Hermann Helmholtz

Unifiers and Diversifiers

Science is largely a bipartisan endeavor. Most scientists have no difficulty identifying with one of two camps, which can be called, with about as much accuracy as names attached to political parties, theorists and experimentalists. An astute observer of scientists and their ways, Freeman Dyson, has offered a roughly equivalent, but more inspired, division of scientific allegiances and attitudes. In Dyson’s view, science has been made throughout its history in almost equal measure by “unifiers” and “diversifiers.” The unifiers, mostly theorists, search for the principles that reveal the unifying structure of science. Diversifiers, likely to be experimentalists, work to discover the unsorted facts of science. Efforts of the scientific unifiers and diversifiers are vitally complementary. From the great bodies of facts accumulated by the diversifiers come the unifier’s theories; the theories guide the diversifiers to new observations, sometimes with disastrous results for the unifiers.

         The thermodynamicists celebrated here were among the greatest scientific unifiers of the nineteenth and early twentieth centuries. Three of their stories have been told above: of Sadi Carnot and his search for unities in the bewildering complexities of machinery; of Robert Mayer and his grand speculations about the energy concept; of James Joule’s precise determination of equivalences among thermal, electrical, chemical, and mechanical effects. Continuing now with the chronology, we focus on the further development of the energy concept. The thermodynamicist who takes the stage is Hermann Helmholtz, the most confirmed of unifiers.

Medicine and Physics

Helmholtz, like Mayer, was educated for a medical career. He would have preferred to study physics and mathematics, but the only hope for scientific training, given his father’s meager salary as a gymnasium teacher, was a government scholarship in medicine. With the scholarship, Helmholtz studied at the Friedrich- Wilhelm Institute in Berlin and wrote his doctoral dissertation under Johannes Muller. At that time, Muller and his circle of gifted students were laying the ground work for a physical and chemical approach to the study of physiology, which was the beginning of the disciplines known today as biophysics and biochemistry. Muller’s goal was to rid medical science of all the metaphysical excesses it had accumulated, and retain only those principles with sound empirical foundations. Helmholtz joined forces with three of Muller’s students, Emil du Bois-Reymond, Ernst Brucke, and Carl Ludwig; the four, known later as the “1847 group,” pledged their talents and careers to the task of reshaping physiology into a physicochemical science.

Die Erhaltung der Kraft

If medicine was not Helmholtz’s first choice, it nevertheless served him (and he served medicine) well, even when circumstances were trying. His medical scholarship stipulated eight years of service as an army surgeon. He took up this service without much enthusiasm. Life as surgeon to the regiment at Potsdam offered little of the intellectual excitement he had found in Berlin. But to an extraordinary degree, Helmholtz had the ability to supply his own intellectual stimulation. Although severely limited in resources, and unable to sleep after five o’clock in the morning when the bugler sounded reveille at his door, he quickly started a full research program concerned with such topics as the role of metabolism in muscle activity, the conduction of heat in muscle, and the rate of transmission of the nervous impulse.

       During this time, while he was mostly in scientific isolation, Helmholtz wrote the paper on energy conservation that brings him to our attention as one of the major thermodynamicists. (Once again, as in the stories of Carnot, Mayer, and Joule, history was being made by a scientific outsider.) Helmholtz’s paper had the title Uber die Erhaltung der Kraft (On the Conservation of Force), and it was presented to the Berlin Physical Society, recently organized by du Bois-Reymond, and other students of Muller’s, and Gustav Magnus, in July 1847.

       As the title indicates, Helmholtz’s 1847 paper was concerned with the concept of “force” in German, “Kraft” which he defined as “the capacity [of matter] to produce effects.” He was concerned, as Mayer before him had been, with a composite of the modern energy concept (not clearly defined in the thermodynamic context until the 1850s) and the Newtonian force concept. Some of Helmholtz’s uses of the word “Kraft” can be translated as “energy” with no confusion. Others cannot be interpreted this way, especially when directional properties are assumed, and in those instances “Kraft” means “force,” with the Newtonian connotation.

          Helmholtz later wrote that the original inspiration for his 1847 paper was his reaction as a student to the concept of “vital force,” current at the time among physiologists, including Muller. The central idea, which Helmholtz found he could not accept, was that life processes were controlled not only by physical and chemical events, but also by an “indwelling life source, or vital force, which controls the activities of [chemical and physical] forces. After death the free action of [the] chemical and physical forces produces decomposition, but during life their action is continually being regulated by the life soul.” To Helmholtz this was metaphysics. It seemed to him that the vital force was a kind of biological perpetual motion. He knew that physical and chemical processes did not permit perpetual motion, and he felt that the same prohibition must be extended to all life processes.

      Helmholtz also discussed in his paper what he had learned about mechanics from seventeenth- and eighteenth-century authors, particularly Daniel Bernoulli and Jean d’Alembert. It is evident from this part of the paper that a priori beliefs are involved, but the most fundamental of these assumptions are not explicitly stated. The science historian Yehuda Elkana fills in for us what was omitted: “Helmholtz was very much committed a priori to two fundamental beliefs: (a) that all phenomena in physics are reducible to mechanical processes (no one who reads Helmholtz can doubt this), and (b) that there be some basic entity in Nature which is being conserved ([although] this does not appear in so many words in Helmholtz’s work).” To bring physiology into his view, a third belief was needed, that “all organic processes are reducible to physics.” These general ideas were remarkably like those Mayer had put forward, but in 1847 Helmholtz had not read Mayer’s papers.

         Helmholtz’s central problem, as he saw it, was to identify the conserved entity. Like Mayer, but independently of him, Helmholtz selected the quantity “Kraft” for the central role in his conservation principle. Mayer had not been able to avoid the confused dual meaning of “Kraft” adopted by most of his contemporaries. Helmholtz, on the other hand, was one of the first to recognize the ambiguity. With his knowledge of mechanics, he could see that when “Kraft” was cast in the role of a conserved quantity, the term could no longer be used in the sense of Newtonian force. The theory of mechanics made it clear that Newtonian forces were not in any general way conserved quantities.

       This reasoning brought Helmholtz closer to a workable identification of the elusive conserved quantity, but he (and two other eminent thermodynamicists, Clausius and Thomson) still had some difficult conceptual ground to cover. He could follow the lead of mechanics, note that mechanical energy had the conservation property, and assume that the conserved quantity he needed for his principle had some of the attributes (at least the units) of mechanical energy. Helmholtz seems to have reasoned this way, but there is no evidence that he got any closer than this to a full understanding of the energy concept. In any case, his message, as far as it went, was important and eventually accepted. “After [the 1847 paper],” writes Elkana, “the concept of energy underwent the fixing stage; the German ‘Kraft’ came to mean simply ‘energy’ (in the conservation context) and later gave place slowly to the expression ‘Energie.’ The Newtonian ‘Kraft’ with its dimensions of mass times acceleration became simply our ‘force.’ ”

      I have focused on the central issue taken up by Helmholtz in his 1847 paper. The paper was actually a long one, with many illustrations of the conservation principle in the physics of heat, mechanics, electricity, magnetism, and (briefly, in a single paragraph) physiology.

Pros and Cons

Helmholtz’s youthful effort in his paper (he was twenty-six in 1847), read to the youthful members of the Berlin Physical Society, was received with enthusiasm. Elsewhere in the scientific world the reception was less favorable. Helmholtz submitted the paper for publication to Poggendorff’s Annalen, and, like Mayer five years earlier, received a rejection. Once again an author with important things to say about the energy concept had to resort to private publication. With du Bois-Reymond vouching for the paper’s significance, the publisher G. A. Reimer agreed to bring it out later in 1847.

          Helmholtz commented several times in later years on the peculiar way his memoir was received by the authorities. “When I began the memoir,” he wrote in 1881, “I thought of it only as a piece of critical work, certainly not as an original discovery. . . . I was afterwards somewhat surprised over the opposition which I met with among the experts . . . among the members of the Berlin academy only C. G. J. Jacobi, the mathematician, accepted it. Fame and material reward were not to be gained at that time with the new principle; quite the opposite.” What surprised him most, he wrote in 1891 in an autobiographical sketch, was the reaction of the physicists. He had expected indifference (“We all know that. What is the young doctor thinking about who considers himself called upon to explain it all so fully?”). What he got was a sharp attack on his conclusions: “They [the physicists] were inclined to deny the correctness of the law . . . to treat my essay as a fantastic piece of speculation.”

        Later, after the critical fog had lifted, priority questions intruded. Mayer’s papers were recalled, and obvious similarities between Helmholtz and Mayer were pointed out. Possibly because resources in Potsdam were limited, Helmholtz had not read Mayer’s papers in 1847. Later, on a number of occasions, he made it clear that he recognized Mayer’s, and also Joule’s, priority.

        The modern assessment of Helmholtz’s 1847 paper seems to be that it was, in some ways, limited. It certainly did cover familiar ground (as Helmholtz had intended), but it did not succeed in building mathematical and physical foundations for the energy conservation principle. Nevertheless, there is no doubt that the paper had an extraordinary influence. James Clerk Maxwell, prominent among British physicists in the 1860s and 1870s, viewed Helmholtz’s general program as a conscience for future developments in physical science. In an appreciation of Helmholtz, written in 1877, Maxwell wrote: “To appreciate the full scientific value of Helmholtz’s little essay . . . we should have to ask those to whom we owe the greatest discoveries in thermodynamics and other branches of modern physics, how many times they have read it over, and how often during their researches they felt the weighty statements of Helmholtz acting on their minds like an irresistible driving-power.”

       What Maxwell and other physicists were paying attention to was passages such as this: “The task[of theoretical science] will be completed when the reduction of phenomena to simple forces has been completed and when, at the same time, it can be proved that the reduction is the only one which the phenomena will allow. This will then be established as the conceptual form necessary for understanding nature, and we shall be able to ascribe objective truth to it.” To a large extent, this is still the program of theoretical physics.

Physics

By 1871, the year he reached the age of fifty, Helmholtz had accomplished more than any other physiologist in the world, and he had become one of the most famous scientists in Germany. He had worked extremely hard, often to the detriment of his mental and physical health. He might have decided to relax his furious pace and become an academic ornament, as others with his accomplishments and honors would have done. Instead, he embarked on a new career, and an intellectual migration that was, and is, unique in the annals of science. In 1871, he went to Berlin as professor of physics at the University of Berlin.

       The conversion of the physiologist to the physicist was not a miraculous rebirth, however. Physics had been Helmholtz’s first scientific love, but circumstances had dictated a career in medicine and physiology. Always a pragmatist, he had explored the frontier between physics and physiology, earned a fine reputation, and more than anyone else, established the new science of biophysics. But his fascination with mathematical physics, and his ambition, had not faded. With the death of Gustav Magnus, the Berlin professorship was open. Helmholtz and Gustav Kirchhoff, professor of physics at Heidelberg, were the only candidates; Kirchhoff preferred to remain in Heidelberg. “And thus,” wrote du Bois- Reymond, “occurred the unparalleled event that a doctor and professor of physiology was appointed to the most important physical post in Germany, and Helmholtz, who called himself a born physicist, at length obtained a position suited to his specific talents and inclinations, since he had, as he wrote to me, become indifferent to physiology, and was really only interested in mathematical physics.”

     So in Berlin Helmholtz was a physicist. He focused his attention largely on the topic of electrodynamics, a field he felt had become a “pathless wilderness” of contending theories. He attacked the work of Wilhelm Weber, whose influence then dominated the theory of electrodynamics in Germany. Before most of his colleagues on the Continent, Helmholtz appreciated the studies of Faraday and Maxwell in Britain on electromagnetic theory. Heinrich Hertz, a student of Helmholtz’s and later his assistant, performed experiments that proved the existence of electromagnetc waves and confirmed Maxwell’s theory. Also included among Helmholtz’s remarkable group of students and assistants were Ludwig Boltzmann, Wilhelm Wien, and Albert Michelson. Boltzmann was later to lay the foundations for the statistical interpretation of thermodynamics. Wien’s later work on heat radiation gave Max Planck, professor of theoretical physics at Berlin and a Helmholtz protege, one of the clues he needed to write a revolutionary paper on quantum theory. Michelson’s later experiments on the velocity of light provided a basis for Einstein’s theory of relativity. Helmholtz, the “last great classical physicist,” had gathered in Berlin some of the theorists and experimentalists who would discover a new physics.