization , so that the total electrical polarization of the system, ether-matter, , was a sum of the ether and matter contributions , being the polarization of the ether. By assuming that could vibrate at natural frequencies, analogously to the massive particles in mechanical theories of dispersion, one could emulate the formalism of Mitschwingungen for and therefore pursue a schema of co-vibrations between and the electric field of the ether. Using these equations, one obtained as a function of the frequency of light, , that was obviously the same as . In the last step, Drude put forward that, in the same way as the electrical polarization of ether was characterized by the dielectric constant, , the polarization of each matter particle was characterized by a new dielectric constant, . In these terms, the divergence coincided exactly with , which played the same role as the ratio mentioned above.12
Through this ingenious method of combining the Mitschwingungen model, electromagnetic variables, and new electromagnetic parameters, Drude reached a twofold goal: first, he restored the equivalence between optical and electromagnetic constants, so that ; and second, he outlined a procedure to modify Maxwell’s equations in cases where the action of matter had to be taken into account, without making general claims about the unification of electromagnetism and mechanics. More specifically, followed the equations of motion of matter, to wit the Mitschwingungen, and in this way contributed to the behavior of the general system. Maxwell’s equations remained formally untouched if one considered instead of . Effectively, Drude had extended to optical dispersion the possibility of switching from the mechanical to the electromagnetic framework through a simple choice of language. Two other assumptions about matter were brought in with the Mitschwingungen model: its microstructure and the independence of each particle in giving rise to macroscopic effects, which hence boiled down to the simple sum of individual actions. No hypothesis about the nature of those particles was offered, as for example their identification with electrolytic ions.
2.2.4 Physik des Aethers and Drude’s Advocacy of the Electromagnetic
Theory of Light
In his first textbook Physik des Aethers (1894), Drude decisively sided with the electromagnetic theory of light. The book was the result of his lectures on electromagnetism at the University of Göttingen between 1892 and 1894. In the first part of the volume, Drude analyzed the properties of the electromagnetic field. His goal was “to derive, on the basis of fundamental experiments, the strictly necessary formulas for the mathematical characterization of observable features” (Drude 1894, vi). In this way, Drude passed over completely the ethos of exactitude of his masters. He did not aim at the determination of the Erklärungssysteme from hypotheses on the ultimate nature of ether, but from below, namely from electromagnetic phenomena. Further, he explicitly restrained himself from any attempt to base electromagnetism on mechanical principles, a task that, according to him, was “only justified […] as a necessity of the natural philosophers” (Drude 1894, vi).
In the second part of the book, Drude tackled optical phenomena from the point of view of the electromagnetic theory of light. Drude pushed for the adoption of this theory in view of the unification of optical and electromagnetic phenomena through the common Erklärungssystem and the coincident manifestations of optical and electromagnetic phenomena in experiments. In particular,
The fact that the equivalence of the properties (of lumiferous and electromagnetic ether) is not serendipitous, but something deeply entrenched in the nature of the thing, was already an idea that
Maxwell articulated in 1865, when one was not so far away from possessing the resources, with which Hertz has proved this analogy in such an evident way. (Drude 1894, 482)
Hence Drude’s unification of electromagnetism and optics implied that the optical ether was electromagnetic in nature, which, for him, meant that the mathematical terms in optical equations should be interpreted using the language of electromagnetism. Drude’s unification of electromagnetism and optics eventually resulted in a divide between electromagnetism and mechanics: the ether was electromagnetic in essence, while mechanics only served to model the dynamics of material objects. If there was nothing beyond equations and the language to describe them, such as mechanical principles, there was no way to unify the two domains of mechanics and electromagnetism. Drude’s move thus went precisely in the opposite direction of
After endorsing the electromagnetic theory of light, Drude turned to optical phenomena that called for the combination of electromagnetic waves with the motion of microparticles of matter: optical dispersion and the natural rotation of light. The second phenomenon consisted in the change in the direction of light polarization when light passed through certain transparent media, e.g. quartz. This change of direction, measured by the angle
, was dependent on the color of the light, hence it showed features similar to dispersion, expressed through the functional relation
. Following his 1893 reasoning, Drude argued that the action of matter particles modified
and being two coefficients related to frictional and vibrational terms, respectively. In the same fashion, to explain the natural rotation of light, Drude assumed that the microcurrents underwent a spiral motion. This other kind of Mitbewegung (co-motion) with the ether was also in good agreement with observable facts.13
Drude concluded his book with a programmatic section, in which he called attention to the state of the art concerning magneto-optical phenomena. As in the case of optical dispersion and the natural rotation of light, these phenomena stemmed from a process of light-matter interaction, the difference being that an external magnetic field was applied. The Kerr effect, mentioned earlier, and the magneto-rotation of light polarization (nowadays called the Faraday effect) were the two most common instances of magneto-optical phenomena then known. The latter consisted of the rotation of light polarization when light passed through a transparent material under the influence of a magnetic field, and it had been first produced by
so far one has only been able to establish one satisfactory mathematical Erklärungssystem for the optical features of magnetically active bodies, without being able to give a physical justification of the Erklärungssystem, in such a way that it would be possible beforehand to compute theoretically the magneto-optical features on the basis of other physical properties of bodies. (Drude 1894, 585–586)
As a matter of fact, Drude did not attempt to give a physical explanation of magneto-optical phenomena, at least not for the time being. But his programmatic claim epitomized a shift in his heuristic strategy: from ether properties to the behavior of microscopic matter particles. Also the phenomena of fluorescence and phosphorescence called for an optical theory based on a physical model of the behavior of molecules in his opinion. In Lehrbuch der Optik, Drude elaborated at length on this lack of a physical interpretation of optical phenomena. But much was still to come between 1894 and 1900.
2.3 Leipzig 1894–1900: From Physik des Aethers to Lehrbuch der Optik
2.3.1 Physik des Aethers and Drude’s Program in Leipzig
Physik des Aethers was very influential in introducing Maxwell’s electromagnetism and electromagnetic optics into German Universities (König 1906), and more specifically, in introducing Drude’s own view of the field. In comparison to the most prominent books on electromagnetism at the time, especially
Physik des Aethers was also crucial for Drude in promoting his career. In August of the year it was published he was offered an extraordinary professorship for theoretical physics in Leipzig, and it was precisely the appearance of Physik des Aethers that tipped the balance in his favor (Jungnickel and McCormmach 1986, 166). Also in 1894, Drude married Emilie Regelsberger, the daughter of a Göttingen jurist. Thus, shortly after the wedding, the couple moved to Leipzig to start a new life, as well as a new chapter in Drude’s career.
Drude’s inaugural speech, held at the University of Leipzig on 5 December 1894, was a clear, programmatic presentation of the approach to optics he had been forging and wanted to pursue in the ensuing years (Drude 1895). Drude’s decision to reduce the physical system to physical language describing the mathematical equations, what he called practical physics in 1892, was reinvigorated and reiterated:
You see, the goals of the current research on theoretical physics are not so extensive as the goals of the old natural philosophers. Today one does not ask about the so-called true essence of things, which goes beyond what is perceptible, not about the ultimate cause of phenomena. The goal of a theory is simply the description of the phenomenal world.14 (Drude 1895, 4)
Drude sided explicitly with
The subsequent shift from ether to matter as the new heuristic around which to develop optical theories was also clearly reflected in Drude’s Leipzig speech. On the basis of the phenomenon of dispersion, Drude argued that “the electromagnetic theory of light calls for the concept of molecules in order to describe the optical properties of matter in the easiest way. I emphasize: of matter, not ether” (Drude 1895, 12). Here, the molecular structure of matter was by no means to be regarded as an ad hoc hypothesis, but was unequivocally associated with observable phenomena. This hypothesis also led to a re-categorization of optical properties: these were properties of matter, not ether, whose traits were already well-fixed by
No sooner said than done, Drude devoted his research in Leipzig to examining in more detail issues relating to the program he advanced in his inaugural talk, while he persisted in his missionary task to spread his own view of electromagnetism in Germany. His work made significant progress through a 1899 paper in which he produced a consistent and encompassing account of optical dispersion and magneto-optical phenomena (Drude 1899), deriving the Erklärungssysteme from physical hypotheses. Two important events led Drude to work in this direction. On one side were novel developments in magneto-optics that changed the field in the period between 1897 and 1899. On the other side was Drude’s plan to write a textbook on optics, Lehrbuch der Optik, during the elaboration of which he was forced to deal with a broader spectrum of insights into the field. Drude had become one of the most prominent figures in the fields of optics and electromagnetism by that time.
2.3.2 Magneto-optics and the Ion Hypothesis
A new magneto-optical phenomenon had been characterized experimentally, which led to a general revamping of the search for optical theories in magneto-optics. In 1897
Drude borrowed von Helmholtz’s ion hypothesis but not von Helmholtz’s overall approach. Drude found inspiration for his approach in the work of
[a]bove all avoided those developments that only had mathematical interest. I have not used the principle of least action for the derivations of equations, but I have derived the motion equations of ions from molecular considerations, in order to attain the easiest interpretation of the equations. For this purpose I use the language of atomism. (Reiff 1896, vii)
Reiff’s procedure consisted in stating first of all the equation of motion of ions of charge density and mass density under the influence of the electric field of light . For example, in the case of dispersion, the ions being presumably subject also to elastic forces, the electrical moment of the ions could be expressed in the following way:
being the coefficient of the frictional force, and
the coefficient for the elastic force. By supposing that both
were wave functions having the frequency of light
, the latter with a phase delay characterized through the index of refraction
, one easily obtained an expression for
identical to the one derived from the Mitschwingungen model. Thus the motion of ions in
Apart from their vibrations, which explained optical dispersion, in 1899 Drude assumed that ions underwent two other, different kinds of motion: spiral motions and also translations perpendicular to the magnetic field. Drude related the first kind of behavior to the
Although his appropriation of the ion hypothesis supplemented nicely Drude’s approach and fulfilled his requirements for a physical interpretation of optics, it must be emphasized that the particular adoption of the ion cannot be justified fully from the point of view of practical physics. The molecular structure of matter and the possibility of particles generating time-varying electrical polarizations was enough for that purpose. Polarizations and frequencies were the measurable quantities in optical phenomena. Hence, assigning an active role in optics to ions, which were characterized by a mass,
, and an electrical charge,
, determined through electrolytic experiments, independent of optical phenomena, was a kind of “external hypothesis” to the dynamics of practical physics. While the ether was reduced to the physical language necessary for
I think that Lehrbuch der Optik could have played a catalyzing role. As Drude wrote in the preface, the endeavor to write a book motivated him to sharpen his own view of the field. Indeed he accepted the offer to write a book from the publishing house because, among other reasons, “I wished for myself the development of new ideas through the deepening of my own view of the field, which is compelling in writing a book” (Drude 1900a, iii). Between 1894 and 1900 Drude worked on various topics related to optics, but it was only at the end, in 1899, that he saw in the adoption of the ion hypothesis the possibility of an overarching account of optics. He never mentioned
Since the advantage of dealing with ions instead of microcurrents was not the possibility of explaining the optical properties of matter, I think that the adoption of the ion offered Drude another kind of advantage: a new heuristics. In fact, the incorporation of the ion into Drude’s picture not only had consequences on an ontological level (e.g. the ions as the specific particles that were optically active), but also epistemologically. For the ion hypothesis allowed Drude to explore new ways to gain knowledge in optics, apart from seeking the right mathematical description of phenomena and the unification of ether theories from below (e.g. adoption of the electromagnetic language). As we will see in the following section on Lehrbuch der Optik, the ion hypothesis allowed Drude to network different domains of knowledge (optics and beyond) through the specific properties of charge and mass of these particles, which should manifest in different phenomena.
2.4 The Lehrbuch der Optik
2.4.1 Lehrbuch der Optik as a Novel Program in Optics
The year 1900 began very productively for Drude. In January he became the new editor of the most prestigious German scientific journal, Annalen der Physik, and he published his second textbook, Lehrbuch der Optik, which was soon translated into English and became the reference book for optics in many European universities. Drude was asked by the publishing house S. Hirzel to write the textbook “because a modern book covering the whole field was lacking” (Drude 1900a, iii). Since he was considered one of the greatest specialists on optical physics at the time, Hirzel “could really not have contacted any one better than Drude for this request” (König 1906).
In fact, Lehrbuch der Optik became the first textbook on optics to make use of only the electromagnetic theory of light and to combine it systematically with a microphysical view of matter (in this case the ion hypothesis). Moreover, Drude did not have much concurrence in Germany. At that time, German students of theoretical optics would resort to compendiums on the subject, written by prominent professors at universities. Famous examples were penned by
Ketteler’s book responded to very different questions than Drude’s. Ketteler had been very active, in the 1870s and 1880s, in the further elaboration of optical theories based on the groundbreaking hypothesis that the ether and matter particles were in Mitschwingungen. But he obviously did not discuss how to deal with the electromagnetic theory of light in the context of mechanical theories of ether, and he subsequently left magneto-optics out of his analysis altogether. These topics flourished first in the early 1890s, when Ketteler died.
By contrast, Voigt was well aware of the difficulties that had arisen in optics due to the spread of the electromagnetic theory of light in Continental Europe by the time he wrote his Kompendium. But he decided to approach optics in the second volume of his Kompendium der theoretischen Physik from a mathematical viewpoint, without committing himself to any hypothesis on the nature of the ether, thus leaving the final decision about the nature of the ether to the readers. He just stuck to the mathematical formulation of phenomena, which in turn meant that he took mechanical principles as undisputed bases. Only for optical dispersion did Voigt introduce additional mathematical terms, , into the differential equations for the ether. Magneto-optical phenomena were simply omitted in his account of optics. Ironically, Voigt was the first one to go beyond his own work. From the late 1890s, he advocated the electromagnetic theory of light and devoted himself precisely to the only domain of optics that was absent from his Kompendium, namely, magneto-optics, as mentioned earlier. In that field, Voigt soon became an authority.
Von Helmholtz’s posthumous collection of lectures thus would have been the most immediate competitor to Drude’s Lehrbuch der Optik in Germany, for von Helmholtz clearly embraced the electromagnetic theory of light, and he was a pioneer in introducing the concept of ions into optics. However, the hot topic at the end of the 1890s, namely magneto-optics, was also missing in von Helmholtz’s book.
Outside Germany, Drude’s book was compared with the works of the British physicists
Thus Drude was offered, by the publishing house S. Hirzel, the great opportunity to pioneer the exploration of essentially virgin territory, in a moment when the questions to ask in optics were changing rapidly. In the 1870s and 1880s, optical theoreticians engaged in a honing of the Mitschwingungen model. In the early 1890s, the main issue in Germany became how to choose between electromagnetic and mechanical theories of light, and the implications of this choice in relation to the ultimate nature of the ether, alongside the translation of the Mitschwingungen model into electromagnetic language. Eventually, in the late 1890s, the field of magneto-optics offered itself as the new boiling pot. Thus Drude arrived at the right moment to take up the most fashionable questions and lay down his own answer.
2.4.2 Lehrbuch der Optik Piece by Piece
The textbook was divided into two parts: geometrical optics and physical optics. Geometrical optics dealt with the optical features of light propagation and came down to four essential laws: linear propagation of light (light rays), the geometrical laws of refraction and reflection, and the possibility that a light ray splits at any point of its trajectory. These laws could be expressed by simple geometrical relations and they sufficed to describe the functioning of most optical instruments: lenses, microscopes, telescopes, and prisms. The second part of the textbook was devoted to physical optics, where geometrical laws did not suffice. One had to introduce hypotheses on the nature of light and the physical mechanism of light-matter interaction in order to account for optical phenomena more complex than reflection and refraction. This part was divided into three big sections: the first, about the general properties of light, in which the constitution of matter did not play a role (such as the interference and diffraction of light); the second about the optical properties of bodies measured when light was reflected by or passed through transparent media (principally, optical dispersion and magneto-optical phenomena); and the third about the emission of radiation from matter, which boiled down to the thermodynamics of radiation.
Drude’s programmatic claims are to be found in the second part of the book. The first part helpfully provided the reader with the necessary knowledge about how to produce and measure optical phenomena with optical instruments, but it did not contain much new knowledge. In fact, Drude constantly referred the reader to the existing literature on geometrical optics to which he himself had resorted.18 Drude devoted the longest and most involved section of the introduction to justifying his approach to physical optics in the second part, namely, the adoption of the electromagnetic theory of light and the ion hypothesis.
The first notion from physical optics that Drude introduced in the main text was that of the constant velocity of light in vacuo, . To support it, Drude put forward a detailed overview of the interferometric experiments to measure . Thereafter, the phenomenon of interference led Drude to introduce the wave nature of light. The mathematical translation of this physical concept was the wave function, with the velocity of light being one of its parameters. Hence, the second step subsumed the first one. In what followed, Drude explored the different ways in which wave functions could be superposed, thus giving rise to different patterns of interference (such as Newton’s rings) and to the diffraction of light (depending on the experimental set up).
Next, to describe the features of the double refraction of light, Drude introduced the concepts of light polarization and transverse waves. With these notions clearly formulated, an indeterminacy in the mathematical formulation appeared. Different conventions concerning the relative orientation of the wave amplitude, its polarization, and the direction of propagation could be adopted. For example, according to
The electromagnetic theory of light concealed these indeterminacies, for the perpendicularity of the two light vectors (electric and magnetic field) to the direction of propagation was inherent to the formulation of the theory. The adoption of the electromagnetic theory of light led one, therefore, to overcome the conflict, but not to resolve it. But beyond this isolated advantage, Drude’s justification of his preference for the electromagnetic theory of light lay in the possibility of unifying optics and electromagnetism through the identification of the velocity of light with the velocity of electromagnetic waves. Because of this, Drude deemed the adoption of the electromagnetic theory of light “one step further in knowledge about nature, since this way two initially parallel domains of knowledge, like optics and electricity, are treated together in a close and measurable relation” (Drude 1900a, 248). With no further explanation, Drude identified the electromagnetic theory of light with
Whereas Maxwell equations accounted well for all the phenomena Drude had described so far, the behavior of light in absorbent media called for additional terms related to the microphysical action of matter. Drude justified this very clearly in his introduction:
First of all, in this way one succeeds in providing an explanation of the phenomenon of dispersion, since the purely electromagnetic experiments only suggest, I would say, macroscopic properties of bodies. To explain optical dispersion it is necessary to make hypotheses on the microphysical properties of bodies. In this sense I have used the ion hypothesis introduced by
v. Helmholtz, because it seems to me the easiest, clearest [anschaulichste] and most consequent one to characterize, apart from dispersion, also the absorption and natural rotation of light polarization, and also the magneto-optical properties and properties of bodies in motion. (Drude 1900a, v)
In the following four chapters, Drude developed in detail his programmatic approach to the optical properties of matter. First of all, he tackled the phenomena of optical dispersion and of the rotation of light polarization, both of which he had already dealt with in Physik des Aethers, but now, he used the novel perspective of the ion hypothesis. Then he explained the singular features of the reflection of light in metals, and expanded upon the magneto-optical phenomena. Let us look again at the example of dispersion to get a better glimpse of Drude’s developments in this direction.
The physical system responsible for the optical properties of matter consisted of the electromagnetic ether, positive ions, and negative ions, both kinds being characterized by natural frequencies of vibration. For the case of optical dispersion, when the electromagnetic waves impinged upon matter, these ions were supposed to be set in vibration at the same frequencies as the impinging light. The displacements of the ions from their equilibrium positions, and , caused the polarization of the material medium, whereas the ether polarization corresponded to the electric field, , of the light. Drude’s idea for incorporating the polarization of the medium into Maxwell equations was the following: the displacement of the ions gave rise to two electric currents, and , of opposite sign, which could be expressed as the product of the respective number of ions, and , their charges, and , and their velocities, and . The total electrical current amounted to the sum of the ion currents and the ether current, . By assuming that ions were subject to elastic forces and , while acted upon by electromagnetic light, Drude eventually obtained this expression for the total electric current:19
within the brackets corresponded to the action of the ether, whereas the other two terms referred to the influence of the positive and negative ions. The expression depended on the electric field of light,
, its frequency,
, two parameters,
, and the elastic constants of the two types of ions,
. Drude had thus managed a combination, in one mathematical expression, of both electromagnetic parameters (electric fields and frequencies) and mechanical parameters (elastic constants). Subsequently, if one defined the dielectric constant,
, of the joint system of matter and ether as the sum of the dielectric constant of the ether,
, and the two ionic terms written above, one could eventually return to Maxwell’s expression for the electric current
, with a modified dielectric constant. This is the way in which the equations of motion of the ions entered
Following the same strategy of modifying constants, Drude continued to account for the other optical properties of matter and magneto-optical phenomena, providing a full derivation of the differential equations for magneto-optics by attributing to each phenomenon a specific kind of ionic motion. While for optical dispersion ions vibrated, for metallic reflection ions were supposed to translate across the metal, and in the phenomenon of rotation of light polarization (through quartz) ions were assumed to combine vibrations and rotations, tracing out helicoidal trajectories. Under the influence of a constant magnetic field, Drude suggested two possible motions for ions, which could modify both the dielectric and the magnetic constants: first, ions could go through proper vibrations and small rotations, resulting in helicoidal motions. Drude argued that the correspondingly modified
In the last chapter devoted to the subject of physical optics, Drude eventually referred to the optical properties of bodies in motion. In this case he referred substantially only to
being the normal components of the direction of wave propagation;
the components of the molecule’s velocity throughout the space and
the light velocity in vacuo. In fact, this was the only occasion in which Drude resorted to Lorentz’s theoretical works. It is very remarkable that Drude reduced
Eventually, in the third part of the book, Drude wrote about the thermodynamics of radiation. It is very significant that Drude devoted more than fifty pages to this matter, for this was the first time that the topic was so thoroughly treated in a textbook on optics. To date, it had been scarcely considered part of optics, since it seemed to have nothing to do with the explanation of light propagation, either through the ether or matter. Thermodynamics of radiation dealt instead with the generation of radiation by matter and the distribution of its energy over different spectral frequencies at different temperatures. The thermodynamics of radiation required, therefore, a very different set of concepts (i.e. distribution of energy, black-body radiation), physical laws (i.e. the second principle of thermodynamics), mathematical procedures (i.e. those of the kinetic theory of gases), and experimental sources (i.e. spectroscopy) than the ones discussed hitherto. In fact, Drude relied on accounts from others, basically
All in all, the ion hypothesis seemed to provide Drude with an insightful way to describe mathematically all kinds of optical phenomena involving light-matter interactions from the standpoint of the motion of particles at the microscopic level. Yet, the ion hypothesis also allowed Drude another route to new knowledge.
2.4.3 The Ion Hypothesis as a New Heuristics
Drude justified the adoption of the ion hypothesis in Lehrbuch der Optik on the grounds that it provided the most anschaulich description of the optical properties of matter, namely, the clearest, most demonstrative, most graphic description. It is true that a moving ion is much easier to picture than a moving particle being crossed simultaneously by an electric microcurrent, which Drude suggested in 1894. But the ion offered much more than a more concrete physical picture; other advantages contributed to its being anschaulich.
On the one hand, the ion hypothesis worked well as a heuristic tool, to model the interaction between light and matter in a more approachable way. On the other hand, the ion had an ontological status as the physical agent of optical phenomena, whose specific properties could be measured through different sorts of experiments. Nevertheless, ions could not be directly viewed or detected. Their properties (such as mass and charge) could be calculated from experimental data only by analyzing these data under the previous assumption that measurable phenomena were caused by the hypothetical ions. Through the sharing of ions as both heuristic tools and physical agents in this way, Drude figured out a new way to network different domains of knowledge.
In the second part of his book, Drude placed special emphasis on
being the magnetic field applied and the frequency of the original D line. This approach offered an exceptional opportunity to obtain a numerical value of for the hypothetical ion from optical experiments. But Drude did not stop there. Drude compared Zeeman’s value with other values for obtained in other experimental contexts outside of optics, like the production of cathode rays and the process of electrolysis. If it were not for their shared reliance on the ion as a hypothetical cause, it is rather unlikely that such diverse phenomena would have been put together in a textbook on optics:
It is remarkable that, from the deviation of cathode rays,
Kaufmann has derived […] almost the same value […] for the relation of the charge to the mass of the accelerated cathode particles. For the ions appearing in electrolysis this relation is much smaller. […] One can think that either the electrolytic ion contains more positively and negatively charged components that hold together for electrolysis but move freely with light waves and in vacuum, or the electrolytic ion is composed by the bonding of a charge of mass (electron) with a bigger neutral mass . (Drude 1900a, 410–411)
This text appears in a footnote, but this does not mean that it was considered ancillary by Drude. Actually, in the ensuing years, his research focused on the extension of the ion hypothesis to the most varied of fields. Most probably, Drude incorporated these insights into his text in the last moments before delivering it to the publishing house. Maybe he learned about Kaufmann’s experiments only in 1899, as Walter Kaufmann gave a talk on the topic in the same session of the 1899 meeting of the German Physical Society as Drude spoke. This would explain why Drude only mentioned Kaufmann in relation to cathode rays. For, in fact, almost simultaneously,
Some further aspects of this triangular comparison of
values should be highlighted. First, only after the same hypothesis of moving charged particles was applied to several different phenomena were ions differentiated into different sorts. Then only the particles responsible for cathode rays seemed to coincide with the ones measured by
Drude’s appropriation of the ion also impacted the third part of the book, specifically when he dealt with the phenomenon of luminescence. According to Drude, luminescence was produced when ions vibrated and emitted radiation at the same frequency as their vibrations. To support this hypothesis, Drude put forward the following argument: he assumed that the number of vibrating ions coincided with the chemical valence number of the material, and that the charge associated with a valence was a universal constant.22
Using these hypotheses, together with experimental values for the amount of light energy emitted per second, he calculated a value for the hypothetical amplitude
of the vibrations of the ions, if regarded as ideal
In this manner, exploitation of the ion hypothesis led to a new way to generate knowledge: this was not the ethos of exactitude, nor physical unification through mathematical equivalence, but a networking of different physical domains through a shared hypothesis. In this case, precise numerical agreement between theory and experiments could not help in checking whether the hypothesis was correct. One had to presume the ion in order to calculate from experimental data. The only way to check the ion hypothesis was the consistency of the speculative picture on the microstructure of matter constructed through the network of insights dependent upon it (electrochemistry, spectroscopy, cathode rays, physical optics, heat radiation).
2.4.4 Content and Narrative in Lehrbuch der Optik
The way in which Drude organized his book is inseparable from the way in which he understood the study of optics, the nature of electromagnetic light, and the role attributed to matter in the production of optical phenomena. From the previous two sections it follows that Drude’s starting point in accounting for physical optics was always the description of an optical phenomenon. Then he gave a mathematical description of the phenomenon, and at the same time identified each mathematical term with its physical meaning. Since the physical system had been reduced to the physical language to describe the formalism, mathematical and physical accounts of optical phenomena mirrored each other (I call it a mathematical-physical approach). Thus there was no space for physical speculation beyond the bounds set out by the formal description of the phenomena. The introduction of phenomena followed a strict order: from those with the simplest mathematical-physical description to those with the most complex, hence from light propagation to magneto-optics. Each step subsumed the former one, both in terms of mathematics (from the parameter of light velocity to complex Erklärungssysteme) and in terms of the physical concepts used (from wave propagation to the interactions of electromagnetic light with ions). There were only two detours on this route. First, when Drude claimed the unification of electromagnetism and optics by introducing an external criterium: the experimental coincidence of the velocities of light and electromagnetic waves. Second, when, for the first time, Drude decided to introduce a speculative element: the ion. A clear gap was apparent between the physical description of mathematical terms (dielectric constants, refractive index, electric currents, light velocity, phase delay, light frequencies, and characteristic frequencies of selective absorption) and the supposition that the motions of ions were the cause of the optical properties of matter. Thus, the ion hypothesis enlarged the physical system beyond the interpretation of the mathematical formalism. Drude called this strategy of organizing the book the “synthetic route.”
From the perspective of a physicist today, the synthetic route might seem a very obvious way to organize a book. Nevertheless, this was not necessarily the case.
Drude’s particular approach to optics clearly reflected another explicit goal, expressed in the introduction of his book: “To preserve a close contact with experiment, aiming at the simplest characterization possible of the field, I have chosen the synthetic route” (Drude 1900a, iii). Thus Drude’s synthetic route aimed at “simplicity,” where simplicity meant using the least number of physical hypotheses to support the mathematical formalism. In this sense, Drude’s strategy can be regarded as a realization, for the field of optics, of the positivistic move he initiated in 1892. Indeed, it is hard to imagine another strategy, different from the synthetic route, that could articulate the existing knowledge into a unitary and consistent view of optics following the basic simplicity principle. Another option would have been seeking to unify the field around, for example, mechanical principles, as
The synthetic route implied a very particular kind of trafficking between the simplest account in principle and the older sources. Previous papers entered the narrative for two principle reasons: first, to provide support for Drude’s unitary view (in the case of experiments); second, as components naturally incorporated into his overall picture. As a matter of fact, he commented with regard to his own previous works on optical dispersion and the
Through the synthetic route, Drude concealed not only older versions of electromagnetism and the ion hypothesis but also the kind of questions that led to alternative conceptions of these subjects, viz. whether electromagnetism and mechanics related to each other in a manner beyond the system of
How can we make a decision among all these possible explanations [he is speaking of the various mechanical and electromagnetic theories of light, mathematically equivalent], if the experiments do not help us? […] Our decision can only be founded on considerations in which our personal views play a big role; in that there are solutions that someone can refuse due to their oddity and other solutions that are preferred due to their simplicity. (Poincaré 1891, 6–7)
Thus, what for
In Drude’s synthetic route, the new questions to be posed appeared almost at the end of the narrative, when the introduction of the ion hypothesis produced a gap between the mathematical formalism and its physical interpretation, breaking in this way the simplicity rule. The “fresh life pulsing” in optics was to be found, as Drude prognosticated in the introduction, in the interplay between optical properties of matter, the corresponding Erklärungssysteme, the physical hypotheses about how ions behaved, and insights coming from other physical fields.
2.4.5 Lehrbuch der Optik as a Modern Book on Optics
Drude’s textbook rapidly became influential in Germany, in the rest of Europe, and even in the United States. An English translation by
Reviews of Lehrbuch der Optik, both of the 1900 German and 1902 English editions, highlighted the modernity of the book, describing it as an advanced text that contained a lot of novel knowledge, upshots of the fast developments in optics in the preceding decades, and never included in textbooks up to that point. For example,
It is a satisfaction to note that there has appeared a translation of this work, which received such instant recognition at the hands of physicists the world over upon its appearance in Germany. […] Descriptively, the book is fully on a par with
Preston’s Theory of Light and mathematically more valuable, as well as more lucid and attractive, than Basset’s Treatise on Physical Optics. (Kent 1903, 75–76)
The aspect of Drude’s account that most satisfied reviewers was his treatment of the electromagnetic theory of light together with the ion hypothesis, well expressed in this English review of the first German edition:
Textbooks of optics, it is true, are numerous, and the reviewer is apt to think that of the making of many books there is no end. Professor Drude’s book, however, contains much that is novel (at any rate, to English books) and the student will find up-to-date information on many points of interest. […] In all this work Prof. Drude has been most successful; the electromagnetic theory, supplemented by the one additional hypothesis of the moving electrons, serves to coordinate in a satisfactory way very many of the phenomena of light. (Anonymous 1900)
Now the question is: in what did the modernity of the book lay? Or put it in another way, what knowledge was left behind as old, once modern knowledge arrived?
In my opinion, the modernity of the book lay not only in the adoption of the electromagnetic theory of light and the introduction of the ion hypothesis, but also in what these decisions implied for the conception of optics as a whole. That is to say, the modernity lay also in the way electromagnetism and the ion hypothesis were redefined in their articulation as part of the synthetic route. Electromagnetic theory was reduced to the
2.5 Giessen 1900–Berlin 1906: Development of Lehrbuch der Optik’s Program up to the Second Edition
2.5.1 Ions vs. Electrons: the Sharpening of Drude’s New Heuristics
The ion hypothesis turned out to provide great gains for Drude in a short time. On 21 April 1899, Drude presented his work on magneto-optical phenomena in the annual meeting of the German Physical Society, in which he used the ion hypothesis for the first time. On 14 December, Drude submitted a paper on the ion theory of metals, in which he accounted for the optical properties of metals by assuming that there existed a kind of light ions (as opposed to massive ions) that could travel freely across the metal (Drude 1900b).25 In January 1900 Drude sent off the preface of Lehrbuch der Optik, where optics was built upon the ion hypothesis. Finally, in February, he sent off a very long paper to Annalen der Physik, in which he extended his optical program to other fields, specifically, to the thermal and electric properties of metals (Drude 1900c; 1900d). From December 1899 to February 1900, in these last papers, the dichotomy between light and massive ions had transformed into a dichotomy between electrons and ions.
In the same span of time, Drude was offered a position as full professor at the University of Giessen and directorship of its Institute of Physics, results of his being “known through his sound and comprehensive works on the field of optics and electric waves” (Lorey 1941, 123). He accepted immediately, and in April 1900 he and his family were already in Giessen, where he spent the five most productive and happy years of his professional life (König 1906; Planck 1906; Voigt 1906; Lorey 1941). He founded the Physikalisches Kolloquium and succeeded in creating a very lively research atmosphere among the doctoral students, resident researchers, and visitors. At the forefront of this research were ions and electrons. As one of his doctoral students,
In terms of effects, the electron was the most significant acquisition of Drude’s research in Giessen, and it enhanced the fruitfulness of the electromagnetic theory and ion hypothesis overall. Analogously to the previous discussion of the various ways in which ions could be productive in Lehrbuch der Optik, we also see several different forms of fecundity for the electron in Drude’s ways of articulating it. Drude’s appropriation of the electron occurred in two steps. First, Drude employed the electron in his electron theory of metals, mentioned previously (Drude 1900c; 1900d). Rather than just the definition of the electron as a universal charged particle, what was useful for Drude was establishing a contrast between the lightness of the electrons and the massiveness of the ions, now relegated to “aggregates of electric cores and ponderable masses that refer to electrolytes” (Drude 1900c, 566). For in this way, Drude could distinguish conceptually between two kinds of microscopic behavior in metals: under the action of an electric field, ions were assumed to be practically at rest, whereas electrons moved freely across the material. This assumption enabled Drude to treat electrons as the particles of an ideal gas, and thereby to make use of the kinetic theory of gases to predict the thermal and electric properties of metals. For a concrete check on his results, he then resorted to
In 1904 Drude turned again to the electron, to give a more precise interpretation of optical phenomena in terms of the microstructure of matter (Drude 1904a; 1904b). In this case, the electrons had both mass and charge. Another post-1900 event also led Drude to reinforce the idea that the electrons and ions had well-differentiated roles in optics. In 1902, another student of Lorentz in Leiden,
Given the assumption that macroscopic effects were the sum of the microactions of either ions or electrons, Drude rewrote, in 1904, the formula for dispersion obtained on the basis of the Mitschwingungen model, in terms of the ratio of charge to mass of the hypothetical particles. The dependance of the index of refraction on of light had the same generic form as in 1872:
Now Drude found the following expression for the parameter as a function of the number of electrons/ions with each proper frequency, , being their charge and their mass:
Applying this expression to already-existing empirical data on dispersion in fluorite, Drude showed the plausibility of his hypothesis. He did it in the following way. He used the two values of obtained by fitting experimental data on dispersion through fluorite into the generic formula, which corresponded to two proper frequencies (or the inverse of two wavelengths ) at which the hypothetical microscopic particles vibrated. One frequency turned out to be in the ultraviolet region, the other in the infrared. As Drude observed, was much larger than . By relating this piece of information to the fact that the value of electrons was much smaller than of ions, Drude proved the plausibility of his hypothesis that electrons vibrated at ultraviolet and ions at infrared frequencies.
On the whole, the parameters and of , which could be computed by fitting macroscopic observations into the formula, turned out to provide an exceptional window into the invisible microstructure of matter: on the one hand, were identified directly with the frequency of the natural vibrations of the corresponding charged particles. On the other, by using either the universal value for of the electrons or the varying ones obtained in electrolysis experiments, one could derive, from the empirical value of , the number of charged particles involved in producing optical phenomena. Thus optical dispersion became a means to count microscopic particles. In this way, the inner structure of molecules could be further characterized through Drude’s interpretation of optical phenomena, while until then this inner structure had remained practically restricted to the domain of chemists.
The electron hypothesis led Drude to suggest another bold connection between optics and an outside scientific domain. In 1904 Drude suggested that the electrons counted in dispersion calculations coincided with valence electrons, to wit the same entities revealed both physical and chemical properties depending on the circumstances. To make this connection between optics and the periodic properties of the elements, Drude relied upon
In the end, the electron hypothesis showed itself fecund in two ways: first, through the conceptual differentiation between electrons and ions, grounded in their mass difference, and second, through the possibility of calculating the charge-to-mass ratio,
, and number,
, from experiments. A network of heterogeneous domains of knowledge was spanned through the connection of the values of
, and chemical valence: cathode rays,
2.5.2 Dispersion Electrons and the Second Edition of Lehrbuch der Optik
The significance of these novel insights for Drude’s program of optics was demonstrated by their incorporation into the second edition of Lehrbuch der Optik, as Drude highlighted in the introduction to the 1906 edition. The electron was indeed the essential modification with respect to the first edition of the book:
In the six years that have elapsed since the publication of the first edition of this book, a fast development of the whole field of physics has taken place through the experimental and theoretical display of the electron theory in a way that is hitherto unique. In optics, this advancement is naturally noticeable in the chapters that, as in the case of dispersion of bodies and their magnetic activity, are built on the ion hypothesis. Basically, the progress consists in replacing the ion hypothesis by the electron hypothesis, namely, by the knowledge that from certain optical phenomena one can derive the same characteristic universal constant as in the case of cathode rays and generally when free electrons appear. (Drude 1906, v)
In 1906 Drude assumed that the charged particles producing optical dispersion, as well as the Zeeman,
In this way the network of phenomena established through the electron hypothesis extended to the whole field of magneto-optics. In the new edition, one question seemed to “pulse fresh life” more than ever: how optical phenomena, taken as a whole, could help us in characterizing the structure of specific chemical substances, once we assumed that electrons were the microscopic causes of their macroscopic features. One important assumption was implicit in Drude’s reformulation of optics, which turned out to be problematic a decade later: in order for macroscopic phenomena to result from the arithmetic sum of microscopic resonances, each electron should interact with light independently of all the other electrons.
2.5.3 Last Year in Berlin
As he was writing the preface to the second edition, Drude and his family were living in Berlin. In 1905 he was offered a full professorship in physics and the directorship of the Berlin Physics Institute, replacing
Just one week after he uttered these dreadful words, Drude committed suicide.
He retained his usual permanently jovial character in his everyday life, inside and outside home, until the last day. While the work at the Institute made its regular progress, he devoted himself with enthusiasm and success again to his scientific activity. He never expressed any idea about drastic relief. On 27 June he wrote the preface to the second edition of his Lehrbuch der Optik […] and on 28 June, just one week before the catastrophe, he gave his inaugural talk at the Academy of Sciences, […] in which he portrayed his scientific career and immediate plans for the future.
He had already complied with the most important duties of the semester, holidays were close. The application to leave on vacation was already signed, his substitution by the assistants arranged, a tour in the Karwendel mountains with his colleague and friend
Willy Wien agreed upon, from the equipment to the last detail of the garderobe prepared for this purpose. (Planck 1906, 628–629)
2.6 Epilogue: Following the Traces of Lehrbuch der Optik
2.6.1 Lehrbuch der Optik at Universities and in Other Textbooks
Drude’s Lehrbuch der Optik became one of the reference books for teaching optics at universities, in particular German universities. For instance,
Electro-magnetic theory I think the book most widely used would have been
Abraham’s. To some extent, although that was not translated into German that I know of, Lorentz’s theory of electrons. Optics? I think Drude’s was probably the commonly used book. Mechanics? I do not quite remember. But this were, in general, lectures tailored after some book. You may read Boltzmann or Kirchhoff....27
Further Drude’s approach was also influential for other textbooks, in particular
Concerning treatments of magneto-optics in general textbooks on optics the one by P. Drude deserves special mention (Lehrbuch der Optik, Leipzig 1900 and 1906), which has a singular hue due to the strong emphasis on the electron theory. Drude confines himself to the easiest case of the Zeeman effect, namely to the easiest sort of magnetically excitable bodies, and thereby the license for rounding and completing the theory lies in his characterization, which does not correspond completely to the real state. (Voigt 1908, 4)
All in all, Drude’s Lehrbuch der Optik and Voigt’s Magneto- und Elektro-Optik had a resounding impact on the ensuing years of optical research in various laboratories in Germany, where experiments on optical phenomena were deemed an appropriate means to explore the microstructure of matter. Most significantly, on the basis of these two works, students of
Drude’s Lehrbuch der Optik, in particular its English edition, was also influential for the American physicist
2.6.2 From a Modern Book to Classical Optics
Drude’s textbook was also referred to in research papers. Eventually, in the context of the emerging quantum theory, Drude’s modern Lehrbuch der Optik was redefined as “classical.” This transition is particularly well-revealed through
The theoretical physicist
In the late 1910s, Sommerfeld’s dream faded for various reasons, but the important point here is the redefinition of Drude’s previously modern approach as classical, within this context. What made Drude’s dispersion theory a classical theory, as opposed to the quantum theory? Was it simply that it was non-quantum? The reason
As a matter of fact, it was the experimentalist
Overall, what was modern in Drude’s textbook, including and beyond the blending of the electromagnetic theory of light and electrons, was also what allowed it to become classical, when its differences from the emergent domain of quantum physics were made apparent. Negotiations of the boundary between classical and quantum physics took place precisely at the points of articulation of knowledge that had been ascribed “fresh life” in Drude’s account: causal relations between moving, independent electrons and macroscopic features, disclosure of the microstructure of matter through the interrelation of phenomena hypothetically manifesting electron properties. But at the same time, this “modernity” of the book was itself the result of an arduous process that was by no means less challenging or innovative than its later development in relation to quantum physics. Classical physics had been constructed through other distinctions both on the epistemological and ontological levels, which were left behind as optics took on a modern form: mathematical formalism vs. the nature of ether, mechanics vs. electromagnetism. Only a long-term analysis enables us to understand the specific “classical” physics with which physicists grappled in the first decades of the twentieth century, and avoid oversimplifying it to mean all of non-quantum physics. Classical optics, and more specifically Drude’s Lehrbuch der Optik, established the field of possibilities, the exploration of whose limits, defined the cognitive space within which the boundary with quantum physics was negotiated.
Abbreviations and Archives
|AHQP||Archive for History of Quantum Physics. American Philosophical Society, Philadelphia|
This paper has had a very long conception. It has accompanied me for more than three years, during which it has become part of my dissertation. I have benefited from a grant of the Catalan Government during my initial stay at the Max Planck Institute for the History of Science in Berlin, and then a pre-doctoral grant of the Max Planck Society to continue work on my dissertation there. In this time I have learned a lot from Luis Navarro from the University of Barcelona, and from personal exchanges with all the members of the international project on the History and Foundations of Quantum Physics. Jürgen Renn, my doctoral advisor, deserves special mention. I would also like to address a special thank to Massimiliano Badino and Jaume Navarro for their great idea and their enthusiastic engagement of us in this fascinating project on the History of Quantum Physics through Its Textbooks. And also for their patience in waiting for my paper and reading the various versions of it. Massimiliano is the person who has participated the most in the process of writing this paper, and to whom I am most indebted for the final result. I am also very thankful to Jeremiah James for his copyediting, which enormously improved the quality of the language. In addition, I would also like to thank the editorial team, led by Nina Ruge, for their steadfast dedication and efforts behind the curtains to make a professional book out of these essays. Sharing an office with Nina I have realized how difficult, important, and, unfortunately, at times invisible, is the task of a book editor.
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All translations are done by the author.
The story of the various theories of the lumiferous ether in the nineteenth century is rather intricate. A good overview can be found in (Whittaker 1910).
In fact, the British physicist Oliver Heaviside had been working on a similar reformulation of Maxwell’s equations since 1885, as Hertz rightly acknowledged in his paper. For more information about the developments of Heaviside and, in general, the work of the so-called “Maxwellians” (George Francis FitzGerald, Oliver Lodge, Oliver Heaviside) in the 1870s and 1880s, see (Hunt 1991).
The e marks a German plural.
Christian Christiansen was the first to measure the discontinuity of light dispersion through fuchsine (Christiansen 1870). Drawing on Christiansen’s experiments, August Kundt systematized the anomalous behavior depending on the kind of substances (dyes), the position of the discontinuity and its relation to other properties of the materials, such as the absorption of light (Kundt 1871a; 1871b; 1871c; 1871d). As a result of these observations the term “anomalous dispersion” was coined.
Lorentz published his electromagnetic theory of optical dispersion as early as 1878, but his results remained unnoticed until the mid-1890s. Buchwald and Olivier Darrigol argue that it was most probably because he wrote in Dutch and, at that time, he did not enjoy international connections. In the case of his 1892 theory, however, the situation did not differ much, due to the use of very complicated mathematical tools such as retarded potentials and the ongoing lack of international connections. On the deep differences between Lorentz’s account and the rest of European physicists’, see (Buchwald 1985, 198–199) and (Darrigol 2000, 322–330). The situation changed when a systematic account in German appeared in 1895 (Lorentz 1895). Also it must be emphasized that, although Lorentz had made use of a mechanical principle in 1892, he was not dogmatic in this respect and soon abandoned general principles, which, on the other hand, were driving von Helmholtz’s approach.
In fact, Lorentz first identified charged particles with electrons in the 1895 German translation of his 1892 paper (Lorentz 1895). As Theodore Arabatzis has remarked, the identification of Faraday’s ions with charged particles presupposed the conviction that electricity had an atomistic structure, as was the case for von Helmholtz (Arabatzis 2006, 72–73). In this direction, by 1881 von Helmholtz had already suggested a possible connection between the concept of ions in electrolysis and the notion of a moving singular charge in electromagnetic theory (von Helmholtz 1903). Ions acquired optical properties only later. See also (Darrigol 2000, 272–274) for further details on this connection.
It is remarkable that Drude took von Helmholtz’s set of mechanical equations for dispersion, laid down in 1875, as a basis for comparison (von Helmholtz 1875), but not von Helmholtz’s 1893 electromagnetic theory. Limiting himself to a formal comparative analysis, Drude chose von Helmholtz’s 1875 mechanical theory, “since it supplied the form of the differential equations in the most precise and anschaulichsten [clearest, most intuitive] way” (Drude 1893, 537).
In fact, in his 1893 paper, Drude mentioned an inspiring exchange of letters with Hertz.
It must be emphasized that Drude’s phenomenological approach entailed an important conceptual difference from Lorentz’s and von Helmholtz’s electromagnetic constructions of optical dispersion: while for the latter two the electrical force exerted on each particle comprised both the electric field of ether and the electrical polarization of the particles, Drude identified external force with the electric field of the ether. I used the term Mitbewegung for brevity’s sake.
“Phenomenal world” is the usual translation of the German philosophical term Erscheinungswelt. Hereafter, the German word will be used.
More specifically, between 1894 and 1899, Drude’s research had been especially fruitful in three directions: electric waves, magneto-optical phenomena and actions at a distance. Concerning the first topic, Drude found experimentally that electric waves, whose frequency lay outside the optical range of the spectrum, also displayed dispersion, and indeed anomalous dispersion through certain liquids. Furthermore, in line with his 1895 claims at his inaugural speech in Leipzig, he immediately related the dispersion behavior to the chemical constitution of the liquids examined (Drude 1896; 1897a; 1898). In 1897 he addressed the Kerr effect again from a theoretical point of view, but without daring to give it a physical interpretation in terms of the properties of matter, as he had himself suggested at the end of the Physik des Aethers (Drude 1897c). The paper was the continuation of an old controversy he had been engaged in since the early 1890s with D. Goldhammer, concerning the best Erklärungssystem for the Kerr effect and which kind of optical constants best described it. For more details about the controversy, see (Buchwald 1985, 215–232). Eventually, Drude also explored the theoretical possibility of reducing actions at a distance such as gravitation, to local actions, mediated by the electromagnetic ether (Drude 1897b).
It is very remarkable that Drude did not mention Lorentz’s account of the Zeeman effect either in 1899 or in 1900; although, he referred to Zeeman’s papers and met Lorentz in 1898 at the conference in Düsseldorf. At that time, Lorentz had already published his theoretical account (Lorentz 1897; 1898). In the 1899 paper, Drude indeed resorted to Voigt’s 1899 Erklärungssystem for the Zeeman effect, but Voigt did not allude to Lorentz either. Darrigol (2000, 331–332) is of the opinion that Drude, and also Voigt, became advocates of the microscopic view of optics abruptly, possibly as a consequence of Lorentz’s presence at that meeting. But the absence of Lorentz in Drude’s 1899 paper and 1900 book, in the context of magneto-optics, hints at another explanation. Possibly Lorentz had an influence on them, but he was not the only reason for Drude’s adoption of the ion. Drude developed, as early as 1893, a microscopic outlook to explain optics, in his contribution to dispersion.
For simplicity’s sake, I have approximated Drude’s formula to the case of no frictional force.
This effect was observed one year after the Zeeman effect (Macaluso and Corbino 1898), for which Voigt had already provided an Erklärungsystem in 1898 and 1899 (Voigt 1899). Damiano Macaluso and his assistant Orso Mario Corbino took a sample of sodium gas and applied a constant magnetic field, as in arrangements that exhibited the Zeeman effect. But in constrast to Zeeman’s experiment, Macaluso and Corbino did not examine the light emitted by the gas. They made white light pass through the gas and measured the change of polarization of the transmitted light. They observed a continuos change of the angle of polarization for the whole spectrum, interrupted only by sharp discontinuities at the D spectral lines of sodium.
The valence number was related to the number of other atoms that one substance required to form molecules. Hence valence was related to empty positions in the atom, not yet to the number of elementary particles—electrons—to be shared in forming molecules. Drude calculated the charge associated with a valence position from electrolysis, using the kinetic theory of gases, thus it was acknowledged that, in electrolysis, the electrolytes of one substance—ions—always transported the same number of valences from one electrode to the other. Drude happily observed that this charge almost coincided with the charge of the electron measured by Thomson. But Drude did not go further in relating the charge of one electron with the charge of valence.
Moreover, two further editions of the English version appeared in 1959 and 2005. Besides them, there was one French translation in 1912 and another into Russian in 1935 (Cardona and Marx 2006).
Italics are mine.
Drude’s inspiration for writing this paper was a work published by Wilhelm Giese in 1889, in which he suggested that electrical conduction through metals was connected to ions (Giese 1889). It must not be just a coincidence that Lorentz, in his 1895 Versuch, grounded his adoption of the ion hypothesis on Giese’s work, among other things. Drude never mentioned Lorentz’s works before Lehrbuch der Optik, where he had to read them to provide a comprehensive account of the field.
“Ich empfinde ein Gefühl der Beklemmung, ob ich durch Anspannung aller meiner Kräfte den an mich gestellten Aufgaben gewachsen sein werde.”
See page 6 of the interview of Minkowski by Thomas Kuhn and John Heilbron in April 1962, AHQP, APS, M/f No. 1419-04-minkowski-r-002.
Lorentz also wrote a very influential book drawing upon the electron theory (Lorentz 1909), containing features on the various domains of physical knowledge that were hypothetically explained through different behaviors of electrons, such as optics and heat. Nevertheless, Lorentz’s was not a book on optics, and it lacked a systematic approach to the field, which included the description of instruments and experiments, from the simplest to the most complex phenomena, separate from a theoretical account of the actions of the electrons.