FIN-DE-SIÈCLE PHYSICS: A WORLD PICTURE IN FLUX
The philosopher and mathematician Alfred North Whitehead once referred to the last quarter of the nineteenth century as "an age of successful scientific orthodoxy, undisturbed by much thought beyond the conventions.... one of the dullest stages of thought since the time of the First Crusade" (Whitehead 1925, 148). It is still commonly believed that physics at the end of the century was a somewhat dull affair, building firmly and complacently on the deterministic and mechanical world view of Newton and his followers. Physicists, so we are told, were totally unprepared for the upheavals that took place in two stages: first, the unexpected discoveries of x-rays, the electron, and radioactivity; and then the real revolution, consisting of Planck's discovery of the quantum of action in 1900 and Einstein's relativity theory of 1905. According to this received view, not only did Newtonian mechanics reign supreme until it was shattered by the new theories, but the Victorian generation of physicists also naively believed that all things worth knowing were already known or would soon become known by following the route of existing physics. Albert Michelson, the great American experimentalist, said in 1894 that "it seems probable that most of the grand underlying principles have been firmly established and that further advances are to be sought chiefly in the rigorous application of these principles to all the phenomena which come under our notice" (Badash 1972, 52). How ironic, then, that Professor Röntgen's new raysthe first of several discoveries that defied explanation in terms of the known "grand underlying principles"were announced only a year later. And how much more important the new physics of the early twentieth century appears if compared with views such as Michelson's.
The received view is in part a myth, but like most myths, it has a foundation in fact. For example, Michelson was not the only physicist of the decade who expressed the feeling that physics was essentially complete and that what remained was either applied physics, more precise measurements, or relatively minor discoveries. When Max Planck entered the University of Munich in 1875, he was warned by a professor of physics that his chosen subject was more or less finished and that nothing new could be expected to be discovered. Yet, although such feelings certainly existed among physicists, it is questionable how widespread they were. Very few theoretical physicists of the 1890s seem to have accepted Michelson's view, and after the amazing discoveries of Röntgen, Henri Becquerel, J. J. Thomson, and the Curies, even the most conservative experimentalist was forced to realize its fallacy.
What about the claim that physics a hundred years ago rested on orthodoxy and a complacent acceptance of Newtonian mechanics? Was there a mechanical worldview, or any commonly accepted worldview at all? Whereas the question of completeness can be discussed, it is squarely a myth that physicists stuck obstinately to the mechanical worldview until they were taught a lesson by Einstein in 1905 (or by Planck in 1900). The most important nonmechanical trend was based on electromagnetic theory, but this was only one of the indications of a widespread willingness to challenge the mechanical worldview and seek new foundations, either opposed to it or radical modifications of it. According to the classical mechanical world picturethe Laplacian version of Newtonianism (not to be confused with Newton's own ideas)the world consisted of atoms, which were the sites of, and on which acted, various forces of long and short ranges. The gravitational force was the paradigmatic example of such forces acting at a distance over empty space. With the advent of field theory, the mechanism of force propagation changed, but Maxwell and most other field physicists continued to seek a mechanical foundation for their models. The most important conceptual shift was perhaps the rise to prominenceindeed, necessityof a universal ether as the quasihypothetical, continuous, and all-pervading medium through which forces propagated with a finite speed.
In 1902, in the final part of a textbook on optics, Michelson declared his belief that "the day seems not far distant when the converging lines from many apparently remote regions of thought will meet on ... common ground." He went on, "Then the nature of the atoms, and the forces called into play in their chemical union; the interactions between these atoms ... as manifested in the phenomena of light and electricity; the structures of the molecules and molecular systems of which the atoms are the units; the explanation of cohesion, elasticity, and gravitationall these will be marshaled into a single compact and consistent body of scientific knowledge" (Michelson 1902, 163). And this was the same Michelson who, eight years earlier, had suggested that physics was near its end. Was it the discoveries of the electron and radioactivity that caused the changed attitude? Or perhaps Planck's discovery of the radiation law based on the notion of energy quantization? Not at all; these recent discoveries were not mentioned in the book. Michelson's enthusiasm was rooted in "one of the grandest generalizations of modern science ... that all the phenomena of the physical universe are only different manifestations of the various modes of motion of one all-pervading substancethe ether."
Maxwell considered the possibility of explaining gravitation in terms of his electromagnetic theory, but abandoned the attempt after realizing that he would then have to ascribe an enormous intrinsic energy to the ether. Other Victorian physicists were less easily discouraged and there were, in the last quarter of the century, many attempts to either explain or revise Newton's divine law of gravitation. Some of these attempts were based on electrodynamics, others on hydrodynamic models. For example, in the 1870s, the Norwegian physicist Carl A. Bjerknes studied the motion of bodies in an infinite and incompressible fluid and was led to the conclusion that two pulsating spheres would give rise to forces between them varying inversely to the separation of their centers. He considered this a kind of hydrodynamic explanation of gravitation, or at least an interesting analogy. Bjerknes's work was taken up by some British theorists and, in 1898, was revived by the German Arthur Korn at the University of Munich, who developed a hydrodynamic theory of gravitation. At that time, however, electrodynamics was in focus, and complicated hydrodynamic models in the style of Bjerknes and Korn failed to arouse much interest.
Related to hydrodynamical thinking, but of more importance and grandeur (if, in the end, no more successful), were the attempts to construct the world solely out of structures in the ether. The most important of the nonelectromagnetic theories was the vortex atomic theory, originally suggested in 1867 by William Thomson (later, Lord Kelvin) and subsequently developed by a whole school of British mathematical physicists. According to this theory, the atoms were vortical modes of motion of a primitive, perfect fluid, usually identified with the ether. In his Adams Prize essay of 1882, young J. J. Thomson gave an elaborate account of the vortex theory and extended it to cover chemical problems, including affinity and dissociation. The theory was also applied to electromagnetism, gravitation, and optics and was an ambitious attempt to establish a unitary and continuous "theory of everything" based solely on the dynamics of the ether. As late as 1895, William Hicks gave an optimistic report on the state of art of the vortex atom at the annual meeting of the British Association for the Advancement of Science (BAAS). Hicks's view of the goal of theoretical physics is worth quoting at some length:
While, on the one hand, the end of scientific investigation is the discovery of laws, on the other, science will have reached its highest goal when it shall have reduced ultimate laws to one or two, the necessity of which lies outside the sphere of our recognition. These ultimate lawsin the domain of physical science at leastwill be the dynamical laws of the relations of matter to number, space, and time. The ultimate data will be number, matter, space, and time themselves. When these relations shall be known, all physical phenomena will be a branch of pure mathematics. (BAAS Report 1895, 595)
As we shall see, very similar views continued to play an important role throughout the twentieth century. Although many of Hicks's contemporaries would have subscribed to his philosophy, by 1895, the vortex theory of atoms had been abandoned by most physicists. Decades of theoretical work had led to no real progress and the grand vortex program was degenerating into sterile mathematics.
Much the same can be said of another hydrodynamic atomic theory, the "ether squirt" theory worked out by the mathematician Karl Pearson in the 1880s and 1890s. According to this theory, the ultimate atom was a point in the ether from which new ether continuously flowed in all directions of space. Like the vortex theorists, Pearson applied his theory to a variety of problems and believed it would be able to explainin principlegravitation, electromagnetism, and chemical phenomena. Although Pearson's theory did not attract the same kind of interest as the vortex theory, it is worth mentioning because it included not only sources but also sinks of etherthat is, a kind of negative matter. Gravitationally "negative" matter, which repels ordinary matter but attracts other negative matter, had already been discussed in the 1880s by Hicks within the framework of the vortex atomic theory, and the strange concept reappeared in Pearson's theory, as well as in other discussions of fin-de-siècle physics. For example, the British physicist Arthur Schuster speculated lightheartedly that there might exist entire stellar systems of antimatter, indistinguishable from our own except that the two stellar systems would be repelled rather than attracted. Not only did he introduce the names "antimatter" and "antiatoms" in 1898, but he also suggested that colliding matter and antimatter would annihilate each other, thus anticipating an important concept of later quantum physics.
In Pearson's version of antimatter, ether poured in at a squirt and disappeared from our world at a sink. Where, in the first place, did the ether come from? According to Pearson, writing in 1892, it would not simply appear ex nihilo, but would possibly come from a fourth dimension, to which it would again return. Here we have another concept, usually seen as an invention of twentieth-century relativity theory, turning up unexpectedly in the physics of the old worldview. In fact, ideas of hyperspaces and their possible significance in physics were not new in the 1890s. In 1870, the British mathematician William Kingdon Clifford used Riemann's notion of curved, non-Euclidean geometry to suggest that the motion of matter and ether was in reality the manifestation of a variation of the curvature of space. This general idea of a "geometrization of physics" was well known at the end of the nineteenth century and inspired several physicists, astronomers, and mathematicians, not to mention science fiction authors, such as H. G. Wells. For example, in 1888, the eminent American astronomer Simon Newcomb suggested a model of the ether based on hyperdimensional space, and in 1900, the German Karl Schwarzschild made much use of non-Euclidean geometry in his astronomical work. Although these and other works were often speculative and always hypothetical, at the end of the century there existed a small group of researchers who considered hyperspace models of the ether or otherwise attempted to link four-dimensional space to problems of physical interest. Speculative or not, such attempts were considered legitimate within the spirit of physics characteristic of the 1890s.
The hydrodynamic ether models differed from the Laplacian program in physics, but they nonetheless rested on mechanical ground and were not attempts to overthrow the Newtonian worldview. Hydrodynamics, after all, is the mechanical science of fluid bodies. Thermodynamics, the science of heat and other manifestations of energy, constituted a much more difficult problem for the classical worldview. This branch of physics was sometimes argued not only to be different from mechanics in principle, but also to have priority over mechanics as a more satisfactory foundation on which all of physics could be built. In the 1890s, together with electrodynamics, thermodynamics entered as a competitor to mechanics as far as foundational problems were concerned. In this decade, there was a continual discussion of the unity of physics, and it was not at all clear what discipline could best serve as the foundation of the unity that almost all physicists believed their science must have.
Whereas the law of energy conservation was successfully explained in mechanical terms, the second law of thermodynamics did not succumb so easily to mechanical principles. For one thing, the laws of mechanics are reversible, or symmetric in time, whereas the second law of thermodynamics expresses an irreversible change in entropy. In his famous statistical-mechanical theory of entropy, developed first in 1872 and more fully in 1877, Ludwig Boltzmann believed he had reduced the second law to molecular-mechanical principles, but his interpretation was challenged and became the subject of much controversy. One of his critics, the German physicist Ernst Zermelo, argued in 1896 from Poincaré's so-called recurrence theorem that the second law could not be derived from mechanics and thus was incompatible with a unitary mechanical world picture. Boltzmann denied the validity of Zermelo's argument and remained convinced that there was no deep disagreement between mechanics and thermodynamics.
According to the physicist Georg Helm and the chemist Ludwig Ostwald, both Germans, energy was the most important of the unifying concepts of the physical sciences. A generalized thermodynamics was therefore held to replace mechanics as the foundation of physics. Helm and Ostwald came to this conclusion about 1890 and called their new program energetics. The new science of energetics was, in many ways, contrary to the mechanical world picture and was thought of as a revolt against what was called "scientific materialism." This revolt included the position that mechanics was to be subsumed under the more general laws of energetics in the sense that the mechanical laws were held to be reducible to energy principles. Another aspect of energetics was its denial of atomism as other than a useful mental representation. Ostwald and some other physical chemists, including Pierre Duhem in France, argued that the belief in atoms and molecules was metaphysical and that all empirical phenomena could be explained without the atomic hypothesis.
The energetics program was considered enough of a challenge to the traditional molecular-mechanical view that it was taken up as a discussion theme at the annual meeting of the German Association of Natural Scientists and Physicians in Lübeck in 1895. The meeting featured a famous discussion between Boltzmann, who attacked the energeticists, and Helm and Ostwald, who argued against the mechanical world picture. It is interesting to note that neither Boltzmann nor others present at the meeting simply defended the classical-mechanical worldview or fully subscribed to the views that Helm and Ostwald criticized. Boltzmann declared that the mechanical worldview was a dead issue and that the "view that no other explanation can exist except that of the motion of material points, the laws of which are determined by central forces, had generally been abandoned long before Mr. Ostwald's remarks" (Jungnickel and McCormmach 1986, 222). All the same, Boltzmann saw no merit in the energetics program and preferred to work on a mechanical foundation, feeling that it alone was sufficiently developed to secure scientific progress.
The energetics alternative received only modest support among physicists and chemists, but criticism of the atomic theory and emphasis on the fundamentality of the energy concept were repeated also by many scientists not directly associated with the energetics program. The leading French physicist, Pierre Curieperhaps better known as the husband of Made Curiemay be an example. In accordance with his positivistic view of science, Curie refrained from materialistic and atomistic hypotheses and favored a phenomenalism inspired by the laws of thermodynamics. He, and several other French physicists, held thermodynamics to be the ideal of physical theory. They argued that energy, not matter, was the essence of a reality that could be understood only as processes or actions. From the early 1880s onward, the Austrian physicist-philosopher Ernst Mach argued for a phenomenological understanding of physics, according to which physical theories and concepts were economical ways of organizing sense data. Mach admitted the usefulness of molecular mechanics, but considered it neither a fundamental theory nor one expressing physical reality. From a foundational point of view, he preferred the energy principles to the laws of mechanics. Again in agreement with Ostwald and his allies, Mach held that atoms were nothing but convenient fictions. Moreover, Mach criticized the very heart of mechanics, the idea of force as expressed by Newton's second law. A somewhat similar foundational criticism of mechanics from a positivistic point of view was undertaken by Heinrich Hertz in his 1894 reformulation of mechanics, building only on the fundamental conceptions of space, time and mass. However, this kind of critical analysis of mechanics did not necessarily involve a wish to abandon the mechanical world picture. In the case of Mach it did, but to Hertz, the new versions of mechanics merely affirmed this picture of the world. In fact, a major aim of Hertz's force-free mechanics was to establish a mechanical theory of the electromagnetic ether.
The mechanical worldview was no longer considered progressive in the 1890s, and even traditionalists had to admit that it was not universally successful. Apart from the troubled relationship between mechanics and the entropy law, there was an older problem related to the kinetic theory of gases. As early as 1860, Maxwell had observed that the measured ratios between the specific heats of diatomic gases at constant pressure ([c.sub.p]) and at constant volume ([c.sub.v]) did not agree with the equipartition theorem based on the mechanical theory. According to this theory, [Gamma] = [c.sub.p]/[c.sub.v] = 1 + 2/n, where n is the number of degrees of freedom of the molecule. The problem was that the predicted result for diatomic gases matched experiments (which gave [Gamma] = 1.4) only if it was assumed that the molecule was rigid and had no internal parts; this assumption seemed inconsistent with the results of spectroscopy, which strongly indicated internal vibrations exchanging energy with the ether. The problem was recognized as an anomaly, but of course, it needed more than a single anomaly to shatter the mechanical world view. Yet the apparent failure of the equipartition theorem was considered serious enough to figure as one of the two clouds in a famous lecture, "Nineteenth Century Clouds Over the Dynamical Theory of Heat and Light," that Lord Kelvin delivered before the Royal Institution in April 1900. The other threat was the failure to explain the motion of the earth through the ether, as exhibited by the ether drift experiment of Michelson and Edward Morley. (For this, see chapter 7.)
The new physics that arose in the early years of the twentieth century was not a revolt against a petrified Newtonian worldview, something analogous to the revolt of Galileo against Aristotelianism. By 1905, the mechanical worldview had been under attack for more than a decade, and for this reason alone, there never was much of a clash between Einstein and Newton. Even more important than the opposition inspired by thermodynamics and energetics was the new and vigorous trend in electromagnetic theory that characterized the 1890s. We shall deal in more detail with this so-called electromagnetic worldview in chapter 8, and here we only emphasize its importance and key elements. The basic problem of physics in the late nineteenth century was perhaps the relationship between ether and matter: Was the ether the fundamental substratum out of which matter was constructed? Or, on the contrary, was matter a more fundamental ontological category of which the ether was just a special instance? The first view, where primacy was given to structures in the ether, became increasingly more common at the turn of the century, when mechanical ether models were replaced by electrodynamic models.
If electromagnetism was more fundamental than mechanics, it made sense to try to derive the mechanical laws from those of electromagnetism, and this was precisely what many theoretical physicists aimed at. Electromagnetism was considered a unifying principle of all science, not unlike the role assigned to energy in Ostwald's energetics. The way in which Ostwald and his energeticist allies spoke of "matter as subordinate to energy" and "all events [being] ultimately nothing but a change in energy" was strikingly similar to the rhetoric of the electrodynamicists, only with "ether" or "electromagnetic field" substituted for "energy." In both cases, materialism was discarded and matter declared an epiphenomenon. Joseph Larmor, the eminent British theorist, had no difficulty imagining a world based on a nonmaterial, transcendent ether. He admitted, as he wrote in 1900, that this might seem "as leaving reality behind us," but defended his ether worldview by arguing that it described an inner reality not directly accessible to the senses (Larmor 1900, vi). This was an argument that Mach, Ostwald, and other phenomenalists would not have accepted. At the beginning of the new century, the monistic, electromagnetic worldview was accepted by a growing proportion of avant-garde physicists in Germany, England, France, and the United States. Physics consisted of the physics of matter and the physics of the electromagnetic ether, and the trend to avoid the unwanted dualism was to identify matter with ether, rather than the other way around. This is not to say that there were no dissenting voices or that the electromagnetic doctrine permeated the entire field of physics. There were physicists whoyears before Einsteinrejected the ether as a metaphysical concept, and there were those who continued to search for mechanical models of the ether or even considered the ether as a special state of ordinary matter. Textbooks of this period usually rested on a mechanical basis and did not reflect the change in worldview discussed in frontier theoretical physics. This is how textbooks usually are: They are by nature conservative and cautious in their attitude toward modern ideas.
The trend of theoretical physics around 1900 was more than a shift in fundamental ideas from mechanics to thermo- and electrodynamics, and it was more than the result of a number of spectacular discoveries. It was part of a change in worldview that had ramifications outside physics and was nourished by the particular Zeitgeist of the period, a spirit of time sometimes characterized as neoromantic. The historian Russell McCormmach has aptly summarized the situation as follows: "The whole cultural configuration at the turn of the century was implicated in the change from mechanical to electromagnetic thinking. The immaterial electromagnetic concepts were attractive in the same measure that the inert, material imagery of mechanics was displeasing" (McCormmach 1970, 495). One important element of this cultural configuration was a widespread antimaterialism. Taking different shapes in the different scientific nations, the antimateralistic doctrine amounted to the belief that "matter is dead." If matter was not the ultimate reality, but merely some manifestation of an immaterial ether, it would not seem unreasonable to challenge other established doctrines derived from the physics of matter, including the permanence of chemical elements and the laws of conservation of matter and energy. Indeed, in some quarters, the very qualities of permanence and conservation were considered suspicious within a world view emphasizing transformation, evolution, and becoming.
As an example, consider the French psychologist and amateur physicist Gustave LeBon, who, in 1896, reported the discovery of what he called "black light"a new kind of invisible radiation that he believed was distinct from, but possibly related to, x-rays and cathode rays. Although LeBon's discovery claim did not fare well, his general ideas of matter, radiation, and ether were received favorably by the public and were, to some extent, representative of the period's Zeitgeist in scientific circles. In his book The Evolution of Matter, a hit that went through twelve editions and sold 44,000 copies, LeBon concluded that all matter is unstable, constantly emitting radiation or "effluvia." Material qualities were held to be epiphenomena exhibited by matter in the process of transforming into the imponderable ether from which it had once originated. According to LeBon, there was no dualism between energy and matter, which just represented different stages in an evolutionary process, the end result of which was the pure ethereal state. Among his many arguments for the continual degradation of matter into ether, LeBon considered radioactivity to be particularly convincing. He shared the view of many physicists that radioactivity is a property exhibited by all matter. Then, if all chemical elements emitted ether-like radiations, would they not slowly melt away and would this not prove the nonmateriality of matter? Or, as LeBon expressed it rather more dramatically, would the ether not represent "the final nirvana to which all things return after a more or less ephemeral existence" (LeBon 1905, 315)? LeBon and many of his contemporaries believed that this was indeed the case.
LeBon's quasiscientific speculations had considerable appeal among the many scientists who were dissatisfied with positivistic ideals and longed for an undogmatic, more youthful science that would better satisfy what they associated with the human spirit. His ideas struck a chord in a period that has been described as a "revolt against positivism" and evenbut less justifiablya "revolt from reason" (MacLeod 1982, 3). Among those who listened with sympathy to LeBon's arguments was the great Henri Poincaré.But LeBon was not a theoretical physicist and his views, although fashionable, were not particularly modern. If he was not taken too seriously by physicists outside France, it may have been because he failed to incorporate the electromagnetic ether into his speculations. Although it is reasonable to speak of a general spirit of physics about the turn of the century, the degree of consensus should not be exaggerated. There were considerable differences among the views of leading individual physicists and there were also important national differences. In Germany and France, for instance, the reaction against the mechanical worldview was more often associated with positivistic virtues and thermodynamic ideals than was the case in England. British physicists typically had no sympathy for the positivistic, fact-oriented view of science championed by Pierre Curie, Duhem, Ostwald, Mach, and others. In 1896, in a critical comment on Ostwald's energetics, the Irish physicist George FitzGerald distinguished between the metaphysically receptive British style and the inductive, unphilosophical German style. "A Briton wants emotion," he wrote, "something to raise enthusiasm, something with a human interest" (Wynne 1979, 171). The battle cry for emotions, actions, and evolutionary processes "with a human interest" was repeated by French neoromanticists, who contrasted their style with that of the supposedly unimaginative Germans. At the same time, they objected to the British style of physics, which they found too mechanistic and lacking in esprit.
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