Phys. perspect. 5 (2003) 4 –20 1422 –6944/03/010004 –17
© Birkha¨user Verlag, Basel, 2003
Planting in his Neighbor’s Garden: David Hilbert and Early Go¨ttingen Quantum Physics Arne Schirrmacher*
David Hilbert (1862 – 1943) played an important role in establishing quantum physics in Go¨ttingen. I analyze the ways in which his influence was decisive by comparison with Woldemar Voigt (1850–1919). Voigt was the leading Go¨ttingen theoretical physicist before the arrival of Peter Debye (1884–1966), who was appointed to a new professorship in 1914 at Hilbert’s instigation. I portray the Go¨ttingen mathematicians, above all Hermann Minkowski (1864–1909) and David Hilbert, as planting the seeds for the blossoming of quantum physics under their student Max Born (1882–1970) in the 1920s.
Key words: David Hilbert; Woldemar Voigt; Hermann Minkowski; Peter Debye; Max Born; Go¨ttingen; quantum physics; theoretical physics.
Introduction Hilbert … had a nice house on Wilhelm-Weber Strasse, with a big garden in back of it, and he was very fond of cultivating fruit trees, pears and apples, and wall trees, on the Spalier [trellis]. On one of the walls of his garden he had a long blackboard with a small roof on top of it so that even in rainy weather he could walk up and down, up and down, and just jot down things on the blackboard and think.1 Go¨ttingen is widely recognized as of great importance for the development of modern physics and its mathematization. The creation of matrix mechanics in 1925 by Werner Heisenberg, Max Born, and Pascual Jordan is the most striking development, but this did not occur overnight (not even on the island of Helgoland). A closer look at physics in Go¨ttingen in the first quarter of the 20th century reveals a rather drastic reorganization of a research program from one that was initially grounded in an experimentally guided phenomenological approach to one that was more speculative and strongly mathematical. How did this marked change come about, and who therefore laid the basis for the glorious (and sometimes glorified) Weimar era of Go¨ttingen physics? I will argue that a considerable share of this reshaping of Go¨ttingen physics was due to the local mathemati*
Arne Schirrmacher received his Ph.D. degree in mathematical physics in 1994 at the University of Munich. He has worked on the history of modern physics and mathematics at the Max-Planck-Institute in Berlin, the Deutsches Museum in Munich, and the Hilbert Edition Project at the University of Go¨ttingen. He is currently a member of the Munich Center for the History of Science and Technology at the Deutsches Museum in Munich. 4
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cians, in particular to David Hilbert (1862 – 1943), who planted the seeds for this development well before the Great War, which then blossomed so beautifully in the 1920s. I will focus specifically on the contrast between Hilbert’s agenda for physics, especially on his investment of time and money in promoting physics research between 1909 and 1919, and that of Woldemar Voigt (1850 – 1919), the leading theoretical physicist in Go¨ttingen at the time. In doing so, my presentation will mirror a particular context of Go¨ttingen academic life, that of an exclusive community living in a garden-city environment.2 In attributing a decisive impact on Go¨ttingen physics to Hilbert, the leader of the Go¨ttingen mathematics community, we might first explore his general attitude toward physics. This clearly stemmed from his axiomatic program, first applied to Euclidean geometry, as demonstrated most prominently in the sixth problem of his 1900 Paris lecture,3 in which he proclaimed the axiomatization of physics to be a major aim of 20th-century mathematics. Then, in 1905, in a lecture course on the ‘‘Logical Principles of Axiomatic Thinking,’’ he demonstrated successful axiomatization of physical theories with examples from mechanics, thermodynamics, electrodynamics, and even psychophysics.4 Hermann Minkowski (1864 – 1909) had raised Hilbert’s interest in physics already before the turn of the century, as their correspondence reveals, but their focus was then on the application of the axiomatic method to physical theories that were considered to be well-established and elaborated.* Their focus, however – and this is one of my main points – changed towards unfinished or incomplete theories, and this change was related to the entry of the quantum into physics. In 1906 Minkowski turned his interest towards Max Planck’s black-body radiation theory, and in the summer semester of 1907 he gave a lecture course on heat radiation. Stimulated by Planck’s work, he and Hilbert also made ambitious plans to begin a joint project on statistical mechanics and heat radiation. ‘‘It is my very intention,’’ Minkowski told his audience, and also Professor Hilbert is of the same opinion and has similar aspirations, to win the pure mathematicians … over to the inspirations that flow into mathematics from the side of physics. It is not unlikely that during the following years we will treat in seminars mathematical-physical theories, in particular of heat radiation.5 Thus, the advent of quantum theory inspired mathematicians, and especially Hilbert after Minkowski’s sudden death in 1909, to reshape Go¨ttingen physics. But let us first look over the fence and view the riches of the physicists’ fields.
The Neighbor’s Garden For mathematicians the neighbor’s garden was physics, theoretical physics in particular. The main representative of this field in Go¨ttingen was Woldemar Voigt, *
Corry concluded that: ‘‘In Hilbert’s view the definition of systems of abstract axioms and the type of axiomatic analysis described above was meant to be retrospectively conducted for ‘concrete’ well-established and elaborated mathematical entities.’’ See Corry, ‘‘David Hilbert’’ (ref. 4), p. 115.
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although both theory and experiment were shared between Voigt and his colleague Eduard Riecke (1845 – 1915). Also in Go¨ttingen were the geophysicist Emil Wiechert (1861 – 1928), the astronomer Karl Schwarzschild (1873 – 1916), and the fluid dynamicist Ludwig Prandtl (1875 – 1953), among others. Voigt was responsible for teaching the theoretical parts of physics and for supervising the more mathematically minded students. To date he has received scant attention.6 Born in 1850 in Leipzig, Voigt (figure 1) grew up under the influence of his merchant family, protestant sermons, and Leipzig music, which instilled in him a deep love of Bach’s cantatas, so much so that he would study and perform them in private ensembles for the rest of his life. He received his doctorate in physics at the University of Ko¨nigsberg in 1874, taught there for a period, and in 1883 became full professor at the University of Go¨ttingen, where he remained for the rest of his life. In his research, he cultivated the seeds sown in his doctoral dissertation at Ko¨nigsberg, which he wrote under the influential physicist and mathematician Franz Neumann (1798 – 1895), and which dealt with the physics of crystals, one of Neumann’s early specialties. Voigt wrote numerous papers on crystalline properties
Fig. 1. Woldemar Voigt (1850 – 1919) around 1910 as he appeared on a postcard series of Go¨ttingen professors. Credit: Manuscript Department, University of Go¨ttingen.
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and effects and consolidated his knowledge in two books in 1898 and 1910.7 Voigt’s work constituted some of the prominent trees in the Go¨ttingen physicists’ garden, and roaming among them was a large international school of students and researchers.8 Not so easy to understand is why Voigt’s work plays a rather secondary role in the history of physics. It would be too simplistic and even incorrect to paint Voigt’s physics as old-fashioned and not abreast of current developments. He was very much interested in the Zeeman effect, for example. He also followed developments in spectroscopy and was well-informed about the emerging quantum theory. Thus, he was among the first physicists who cited Planck’s black-body radiation theory in a textbook of 1904, but he did not make much of it.9 He presented Planck’s black-body radiation formula and acknowledged its experimental adequacy, but he did not discuss any of its conceptual implications. Paul Drude, Voigt’s student and disciple, went further in the second edition of his well-known textbook on optics of 1906, which would not have eluded Voigt, but just as with Albert Einstein’s penetrating lecture on the present state of the radiation problem in Salzburg in 1909, which Voigt witnessed, did not prompt any second thoughts in him.10 One reason that these early ideas on quantum physics made little impact on Voigt can be traced to his deep doubts about microscopic models and mechanisms. To him they were just Arbeitshypothesen, working hypotheses, apart from physical reality. They merely reflected personal tastes and, as he put it, the ‘‘difference in the organization of the human mind.’’ Although he welcomed the variety that he found in the sciences, as in the arts, he was looking for more general truths, which he believed he would find in symmetry principles and mathematical structures that were independent of the details of these more or less imaginative microscopic models.11 He argued, for example, that the high expectations that spectroscopic data would suggest molecular properties were unfulfilled. Even worse, the laws of spectral series appeared to hold not for normal, healthy molecules but only for damaged and ill ones. No matter how important a ‘‘pathology’’ of molecules will become with time, so far we know so desperately little about the structure and inner life of these objects that we currently can hardly expect fruits from the study of their ‘‘symptoms of disease.’’ As a result we must refrain completely from asking the question as to what extent at all the light phenomena correspond to the ‘‘material bone structure’’ of the molecule and to what extent they can provide information about it.12 Voigt’s doubts about whether spectral analysis could be seen as a healthy and fruitful branch of physics surfaced in his voluminous textbook on crystal physics of 1910. Since ‘‘the success of structural theories does not reach very far,’’ he wrote in his magnum opus, ‘‘there is no cause to devote much space to structural theories in a textbook on crystal physics.’’13 On the contrary, it is ‘‘more rational’’ to start from potential functions than from molecular forces.14 Even when atomistic treatments and the use of the quantum hypothesis became widespread among Go¨ttingen physicists, Voigt did not change his point of view. In 1915 he still embraced his phenomenological approach and gave a careful argument in its favor in an article
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in the volume on physics in the impressive German encyclopedia, Die Kultur der Gegenwart (The Culture of the Present).15 Voigt did not believe in the simplifying power of molecular reductionism, but he advocated a no less modern program for the unification of physics: the organization of the known facts and properties of crystalline matter according to their mathematical nature (more precisely, according to the transformation and symmetry properties of the mathematical objects that describe their effects). To devise a classification scheme according to rather external categories was to Voigt the most progressive approach. Thus, in Voigt’s physical garden all plants, that is, all physical effects, were labeled meticulously and ordered not according to their color or size but according to a certain mathematical scheme of symmetries. Look at the chapter headings in his 1910 Kristallphysik (figure 2). We see that, just as in systematic botany, the crossing of attributes (a scalar with a vector, a scalar with a tensor triple, a vector with a vector, and so on) results in observable ‘‘hybrids’’ (pyroelectricity and pyromagnetism, heat dilatation and tensor pyroelectricity, and so on). That a reorientation of Go¨ttingen physics towards quantum problems and atomistic reductionism would not come from Voigt followed from his deep conviction that a physical ‘‘genetics’’ (according to this analogy) would not be able to simplify the structure of the flourishing variety but rather would lead one astray: ‘‘Any solved question,’’ Voigt explained in a rectorial address to the university in June 1912, only gives birth to ten new ones and the mysteries become more and more enigmatic. To mention a single one: All those new results that are accumulated in huge quantities make the constitution of the atom nothing but more incomprehensible as they show the most unexpected phenomena. What kind of an object of inconceivable smallness is this that has the ability to execute and emit thousands of different but at the same time fully determined oscillations that are characteristic of the substance?16 Voigt not only mistrusted bold atomistic approaches in analyzing the structure of matter; he also concluded that he simply did not possess the intellectual resources for such ambitious research. He complained to Hendrik Anton Lorentz that while Planck and Lorentz ‘‘would progress in the ether of the most general questions I grub as a mole for small specialties in the soil.’’17 Hilbert’s visitors would be told by his housekeeper to turn their eyes in the opposite direction: ‘‘If you don’t see the professor, look up in the trees.’’18
Introducing New Plants and Fertilizers By the time that Voigt in 1912 made his pessimistic statements above, Hilbert had already incorporated modern physics into his teaching. A year earlier, in the summer semester of 1911, he had treated recent physical theory in his course on mechanics and had included in it brief discussions of relativity and black-body radiation. Then, in the following winter semester of 1911 – 1912, he treated these and other modern subjects much more extensively in his course on the kinetic
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Fig. 2. Source: Voigt, Lehrbuch der Kristalloptik (ref. 7), page XV. The heading of Chapter IV is ‘‘Correlations between a scalar and a vector. (Pyroelectricity and Pyromagnetism)’’ and that of Chapter V is ‘‘Correlations between a scalar and a tensor triple. (Thermal Dilation and Tensorial Pyroelectricity).’’
theory of gases. This latter course stands in stark contrast to Voigt’s methodological views and must be seen as a criticism of them. Hilbert made his standpoint clear immediately at the beginning of his course on kinetic theory. The phenomenological point of view, which he called A, must be discarded, because it has no unifying power; it merely fragments the whole of physics into many single chapters, each with its own principles. Hilbert argued that based on the atomic theory and an axiomatic formulation a better approach is guaranteed for all of physics, which he called B, and which he would follow in his current lectures. The best approach, however, which he called C, would be a theory based on the molecular structure of matter, and he would follow this approach in future lectures.19 Thus, from Hilbert’s introduction to his course on kinetic theory, I have garnered the quotations presented in table 1, which display his analysis of the approaches A, B, and C with respect to their unifying power, the level of understanding and knowledge they provide, the mathematical tools and techniques they involve, and their proponents, with Hilbert clearly intending Voigt to be seen as the proponent of the phenomenological approach A.
‘‘partial differential equations’’
[Voigt]
proponent
‘‘urgently to be left behind in order to penetrate into the actual sacred objects of theoretical physics’’
‘‘a first step in understanding’’
mathematics used
knowledge status
‘‘whole of physics is fragmented in single chapters: thermodynamics, electrodynamics, optics etc.’’
unifying power
‘‘each field builds on specific basic assumptions’’
‘‘A) … phenomenological’’
approach
‘‘this lecture’’ (Hilbert 1911–1912)
‘‘entirely different’’ ‘‘not yet fully developed’’ ‘‘probability calculus’’
‘‘attempt to find a system of axioms valid for all physics’’
‘‘single point of view for all phenomena’’
‘‘B) … on the basis of atomic theory’’
‘‘one of the next semesters’’ (Hilbert 1912–1913)
? [new mathematics]
? [deeper foundation, axioms=reality]
‘‘goes much beyond B’’
‘‘C) … a theory of the molecular structure of matter’’
Table 1. Citations from the introduction of Hilbert’s lecture notes on ‘‘Kinetische Gastheorie,’’ winter semester 1911–1912 (ref. 19).
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We see in table 1 a certain parallel between the reduction of mathematics to a few basic axioms and the reduction of physics to a few basic properties of atoms. Hilbert’s major aim thus appears to have been a theory of the molecular structure of matter that was based on atomic theory and would permit all physical properties to be deduced from something even deeper than the system of axioms called for in approach B. What approach C actually should look like is not entirely clear, since Hilbert did not comment on the level of understanding and knowledge it would provide and on the mathematics it would involve. His scheme, however, suggests how he would fill in these blanks. After a ‘‘first step in understanding’’ by phenomenological means (A) and a successful axiomatization ‘‘on the basis of atomic theory’’ (B), Hilbert’s objective clearly was to relate the basic notions employed in the axiomatization of physics to actual physical objects (C). Furthermore, just as partial differential equations (A) are the toolkit for phenomenologists, mathematics like the probability calculus (B) is employed by atomists. Thus, in the realm C, which was the goal of people like Hilbert who believed in a pre-established harmony in nature, one could hope that advanced or novel mathematics would reveal the identity of the axiomatic model and physical reality. (This is a view that is not so unfamiliar to physicists today when they say, for example, that elementary particles are representations of certain symmetry groups.) To see the extent to which Hilbert’s alternative to Voigt’s physics was related to quantum discussions around 1911, we can compare their characteristic elements with Hilbert’s interests. Thomas S. Kuhn identified three indicators for taking the quantum seriously: concern with the black-body radiation law, the quantum discontinuity, and the theory of specific heats as related to atomic structure.20 Planck’s black-body radiation law, as we noted above, was considered by Hilbert as worthy of appearing in his lectures on mechanics in the summer semester of 1911. Furthermore, in his course on ‘‘Radiation Theory’’ in the summer semester of 1912, Hilbert emphasized that ‘‘the atomic theory, the principle of discontinuity, which emerges clearer and clearer is no hypothesis anymore, but like the theory of Copernicus is experimentally proven fact.’’21 Finally, the theory of specific heats and the kinetic theory of matter became topics that Hilbert treated in his lectures on the ‘‘Molecular Theory of Matter’’ in the winter semester of 1912 – 1913.22 Thus, in Kuhn’s sense, Hilbert was one of the early Go¨ttingen converts to the quantum theory. From this I think it is clear that Hilbert’s understanding of axiomatics had changed considerably since 1905; it appears, in fact, that he reinterpreted his axiomatic method around 1911 when his interests in physics changed and he turned his attention to quantum theory. Roughly speaking, Hilbert’s turn was one from applying his axiomatic method to well-established physical theories like mechanics and thermodynamics to a concern with current research questions. Instead of only laying deeper foundations for physics, the axiomatic method became for Hilbert a genuine methodology for always and from the outset revealing basic physical assumptions and simultaneously checking for the consistency of physical theories.23 He became increasingly aware that modern physical theories evolved by attempting to add new hypotheses to the established corpus of knowledge, as in the case of the quantum hypothesis or the principle of entropy increase, which made
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the question of consistency imperative. Only clarity about the independence and consistency of the basic assumptions of physics appeared to serve as a successful guide for further research. Moreover, it would be wrong in the empirical sciences to wait for their maturation before attempting an axiomatic treatment of them. In Hilbert’s private notebooks one can find, for example, the following entry written sometime between 1905 and 1911: ‘‘I protest against the objection that physics was not developed enough to be axiomatized. Any science is at any time not only ripe enough but necessarily requires axiomatization, understood in the correct sense.’’24 More statements of this type can be found in later years as Hilbert had to explain again and again what he took to be the correct sense of his axiomatic method, which in any case was not the formalistic procedure many later mathematicians attributed to him. Hilbert’s view eventually led him to something that one could characterize best as disciplinary imperialism. In a famous lecture in Zurich in 1917 on the broad topic of ‘‘axiomatic thinking,’’ he asserted: I believe: Everything that can be the object of scientific thought at all becomes the object of [6erfa¨llt] the axiomatic method and hence of mathematics as soon as it is ripe for forming a theory. By progressing to deeper and deeper layers of axioms in the above described sense, we also gain deeper and deeper insight into the nature of scientific thought itself and realize the unity of our knowledge more and more. Under the sign of the axiomatic method mathematics appears to be called upon to have a leading role in science.25 Thus, by 1917 Hilbert was convinced that by posing scientific problems correctly in mathematical terms their solutions would be guaranteed. Reducing physics, and even chemistry and biology, to mathematics would eventually lead to a kind of unified science. Needless to say, Hilbert’s view was far too optimistic and overlooked the particular complexities of the various fields of science. His view, nonetheless, was the driving force for him to invest heavily in physics, which contributed to a marked change in the conditions under which physics flourished in Go¨ttingen after the Great War. Before I describe in more detail some of the plants and fertilizers that Hilbert and the Go¨ttingen mathematicians deployed in the physicists’ garden, let me first say a few words about Hilbert’s background and personality. Born in Ko¨nigsberg in 1862, twelve years after Voigt, Hilbert (figure 3) came from a family of protestant merchants and judges. He was educated in the humanistic tradition at the best Ko¨nigsberg Gymnasium, which was neither a happy nor a particularly formative experience. He studied mathematics to avoid memorizing facts. He left the church and had no interest in religious art or music, but popular culture and politics appealed to him. He behaved unconventionally and showed a certain unworldliness, which often were said to be drawbacks of his genius. This, however, probably makes more sense if interpreted as a demonstration of power: He made it clear that he did not have to obey the rules of Kaiserreich academic conduct, while others like Voigt were the personification of the hierarchical order of imperial Germany. Also unlike Voigt, Hilbert changed his field of research a number of times to include the theory of invariants, number theory, the foundations of geometry, integral equations, physics, and other areas. He thus remained in the a6ant-garde. As Hermann
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Fig. 3. David Hilbert (1862 – 1943) around 1910 as he appeared on a postcard series of Go¨ttingen professors. Credit: American Institute of Physics Emilio Segre` Visual Archives, Lande´ Collection, photograph by A. Schmidt, Go¨ttingen.
Weyl remarked, Hilbert was the Pied Piper whom the young mathematicians followed.26 In 1912 Voigt bought a church organ for the Gothic hall in his house at Gru¨ner Weg 1 (now Wagnerstrasse) in Go¨ttingen, and only on rare occasions would he open the windows so that a Bach chorale like Nun lob’ mein Seel could be heard in the garden in front of his veranda. In Hilbert’s house at the other end of the professorial garden city (the so-called Ost6iertel) on Wilhelm-Weber-Strasse, Hilbert’s physics assistant Alfred Lande´ had as part of his duties (which he detested) the playing of the latest music-hall hits (Schlager) on Hilbert’s phonograph at parties using a large needle, which at that time produced the highest volume.27 Hilbert tried to generate the largest scientific volume in Go¨ttingen by inviting leading physicists and mathematicians interested in physics. In 1909 he invited Henri Poincare´ from Paris and in the following year Hendrik Antoon Lorentz from Leiden for special one-week lecture series, and in 1912 he invited Arnold Sommerfeld from Munich to give two lectures on the quantum theory in his class, and on
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the same occasion Sommerfeld reported on Max Laue’s discovery of X-ray diffraction to the Physikalische Gesellschaft (Physical Society), the official seminar of the physics professors. Then, in the last week of April 1913, Hilbert organized a physics congress in Go¨ttingen with Planck, Walther Nernst, Lorentz, Marian von Smoluchowski, Sommerfeld, and Peter Debye as speakers. In this way, Hilbert imported discussion topics and a number of participants in the first Solvay conference to his university,28 and as a consequence strongly influenced and nearly defined future discussions on physics in Go¨ttingen. Most significantly, to support these endeavors, Hilbert diverted money that was dedicated to a specific mathematical field to enrich the physicist’s garden. The money came from the Wolfskehl fund, which was established as a prize for the person who would prove Fermat’s famous last theorem. In this way, Hilbert arranged for number theory to subsidize quantum physics. Additional indicators that show how Go¨ttingen mathematicians became interested in and supported physics research are the increasing proportion of lectures on physics in the Mathematische Gesellschaft (Mathematical Society), and the favorable changes in remuneration of Hilbert’s physics assistants as compared to his mathematics assistants between 1909 and 1919.29 Moreover, an often-overlooked continuity in Go¨ttingen physics through the Great War was the presence of Peter Debye (1884 – 1966) from 1914 to 1920. When one compares Debye’s activities to Hilbert’s interests around 1913 – for example, Debye’s presentation of a paper on Nernst’s heat theorem (the third law of thermodynamics) to Go¨ttingen physicists in January 1913 – the parallels are striking. Hilbert must have been surprised that Debye (figure 4) had anticipated many of his own interests, and this must have been the reason that Hilbert invited Debye to the Wolfskehl congress that April as a replacement for Einstein, who was deeply absorbed in his theory of gravitation.30 Debye’s presentation at the congress made it clear to Hilbert that he should secure him for Go¨ttingen. Hilbert changed his plans to arrange visiting professorships for the Leiden theorist H. A. Lorentz, the Manchester experimentalist Ernest Rutherford, and the Parisian mathematician Jacques Hadamard, and instead invited Debye to Go¨ttingen for the summer semester of 1914. In a letter to the ministry, Hilbert argued that Debye was – with Einstein and Laue unavailable – the next ‘‘outstanding representative’’ of the ‘‘new direction’’ in theoretical physics.31 Debye’s research record clearly classified him as a quantum physicist following in the footsteps of, and at times preceding those of Einstein, whom he had succeeded in Zurich in 1911. In his lecture at the Wolfskehl congress, Debye asserted that the atomistic picture of solids ‘‘agrees in all essential points with reality’’ and that one should test this physical theory experimentally.32 His paper, which was on the equation of state and the quantum hypothesis, combined the well-established classical field of thermodynamics with atomistic reasoning and quantum theory, making him not only the sole available quantum physicist for Go¨ttingen, but also an ideal mediator between the classical physicists Voigt and Riecke, on the one hand, and the mathematicians like Hilbert and Richard Courant who were invading the new physical territory, on the other. Debye was a quantum physicist who was responding to the failures of classical theory. Thus, to Hilbert, the energetic Debye must have represented the
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Fig. 4. Peter Debye (1884 – 1966) in private surroundings. Undated photograph, presumably from the 1920s. Credit: American Institute of Physics Emilio Segre` Visual Archives, Fankuchen Collection.
best chance to plant the fallow ground of quantum physics in Go¨ttingen, to bring the quantum into all of physics, theoretically and experimentally, and to assure the influence of mathematics in this endeavor. To secure Debye for Go¨ttingen, however, was not easy. Debye realized his value and increased his self-confidence during his term as Gastprofessor in the summer semester of 1914. When it then was rumored that Zurich would offer him a salary of 20,000 marks, Go¨ttingen tried to match this lucrative salary,* but fell far short of it. The allotted Go¨ttingen salary had to be supplemented by a contribution from the Wolfskehl fund and one from an unidentified private source, which somewhat ironically turned out to be no one other than Woldemar Voigt. In August 1914 Debye signed an agreement to accept a newly created professorship in theoretical physics in Go¨ttingen, a most unusual event. There are additional instances in which Hilbert and Go¨ttingen mathematicians devoted effort and money in attempting to shape physics in Go¨ttingen. Thus, when
*
In 1914, 20,000 German marks was about $5000, which at the time represented around four or five times the typical annual salary of an American professor.
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Riecke died in 1915 and a successor to him was sought, the Wolfskehl fund again was used to support interviews, and Hilbert was deeply involved in attempts, ultimately unsuccessful ones, to appoint Wilhelm Wien and Friedrich Paschen, both of whom were clear proponents of experimental research in quantum physics.
Harvest What were the consequences of diverting financial and human resources from mathematical to physical fields in Go¨ttingen? Did the investments pay off? How did the short-term consequences differ from the long-term ones? An immediate consequence was Debye’s establishment of courses on quantum theory in the physics curriculum. In addition, Debye and Hilbert offered a famous joint seminar ‘‘On the Structure of Matter,’’ which became the most influential forum for the discussion of this subject by professors, Pri6atdozenten (lecturers), and advanced students. The boldness of Hilbert’s view that the molecular realm is accessible found its realization in a research project that Debye worked on with Paul Scherrer. What is now known as the Debye-Scherrer method of X-ray crystal analysis arose out of their attempt to measure the size and arrangement of the electron orbits in the Bohr atom. Their main idea was that even if the atoms were randomly oriented in space, their constitution should be revealed in the X-ray diffraction pattern they produced. This idea failed for the Bohr atom but not for tiny crystals of the substances they used. In a typically opportunistic move, Debye and Scherrer quickly redefined their objective and developed this powerful method for its own sake.33 This development sheds light on an important general point: The initial objectives, visions, and driving forces of scientists often do not produce the expected scientific results. But in this case, only when we attempt to identify such forces, does Hilbert’s role in establishing quantum physics in Go¨ttingen become visible. For some time it appeared to Hilbert that his dreams had come true. In January 1915, when the German war effort still appeared destined for victory, he wrote to Geheimrat Ludwig Elster, the person in the Prussian Ministry of Culture in charge of Debye’s appointment, that during the ‘‘great revolutionary events in the world outside,’’ a most important development had taken place in the Go¨ttingen mathematical and scientific community. With Debye’s appointment, the discussions in the mathematical seminar, which were attended by almost all Pri6atdozenten in mathematics and physics, had become ‘‘scientific feats.’’ The draft of Hilbert’s letter (figure 5) shows that at first he was tempted to characterize Debye as ‘‘the Newton of chemistry,’’ but he then changed this to ‘‘the Newton of molecular physics.’’ With Debye the much-sought ‘‘mathematical chemistry’’ had arrived. Hilbert concluded that Debye had become a ‘‘true replacement’’ for his esteemed and deceased colleague, Hermann Minkowski, in both personal and scientific respects.34 In early 1915, Debye published a paper in which he attempted to explain the constitution of the hydrogen molecule on the basis of the Bohr atom, and since the properties he calculated seemed to agree with experiment, he asserted that the success of the theory was ‘‘indisputable.’’ Sommerfeld later would wonder about the optimism with which many scientists greeted Debye’s concepts at the time. Even
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Fig. 5. Detail of a draft of a letter from David Hilbert to Geheimrat Ludwig Elster of January 25, 1915. Note that the words ‘‘Newton der Chemie’’ have been struck out and replaced with ‘‘Newton der Molekular Physik.’’ Credit: Manuscript Department, University of Go¨ttingen.
though their optimism turned out to be unjustified, Debye nevertheless exerted considerable influence in making research on atoms and quanta central in Go¨ttingen physics. Hilbert’s characterization of Debye as a true replacement for Minkowski both scientifically and personally can only be understood in light of the ambitious plans that Hilbert and Minkowski had entertained for physics in Go¨ttingen. When Hilbert was twice asked to propose candidates for the Nobel Prize in Physics for 1916 and 1917, he naturally named Debye both times.35 As it turned out, Hilbert’s initial impression of Debye was correct: Hilbert’s ‘‘Newton of chemistry’’ would receive the Nobel Prize for Chemistry two decades later, in 1936. With Debye and his research on concrete and complex quantum problems, Hilbert realized that he would not be able to go on as before on the quantum path. In particular, at this time Hilbert turned to general relativity completely, where he again would make crucial contributions. These contributions, however, became known through his publications, in contrast to those he made in promoting quantum physics in Go¨ttingen, which occurred at the local level through his teaching and academic political activities. These, however, reaped a brilliant harvest for Go¨ttingen physics in the long run through his transplantation of mathematical methods, attitude, and culture into physics, which defined the specific Go¨ttingen flavor of physical theory. Hilbert’s seminar on the ‘‘Structure of Matter,’’ which he introduced in 1914, continued through the period that saw the creation of quantum mechanics in 1925 – 1926 and served as an important forum for the exchange of ideas and discussion of research in quantum and atomic physics. Like Debye, Max Born (1882 – 1970), together with Alfred Lande´ (1888 – 1975), one of Hilbert’s former physics assistants, worked on quantum problems during the Great War. Formally on war duty in Berlin, Born, like Debye, was pursuing the implications of Bohr’s atomic theory. Unlike Debye, however, Born and Lande´ found a negative result: The elastic properties of crystals came out completely wrong when they tried to deduce them from Bohr-like planetary atoms. They concluded that the electrons must be distributed three-dimensionally in the crystal atoms.36 Bohr’s planetary model thus failed in this case, and the problem of how
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electrons could move in orbits that fill three-dimensional space foreshadowed the concept of electron clouds. In this respect, when Debye left Go¨ttingen in 1920, Born was a fitting replacement for him the following year, especially as Born also managed to secure a position there for his friend and experimental alter ego James Franck (1882 – 1964). Born’s research program in Go¨ttingen had its roots in his wartime researches, and was aimed at pressing quantum theory to its limits to see where it might fail. In this way, well before the creation of matrix mechanics in 1925, there was talk about and a certain understanding of ‘‘quantum mechanics.’’ This term appeared in Hilbert’s course ‘‘On the Unity of Scientific Knowledge’’ in the winter semester of 1923 – 1924, and it served as the title of one of Born’s publications in 1924.37 After 1921, when Born, Franck, and Robert Pohl (1884 – 1976) were cultivating the physics fields in Go¨ttingen, the fence between their garden and that of the mathematicians was again high. Only occasionally did Hilbert spend some time on the physics side, as for instance in the winter semester of 1926 when, with the help of Lothar Nordheim, he lectured on quantum mechanics. But he now only came to visit, not to plant. Especially the high teaching loads demanded by the dramatically increased number of students after the war strengthened the disciplinary divide between the mathematics and physics curricula and greatly reduced the time available for interdisciplinary exchanges. Now the accumulated methods, attitude, and culture of a mathematician like Born, who had turned into a theoretical physicist under Hilbert, remained effective even when the master Hilbert was again busy cultivating his own garden. While the mathematical treetops developed further and reached over to its neighboring field of physics, the mathematical roots, the axiomatic foundations of logic and arithmetic, remained too deep and even beyond the ready grasp of Hilbert. Acknowledgments I am greatly indebted to Roger H. Stuewer for his careful editorial work on my paper. I also have benefitted from discussions following presentations of earlier versions of this paper at the History of Science Society meeting in Kansas City in 1998 and at a RIP workshop of the Mathematical Research Institute in Oberwolfach in May 2000. References 1 2
Interview with Paul P. Ewald by Thomas S. Kuhn and George Uhlenbeck, May 8, 1962, Archive for the History of Quantum Physics (AHQP), p. 12. That the university and the garden city areas, where the professors’ villas could be found, were the two characteristic features of Go¨ttingen was a view that can be found, for instance, in the promotional silent film, ‘‘Go¨ttingen die Gartenstadt und Sommeruniversita¨t’’ (Stadtarchiv Go¨ttingen) produced in 1928. For Go¨ttingen architecture and city development, see Maren C. Ha¨rtel, ‘‘Go¨ttingen im Aufbruch zur Moderne. Architektur und Stadtentwicklung, 1866 –1989,’’ in Rudolf von Tadden, et al., ed., Go¨ttingen: Geschichte einer Uni6ersia¨tsstadt (Go¨ttingen: Vandenhoeck & Ruprecht, 1999), pp. 761 – 818; on the conception of the Ost6iertel, see especially p. 768.
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David Hilbert, ‘‘Mathematische Probleme,’’ Nachrichten 6on der Gesellschaft der Wissenschaften zu Go¨ttingen, Mathematisch-physikalische Klasse (1900), 253 –297, with additions in the Archi6 der Mathematik und Physik 1 (1901), 44 – 63, 213–237; English translation in the Bulletin of the American Mathematical Society 8 (1902), 437 –479. This part of Hilbert’s work has been widely discussed in the literature. A comprehensive recent account has been given by Leo Corry, ‘‘David Hilbert and the axiomatization of physics (1894 –1905),’’ Archi6e for History of Exact Sciences 51 (1997), 83 –198. Hilbert’s 1905 lectures are discussed here in detail. Compare also David E. Rowe, ‘‘Einstein meets Hilbert: At the crossroads of physics and mathematics,’’ Physics in Perspecti6e 3 (2001), 379 –424. Hermann Minkowski, ‘‘Wa¨rmestrahlung,’’ manuscript of his summer semester 1907 lecture course; Hilbert papers, Niedersa¨chsische Staats- und Universita¨tsbibliothek Go¨ttingen, Cod. Ms. D. Hilbert 707, p. 2. Apart from obituaries and the like, there are only a few studies of Voigt in the literature. See Gisela Torkar-Oittner, ‘‘Die Ehrendoktorate des Woldemar Voigt – Auszu¨ge aus den Aufzeichnungen seiner Ehefrau Marie,’’ Wissenschaftliches Jahrbuch (Mu¨nchen: Deutsches Museum, 1989), pp. 159 –174; Stefan L. Wolff, ‘‘Woldemar Voigt (1850 –1919) und Pieter Zeeman (1865 –1943) – eine wissenschaftliche Freundschaft,’’ in Dieter Hoffmann, Fabio Bevilacqua, and Roger H. Stuewer, ed., The Emergence of Modern Physics (Pavia: Universita` degli Studi di Pavia, 1996), pp. 169 –177; Stefan L. Wolff, ‘‘Woldemar Voigt (1850 – 1919) und seine Untersuchungen der Kristalle,’’ in Bernhard Fritscher, et al., Toward a History of Mineralogy, Petrology, and Geochemistry (Mu¨nchen: Institut fu¨r Geschichte der Naturwissenschaften, 1998), pp. 269 –280. On Voigt’s physics in historical context, see Christa Jungnickel and Russell McCormmach, Intellectual Mastery of Nature. Theoretical Physics from Ohm to Einstein. Vol. 2. The Now Mighty Theoretical Physics, 1870 – 1925 (Chicago: University of Chicago Press, 1986), Chapter 19, and John L. Heilbron, ‘‘The virtual oscillator as a guide to physics students lost in Plato’s cave,’’ Science and Education 3 (1994), 177 –188. Woldmar Voigt, Die fundamentalen physikalischen Eigenschaften der Krystalle in elementarer Darstellung (Leipzig: von Veit & Comp., 1898); Lehrbuch der Kristallphysik (mit Ausschluss der Kristalloptik) (Leipzig: Teubner, 1910). Jungnickel and McCormmach, Theoretical Physics, p. 269, mention that Voigt in 1906 had 13 and in 1910 24 advanced students working under his supervision. Voigt called Planck’s theory a ‘‘noteworthy combination of probability considerations with the theory of the emission of waves by electric resonators.’’ Woldemar Voigt, Thermodynamik. Vol. 2 (Leipzig: Go¨schensche Verlagshandlung, 1904), p. 355. Cited in Thomas S. Kuhn, Black-Body Theory and the Quantum Discontinuity (New York: Oxford University Press, 1978), p. 135ff. Paul Drude, Optik, Zweite Auflage (Leipzig: Hirzel, 1906), pp. 512 –519; Russell McCormmach, Night Thoughts of a Classical Physicist (Cambridge, Mass.: Harvard University Press, 1982), p. 197. Woldemar Voigt, ‘‘U8 ber Arbeitshypothesen,’’ Nachrichten 6on der Gesellschaft der Wissenschaften zu Go¨ttingen, Mathematisch-physikalische Klasse (1905), 98–116, on p. 114. Voigt, Lehrbuch der Kristallphysik (ref. 7), p. 5ff. Ibid., p. 111. Ibid., p. 120. Woldemar Voigt, ‘‘Pha¨nomenologische und atomistische Betrachtunsweise,’’ in Die Kultur der Gegenwart. Ser. 3, Vol. 3, Teil 1. Physik, ed. Emil Warburg (Leipzig: Teubner, 1915), pp. 714 –731. Woldemar Voigt, Physikalische Forschung und Lehre in Deutschland wa¨hrend der letzten hundert Jahre (Festrede im Namen der Georg-August-Uni6ersita¨t zur Jahresfeier der Uni6ersita¨t am 5. Juni 1912) (Go¨ttingen: Dietrichsche Universita¨ts-Buchdruckerei, 1912), p. 22. Woldemar Voigt to Hendrik Antoon Lorentz, August 19, 1911, Lorentz Correspondence IV (AHQP, microfilm LTZ-4). According to Constance Reid, Hilbert (New York: Springer, 1970), p. 109, this was a frequent saying of Hilbert’s housekeeper to visitors looking for Hilbert. David Hilbert, ‘‘Mechanik der Kontinua aufgrund der Atomtheorie (WS 1911/12),’’ lecture notes taken by Erich Hecke, Staatsbibliothek Preussischer Kulturbesitz, Berlin, Born papers, III.2 folder 1816; the Go¨ttingen copy in the Mathematisches Institut of these lecture notes by Hecke carries the title, ‘‘Kinetische Gastheorie.’’ To be published in David Hilbert, Writings on the Foundations of Mathematics and Natural Science, ed. Ulrich Majer, et al., Vol. 4. Foundations of Physics (Berlin: Springer); hereafter cited as WoFH.
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Kuhn, Black-Body Theory (ref. 9), Chapter 9. David Hilbert, ‘‘Strahlungstheorie,’’ summer semester 1912, lecture notes by Erich Hecke, Mathematical Institute of the University of Go¨ttingen, from the introduction, p. 1ff, to be published in WoFH. David Hilbert, ‘‘Molekulartheorie der Materie,’’ winter semester 1912 –1913, lecture notes by Erich Hecke, Mathematical Institute of the University of Go¨ttingen, to be published in WoFH. Max Born, ‘‘Hilbert und die Physik,’’ Die Naturwissenschaften 10 (1922) 88–93, on 92. Hilbert papers, Cod. Ms. D. Hilbert 600:3, Notebook III, p. 105. David Hilbert, ‘‘Axiomatisches Denken,’’ Mathematische Annalen 79 (1918), 405 –415, on 415. See for example, Umberto Bottazzini, Il flauto di Hilbert: Storia della matematica moderna e contemporanea (Torino: UTET, 1990), p. 5. Marie Voigt, ‘‘Erinnerungen,’’ Microfilm at Deutsches Museum FR 346 (original in manuscript department of Niedersa¨chsische Staats- und Universita¨tsbibliotek, Go¨ttingen), p. 212ff.; Reid, Hilbert (ref. 18), p. 134. Max Born, ‘‘Zur kinetischen Theorie der Materie. Einfu¨hrung zum Kongreß in Go¨ttingen,’’ Die Naturwissenschaften 1 (1913), 297 –299; Max Planck, P. Debye, W. Nernst, M. v. Smoluchowski, A. Sommerfeld, and H. A. Lorentz, Vortra¨ge u¨ber die kinetische Theorie der Materie und der Elektrizita¨t. Gehalten in Go¨ttingen auf Einladung der Wolfskehlstiftung (Leipzig: Teubner, 1914). Arne Schirrmacher, ‘‘The Establishment of Quantum Physics in Go¨ttingen 1900 –24. Conceptional Preconditions-Resources-Research Politics,’’ in Helge Kragh, et al., ed., History of Modern Physics. Proceedings of the XXth International Congress of History of Science (Lie`ge 20 – 26 July, 1997) (Turnhout: Edition Brespol), forthcoming. Arnold Sommerfeld to David Hilbert, November 1, 1912: ‘‘Einstein apparently is so deeply mired in the gravitation problem that he turns a deaf ear to everything else … ’’; cited in Albert Einstein, The Collected Papers of Albert Einstein, Vol. 5. The Swiss Years, Correspondence, ed. Martin J. Klein, A. J. Kox, and Robert Schulmann (Princeton: Princeton University Press, 1993), p. 506. Dekan Ko¨rte to Minister, May 28, 1914, Geheimes Staatsarchiv Preussischer Kulturbesitz, Berlin, Rep. 76 V a, Sekt. 6, Tit. IV, Nr. 1, Bd. XXIV, p. 74. Peter Debye, ‘‘Zustandsgleichung und Quantenhypothese mit einem Anhang u¨ber Wa¨rmeleitung,’’ in Planck, et al., Vortra¨ge (ref. 28), pp. 17 –60, on p. 29. Peter Debye and Paul Scherrer, ‘‘Interferenzen an regellos orientierten Teilchen im Ro¨ntgenlicht I,’’ Nachr. Ges. Wiss. Go¨tt. (1916), 1 – 26; also in Physikalische Zeitschrift 17 (1916), 277 –300. Hilbert to Ludwig Elster, January 25, 1915, Cod. Ms. D. Hilbert 466, item 1. Elisabeth Crawford, J. L. Heilbron, and Rebecca Ullrich, The Nobel Population 1901 – 1937. A Census of the Nominators and Nominees for the Prizes in Physics and Chemistry (Berkeley: Office for History of Science and Technology, 1987), pp. 64 –65, 68–69. Max Born and Alfred Lande´, ‘‘U8 ber die Berechnung der Kompressibilita¨t regula¨rer Kristalle aus der Gittertheorie,’’ Verhandlungen der Deutschen Physikalischen Gesellschaft 20 (1918), 210 –216, on 216. David Hilbert, ‘‘U8 ber die Einheit der Naturerkenntnis,’’ winter semester 1923 –1924, lecture notes by F. Diestel, Mathematical Institute of the University of Go¨ttingen, see for instance pp. 64 and 71. Max Born, ‘‘U8 ber Quantenmechanik,’’ Zeitschrift fu¨r Physik 26 (1924), 379 –395. According to Helge Kragh, Quantum Generations: A History of Physics in the Twentieth Century (Princeton: Princeton University Press, 1999), p. 86, Einstein in 1922 probably was the first person to use the term ‘‘quantum mechanics’’ in an article. Munich Center for the History of Science and Technology Deutsches Museum Museumsinsel 1 D-80538 Munich, Germany e-mail:
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