[Lloyd Gillespie]

On the Co-Creation of Classical and Modern Physics

Richard Staley*


ABSTRACT
While the concept of "classical physics" has long framed our understanding of the environment from which modern physics emerged, it has consistently been read back into a period in which the physicists concerned initially considered their work in quite other terms. This essay explores the shifting currency of the rich cultural image of the classical/modern divide by tracing empirically different uses of "classical" within the physics community from the 1890s to 1911. A study of fin-de-siècle addresses shows that the earliest general uses of the concept proved controversial. Our present understanding of the term was in large part shaped by its incorporation (in different ways) within the emerging theories of relativity and quantum theorywhere the content of "classical" physics was defined by proponents of the new. Studying the diverse ways in which Boltzmann, Larmor, Poincaré, Einstein, Minkowski, and Planck invoked the term "classical" will help clarify the critical relations between physicists' research programs and their use of worldview arguments in fashioning modern physics.

DESCRIPTIONS OF THE TRANSITION from classical to modern physics have long provided the most powerful framework in which to present the great transformations in physical understanding that occurred at the end of the nineteenth century. However loosely, this language links the physics of the day to its era, gesturing at a common struggle through which fields as disparate as art, literature, and technology broke free of tradition to forge key elements of the modern world. While it pervades writings across the spectrum, from physicists through historians and popular authors, the origins of this framework are at present largely unknown. This essay aims to establish when and why physicists first started to think of "classical" and "modern" physics in the way we now take for granted.
Consider first a representative use of the concepts from a major protagonist. This will indicate the subtle historiographical situation we have to deal with. Describing his discovery of energy quantization in a 1931 letter to Robert W. Wood, the Berlin theorist Max Planck (18581947) wrote of his distaste for dubious adventures. But by 1900 he had been "wrestling with the problem of the equilibrium between radiation and matter for 6 years, without success." After finding an empirically accurate formula for the energy distribution in the spectrum of a blackbody in October, he deemed the final step of providing a theoretical interpretation worth any price. In his "act of desperation," there was an important casualty: "Classical physics was not sufficient, that was clear to me. For according to it, energy must, in the course of time, transform completely into radiation from matter. In order for it not to do so, we need a new constant that assures that the energy does not disintegrate [indefinitely]."1
Planck's invocation of classical physics is at once epochal in gesture and highly specific (his reference to the transfer of energy from matter into radiation is a brief account of the consequences of the equipartition theorem, a subject we shall return to). But despite the power and clarity with which Planck links the physics of an era with an emblematic principle, careful historical research has taught us to question whether he in fact won his way to modern physics in 1900.
In an extraordinary 1978 study, Thomas S. Kuhn argued that despite his formal use of energy elements in forging a new interpretation, Planck did not regard himself as introducing the radical new understanding of energy quanta we now associate with modern physics.2 Planck's 1900 papers support the point. Rather than emphasizing energy quantization or the law itself, Planck highlighted both its use of two natural constants, h and k (later named Planck's and Boltzmann's constants), and the quantitative links it established between electromagnetic theory and the properties of electrons and atoms. Planck had delivered new natural constants and opened glimmers of insight into the processes conditioning the largely inaccessible world of microphysics; but his writings show little evidence that he thought he had won a new kind of physics.3
Kuhn convincingly demonstrated that Planck did not articulate a broadly conceived quantum physics in 1900, even if the blackbody law was later taken to found one. But he held fast to the other side of the story, insisting that Planck's approach was still "fully classical," even as late as his 1906 Lectures on the Theory of Heat Radiation. Kuhn's recourse to this overarching interpretative framework is widely shared. Allan Needell and Olivier Darrigol have both suggested that "classical physics" is an idealization formed in the 1910s and that its application to the fluid situation of turn-of-the-century physics is anachronistic. Nevertheless, benchmark accounts of the period and its major figures routinely invoke the term in describing the conceptual environment in which physicists developed their research programs.4 Once again noting the power and clarity of this language, we need to question whether we should understand the physics of the era as "classical."
Analytically, one can offer a clear rationale for Kuhn's insistence. If quantization defines the new physics, and the classical and modern form two mutually exclusive theoretical stances, the fact that Planck makes no recourse to discrete energy values renders his approach classical by definition. Planck's 1931 letter shows that by then he held something like this analytic perspectiveand applied it to his earlier struggles. But noting that, just as he made no explicit use of the concept of energy quantization in 1900, Planck then made no explicit reference to "classical physics," this essay will address the question, When, why, and how did Planck and his community first start using concepts of "classical physics" in their work to shape new theory?
Given the widespread use of the language of the "classical" and the "modern" in fields as fundamental to European nations as education and as highly visible as art and technology, this empirical question holds the promise of establishing significant links between research physics and cultural history. It is important to note at the outset, however, that in turn-of-the-century schooling, art, literature, or science any particular deployment of these evocative but open words was likely to meet controversy and contest. After all, the debate over the status, values, and content of classical and modern approaches to secondary and tertiary education in 1890s Germany was so bitter that contemporaries described it as the "Schulkrieg."5 Given this environment, we will have to guard against reading a meaning into early uses of such terms that was in fact won only later.
I will focus in the first instance on the concept "classical," for specific deployments of that word were more significant than an invocation of "modernity" in the formation and propagation of new theory in physics.6 Searching for patterns of use rather than definitively first appearances, I present a comparative examination of three addresses surveying the state of physics circa 1900. This will show, first, that the word "classical" was then used in several distinct ways (some of them in considerable tension with others); it will also suggest that the word was employed differently in different language-speaking areas. In this early period "classical" was applied most concretely to mechanics. The following section will explore the relationship between a newly minted "classical mechanics" and the emerging theory of special relativity. The third section turns to early quantum theory, showing that the expansion of the concept of the classical to cover physics as a whole followed the development of a new understanding of statistical mechanics. Charting the long process through which physicists extended the meaning of the word "classical" will provide the foundation for my argument that classical physics and modern physics were very importantly created at the same time. Despite the power of Planck's retrospective application of the term "classical" to an entire epoch, classical and modern physics were co-creations, mirror image twins of the fault line between the physics of the past and that of the future.
FIN-DE-SIÈCLE PHYSICSBoltzmann's "Classical Physics"
By the end of the nineteenth century, Ludwig Boltzmann (18441906) had built an extraordinary reputation on the basis of pioneering work in statistical mechanics, interpreting the thermodynamic concept of "entropy" as a measure of the probability of a collection of atoms. His celebrated H-theorem explained the fact that entropy decrease is never observed in an isolated system as an essentially statistical property of a distribution of a large number of molecules (and his work provided the source and departure point for one of the most important features of Planck's new blackbody theory). In 1899 the Viennese physicist spoke on the methods of theoretical physics to a broad scientific audience at the annual meeting of the German Society of Natural Scientists and Physicians, the Naturforscherversammlung, in Munich.7 Like the other papers considered in this section, this was self-consciously a "turn-of-the-century" address, offering an overview of physics in a period of extraordinary and rapid change.8 Examining works of this kind will help us assess the extent to which diverse uses of "classical" were integrated with understandings of the content and character of disciplinary transformation. While we will soon see that Boltzmann's use of the term was idiosyncratic, it will indicate how deeply the earliest general invocations of such concepts were implicated in significant foundational debates. The distinctions we will recover between different invocations of "classical" theory in mechanics and thermodynamics have long been lost to our present concept of classical physics; but later sections will show how important they were to the formation of that concept itself.


Boltzmann introduced the concept of the classical in science as part of a sociological insight into methodological change. Approaches that had once looked capable of serving the development of science (or other disciplines like poetry, art, or music) forever might suddenly be revealed as exhausted, prompting attempts to find other, quite disparate methods. Then, Boltzmann wrote, followers of the old approach will find their point of view being described as outdated and outworn, while they in turn "will belittle the innovators as corrupters of true classical science." He held that this process recurs across the developmental history of all branches of intellectual endeavor:

Thus many may have thought at the time of Lessing, Schiller and Goethe, that by constant further development of the ideal modes of poetry practised by these masters dramatic literature would be provided for in perpetuity, whereas today one seeks quite different methods of dramatic poetry and the proper one may well not have been found yet.

Just so, the old school of painting is confronted with impressionism, secessionism, plein-airism, and classical music with music of the future. Is not this last already out-of-date in turn? We therefore will cease to be amazed that theoretical physics is no exception to this general law of development.9

Boltzmann's account shows how important it will be to recognize links to the cultural setting in understanding physicists' use of "classical." A significant local dimension animated his reference to secessionism, for example. Secessionism was pioneered in Munich from 1892; Gustav Klimt had recently founded a second secessionist movement in Vienna and was to stimulate extraordinary controversy with his paintings for the University of Vienna that reimagined traditional figures (see Figure 1).10 Perhaps the most important general point to emerge from Boltzmann's lists is his implication that, whatever their virtues, the new trends in art and poetryand physicsare likely to be less reliable than tried and true methods. But the specific way in which Boltzmann applies the word "classical" to his own discipline is even more interesting, because he depicts physics as being already in a postclassical phase.

(144 kB)Figure 1. The secessionist Gustav Klimt's sketch Philosophy, intended for the ceremonial hall of the new University of Vienna, was displayed in 1900 and survives only in this photograph. University academics repudiated its depiction of nebulous ideas in nebulous form, an indication of the stakes involved in reworking traditions. Boltzmann described mathematical phenomenologists as "moderate secessionists": Ludwig Boltzmann, "On the Development of the Methods of Theoretical Physics in Recent Times" (1899), in Theoretical Physics and Philosophical Problems: Selected Writings, ed. Brian McGuinness, trans. Paul Foulkes (Vienna Circle Collection) (Dordrecht/Boston: Reidel, 1974), pp. 77100, on p. 93. [Courtesy of Galerie-Welz, Salzburg.]

Boltzmann began by outlining the approach, fueled by the achievements of Galileo and Newton, that sought explanations along the lines of Newton's theory of gravitation (supplemented by repulsive forces). The task of physics had looked as if it might forever consist of seeking "the law of action of a force acting at a distance between any two atoms and then integrating the equations that followed from all these interactions under appropriate initial conditions." In the 1870s and 1880s the work of James Clerk Maxwell and Heinrich Hertz that developed and confirmed the theory of the electromagnetic field had broken through this program. One rich consequence was epistemological. Now, following Maxwell's understanding of the limitations of mechanical models and Hertz's insistence that understanding should be based on the equations, physicists recognized that it was not their task to say what reality truly is. Rather, they sought a picture [Bild] that is both as simple as possible and that represents phenomena as accurately as possible. J. L. Heilbron has noted that this "descriptionist" stance was characteristic of turn-of-the-century attitudes toward the aims of physical theory.11
In addition to the rise of new methods in electromagnetism, Boltzmann discussed philosophically motivated criticisms of the foundations of mechanics. Both Gustav Kirchhoff's 1876 lectures and, especially, Hertz's recent posthumous volume on mechanics had mounted what Boltzmann described as a formal and programmatic attack on "the old classical mechanics." Discerning a lack of clarity, their work had focused on providing a new treatment of the concept of force. In Boltzmann's view this remained a program for the distant future, one that had not yet superseded the old mechanics (and we should note that he left the critical contributions of his Viennese colleague and rival Ernst Mach unmentioned).12 Boltzmann's own endeavor had been toward an extension of mechanical principles in kinetic theory, promoting molecular and atomic approaches. Despite the respect in which he fought for an as-yet-unfinished program, Boltzmann characterized himself as a monument to ancient scientific memories, the only one who still grasped the old doctrines with unreserved enthusiasm: "I regard as my life's task to help to ensure, by as clear and logically ordered an elaboration as I can give of the results of old, classical theory, that the great portion of valuable and permanently usable material that in my view is contained in it need not be rediscovered one day."13
This is both the earliest and the most elaborate discussion of classical physics that I know. In it Boltzmann marks himself as the first and perhaps the only figure of the nineteenth century who understood himself to be a classical physicist. At least one of his students saw him that way (see Figure 2), but it is worth noting that few, if any, others took up or commented on Boltzmann's self-definition.

(47 kB)Figure 2. Der Naturphilosoph, a drawing of Boltzmann by his student Karl Przibram. Przibram also drew Boltzmann riding a bicycle. This image appeared as front material for John Blackmore, Ludwig Boltzmann: His Later Life and Philosophy, 19001906, Bk. 2: The Philosopher (Boston Studies in the Philosophy of Science, 174) (Dordrecht: Kluwer, 1995), p. vi. [Courtesy of Setsuko Tanaka.]

Boltzmann's conception of himself in these terms is likely to have been relatively recent. To my knowledge, he first wrote of "classical mechanics" in introducing his lectures on the principles of mechanics in 1897. Forgoing the urge to give the discipline "a completely new garb," Boltzmann there did what he could to avoid the problems facing mechanics by offering instead a representation that was as true as possible to "its old, classical form."14 It is revealing that these two adjectives appear together, and Boltzmann may well have been the first to bring the second into play. Those who pioneered criticisms of mechanics had framed them as critiques of current understandings. Mach and Hertz wrote, for example, of its "present form" and "customary representation."15
These critical developments provide one rationale for Boltzmann's delineation of a "classical mechanics." A second spur is likely to have been the different sense in which others were beginning to write of "classical thermodynamics"with both terms emerging as a legacy of vigorous debate on a possible energetic foundation for physics. From the late 1880s Georg Helm and Wilhelm Ostwald had championed energy as the primary concept in science, seeking to derive mechanics and ultimately all physical laws from an energy principle. In 1895 Boltzmann publicly opposed their methods at the Naturforscherversammlung in Lübeck, and subsequently disputants on both sides of the controversy used classical coinages to assert different continuities with tradition.
I do not yet know which came first. However, it is significant that Helm included a section on "classical thermodynamics" in his 1898 book on the historical development of energetics. Helm justified his linguistic choice by writing that the understanding of the relations between heat and work gained by the mid 1850s formed a complete system that was now so generally accepted and well established "that it can certainly be called `classical.'" He added that the label had first been given by "the opponents of all efforts to develop it further." Whoever was responsible for the first use of "classical thermodynamics," Helm probably saw good reasons to promote that term as a way of insulating thermodynamics from the strong dependence on mechanics suggested by phrases like "the mechanical theory of heat." The new terminology could thus serve to distinguish the phenomenological, energetic approach Helm took to thermodynamics from the very different stance pursued by Maxwell and Boltzmann. Their work on the kinetic theory of gases sought to provide proofs of the laws of thermodynamics on the basis of mechanical, molecular, and statistical models.16 As a result, Boltzmann's appropriation of "classical" to describe first mechanics and then his own personal aims may have constituted an attempt to wrest that word from opponents like Helm. His writings would claim "classical" from the more recent field of thermodynamics on behalf of what Boltzmann undoubtedly regarded as the even more fundamental and venerable field of mechanicswhich formed the basis for his own innovative and controversial contributions to thermodynamics.
Larmor's "Classical" Volumes
We can now see that early, general uses of the word "classical" played into contested terrain. Later sections will show how far twentieth-century uses came to depart from Boltzmann's example. First, however, it is important to see how others outside the German-language realm invoked the term. In 1900 Joseph Larmor (18571942) was a lecturer in mathematical physics at the University of Cambridge. In the mid 1890s, and drawing also on the work of H. A. Lorentz, he had reformulated Maxwell's theory of electromagnetism into what became known as an "electronic theory of matter."17 Larmor introduced negative and positive electrons as the fundamental carriers of electric charge and the sole constituents of matter moving in a sea of ether. The electrodynamics of moving bodies was central to his research, and Larmor used new space-time and electromagnetic transformations in which what later became known as the Lorentz transformations offered a way of explaining the null result of all attempted ether-drift experiments. The work of both Larmor and Lorentz provided fundamental ground for the subsequent development and reception of relativity physics. In 1900 Larmor published his best-known book, Aether and Matter, and gave a presidential address to the British Association for the Advancement of Science. Larmor was clearly responding to just the kind of vision Boltzmann offered, and the word "classical" recurred often. But he kept his discussion of change well apart from the terms in which he described the great works in his discipline.
Larmor spoke of a "classical treatise" on infinitesimal calculus and the "classical volumes" of the British Association, with their reports on the state of different fields in physics. He also described the modern theory of electric and magnetic phenomena as having received its "classical exposition" with the publication of Maxwell's treatise. Rather than identifying a broader tradition, Larmor thus used the word to convey the achievement of specific works. This is exactly how most nineteenth-century physicists used "classical": to describe theoretical or experimental work of the first rank that might constitute a standard or model, whether or not it could be regarded as complete or definitive.18 The most significant example is the series of papers and books republished as "Classics in the Exact Sciences" from 1889 under Ostwald's general editorship. Its first volume was a reprinting of Helmholtz's Erhaltung der Kraft of 1847, and by 1900 the series numbered 119 volumes.19 Among its many aims, this venture may have been a way of insisting that the sciences, like the arts, had their classics.
Despite the specificity of Larmor's references to "classical" publications, he was deeply concerned with the great changes physics had seen in general. While recognizing the increasing disposition to replace Newtonian dynamical principles with a descriptionist agenda that renounced causal relations, he finessed the consequences of Maxwell's work rather differently: "The question has arisen as to how far the new methods of aetherial physics are to be considered as an independent departure, how far they form the natural development of existing dynamical science. In England, whence the innovation came, it is the more conservative position that has all along been occupied."20
Larmor thought there were strong grounds for giving up the attempt to explain electrodynamics as the mechanical consequences of concealed structure in the ether, but he defended the continued relevance of a dynamical understanding of the ether and electronsmatter on a molecular levelthrough the principle of least action.
Poincaré on "The Classical Mechanics"
Our final fin-de-siècle publication comes from Henri Poincaré (18541912). Although known initially for his pioneering mathematical work in celestial mechanics, the theory of automorphic functions, and algebraic topology, Poincaré had become one of France's most respected and broadly honored scientists. In 1900 he gave keynote lectures at international congresses of mathematics and physics held in conjunction with the Paris World's Fair. His 1902 book La science et l'hypothèse gathered together recent addresses, moving through mathematics and epistemology to discuss current physics (Chapters 9 and 10 reprinted his speech to the Congress of Physicists). Offering a potent mix of practical scientific philosophy, prognosis, and prospect, the book became extremely well known, with German and English translations appearing in 1904 and 1905.21
After treatments of arithmetic and geometry, Poincaré began his section on "Force" with a chapter entitled "The Classical Mechanics." Without explicitly stating what this meant, Poincaré launched an attack on several concepts that had been central to mechanics since Newton and were increasingly being questioned, notably by Mach. Declaring that there is no absolute space, no absolute time, and no direct intuition of simultaneity and, finally, that it might be possible to enunciate mechanical facts with reference to a non-Euclidean space, Poincaré swept the slate clear before provisionally accepting the use of absolute time and Euclidean geometry.22 That provided the basis for an examination of the relations between concepts of force, mass, and the principle of action and reaction in an account of Newton's laws as conventions, experimentally founded without being amenable to experimental invalidation. Poincaré had set out an argument of this type in earlier chapters on the foundations of geometry. As Peter Galison has recently demonstrated, the term "convention" offers a bridge toward understanding the rich cultural associations at play in Poincaré's work. The philosophical dimensions of Poincaré's focus on that concept can also be linked to the central role of the adoption of specific conventions in various political and physical realms in which Poincaré was active as a scientist and bureaucrat.23
Poincaré discussed the approaches to mechanics of Kirchhoff, Hertz, and the "thread school" that Jules Frédéric Charles Andrade had described in 1898.24 Together with his own critical commentary, these alternatives provide a good reason for distinguishing the traditional approach as "the classical mechanics." But it is particularly important to note that when he discusses energeticism it becomes clear that Poincaré limited classical mechanics to Newton's laws alone, despite the apparently broad scope of his reference to the advances involved in moving from "the classical mechanics," "the classical theory," or "the classical system" to the energetic.25 Poincaré wrote, for example, of the principle of conservation of energy and Hamilton's principle as teaching more than the fundamental principles of the classical theory. They had both extended the realm of applications of mechanics and introduced new restrictions on the kinds of motion possible.26 Although his language is somewhat ambiguous, "classical" thus provided Poincaré with a way of distinguishing a particular interpretation in a specific field rather than describing an epoch or worldview.
When he turned to providing an overview of current science, Poincaré's discussion once again shared many features with Boltzmann's, although his writing echoes distinctively French concerns with economical images of the scientific machine.27 For Poincaré, rapid change had left foundations uncertain; the new radiations had opened up a new world. Scientific progress involved a continual interplay between the achievement of apparent simplicity and the recognition of new complexity. It was not image or ontology that provided secure foundations, but the true relations expressed in hard-won equations and, especially, in general principles. Rather than explanatory mechanisms, the true goal of physics was unity. His focus on a principle-based unity shows that, despite a similar diagnosis of its present state, Poincaré thought that the search for permanently usable features of past physics was to be resolved quite differently than through Boltzmann's emphasis on classical, mechanical foundations. Moreover, not a whisper of the classical system he discussed before enters Poincaré's treatment of the past or present aims of science in these chapters.28
Reaching across local research contexts toward international and national registers, addresses and books of this nature also constituted conscious attempts to move between the concerns of research physics and broader, nonspecialist audiences. Disclosing a traffic of resonance and meaning between the research front and the public that is both multivalent and multidirectional, they provide important openings for a study of links between science and cultural history.29 In particular, building up a sense of the understanding of change they display has now given us an appropriate touchstone for evaluating different invocations of "classical." Circa 1900, "classical" was a concept with a range of uses. It is especially important to note thatin expressing the value accorded outstanding contributions or designating in particular traditional (but contesting) approaches to mechanics or thermodynamicsthe word formed only a minor part of the vocabulary with which physicists discussed the past and considered change. Physicists shared an understanding that their discipline had witnessed a long-standing criticism of foundations and the rise of new programs, especially following the success of Maxwell's work. Change was rapid, the field open. Boltzmann alone gave the term "classical" a highly general and importantly sociological meaning, and it is therefore in the German-speaking world that we can see emerging the possibility of speaking of "classical physics" or "classical physicists." This view is supported by different editions of La science et l'hypothèse. In the original, Poincaré confined "The Classical Mechanics" to Newton's laws alone and referred in passing to the classic system of electrodynamics, incomplete as it was. Significantly, Ferdinand Lindemann's preface to the German edition described Poincaré's discussions as extending to the whole of theoretical physics, both "in its classical form as well as in its most recent development." In a German reading, Poincaré's account of change could be subsumed within an epochal understanding of the past as classical. As it happens, Joseph Larmor wrote the introduction for the 1905 English edition and never used "classical" so broadly.30
But do all these fine distinctions in the use of an open and more or less general concept matter? Is this just splitting hairs? To understand how thoroughly particular uses of the concept of the classical could enter the practice of physics and shape perceptions of its periodization, we need now to consider their role in the development of two new theories. Histories of relativity and quantum theory are commonly used to draw conclusions about the nature of modern physics and the struggle required to break free of the classical past. Here I will move in just the opposite direction, analyzing uses of the concept of the classical within these theories themselves in order to shed new light on their development. In this regard, relativity and quantum theory reveal very different dynamics, incorporating concepts of classical theory in different ways and at different times. Displaying these differences will highlight the extent to which the concept of classical physics we now accept was both constructed in the light of the modern and defined by proponents of the new.