I f Planck was considered the dean of German theoretical physics, then Sommerfeld was the professor. Ever since his 1906 appointment as Boltzmann’s successor in Munich, Arnold Sommerfeld had produced a steady stream of world-class theoretical atomic physicists. His textbook, Atombau und Spektrallinien, had educated an entire generation of physicists, and even after Hitler’s rise to power his institute remained a center for theoretical research. But two years into the Third Reich, his tenure in Munich neared its end. On January 21, 1935, Reich Minister Rust promulgated a new law, under Hitler’s signature, mandating retirement for university teachers over the age of 65 at the end of the semester. 1 Sommerfeld was 66.
Professor Sommerfeld must have learned privately of the new law before its official enactment: in early January he repeated the choice he had made for his successor back in 1928 — Werner Heisenberg. Heisenberg, barely half Sommerfeld’s age, again could think of no better place to settle than his home town, where his friends, his mother, the blue skies and Alpine hills of Bavaria, and the Sommerfeld tradition all beckoned his return. Leipzig had been only a temporary way station until he could realize his dream of returning to the place of his formative youth. Once again, he gratefully accepted the honor as Sommerfeld’s chosen heir. “If fate should place me in this position,” he wrote his former mentor, “I will make every effort to hold up the tradition of the ‘Sommerfeld school.’” 2 Anticipating difficulties with the party, he outlined for Sommerfeld his political background in case the information
should be needed — as indeed it was. But the initial hurdles to Heisenberg’s appointment were bureaucratic, not political.
Heisenberg was still Gottingen’s choice as intended successor to Max Born. In addition, Debye was in line to succeed Nernst in Berlin and had just accepted the directorship of the soon-to-be-built Kaiser Wilhelm Institute for Physics, Hund was under consideration for a call to Konigsberg, and Otto Scherzer, Sommerfeld’s assistant, was likely to move to Darmstadt. 3 Despite Stark’s ravings against theoretical physics, both the Saxon and Bavarian ministries worried that such a reshuffle would leave Munich or Leipzig without a theoretical physicist. (Their concerns, however, did not deter the new round of dismissals that spring.)
Cause for optimism abounded, nonetheless. With Rust’s approval, the Bavarian Culture Ministry accepted an urgent request from the Munich faculty to allow Sommerfeld to substitute for himself until a successor could be found. 4 The law permitted such a bureaucratic circumvention. More important, the local Nazi lecturer Fuhrer— appropriately named Dr. Fuhrer — who had assigned himself the task of evaluating and approving all personnel matters offered no objection. 5 After Debye assured Sommerfeld that he would not take Heisenberg with him to Berlin and that Heisenberg truly wanted to go to Munich, 6 the Munich faculty submitted its list of candidates to the Bavarian ministry in early summer 1935. According to one source, the list consisted of a single name — Heisenberg. “We would like to help arrange for Heisenberg to work in the place of his choosing,” it proclaimed. 7
Neither the Munich rector nor the Bavarian ministry objected to the prospect of employing one of the most famous physicists remaining in Germany. Heisenberg’s candidacy was duly forwarded to the man who now controlled all university appointments in the new Reich — the chemist Franz Bacher, mathematician Theodor Vahlen’s deputy chief in office W-I of the Berlin Reich Education Ministry (REM).
Anyone who remained in Nazi Germany after the first wave of dismissals was well aware that compromises were required. This was especially so for professors, who were civil servants — that is, employees of the National Socialist state. Those who chose to remain in their teaching positions and those who attempted to advance their careers by obtaining an appointment to another post also chose to accept obvious compromises. The Hitler salute was required before all public lectures, official correspondence had to be signed “Heil Hitler,” and participation in faculty marches, outings, and indoctrination camps could not be avoided. One of the more significant compromises involved professional
association with influential government bureaucrats, most of whom had attained their positions solely through their Nazi connections.
Since by late September no decision had been made regarding Heisenberg’s call to Munich, Debye visited Werner Studentkowski, the Dresden bureaucrat in charge of Saxon university affairs, on Heisenberg’s behalf. Studentkowski had earlier demonstrated his “concern” for objective scholarship by founding the Nazi Students League in Leipzig. He had served as Germany’s first professor of Nazi indoctrination, also in Leipzig. 8 Debye found in Studentkowski a surprisingly ready supporter of his former colleagues, the famous scientists under his administration. After discussing Heisenberg’s transfer to Munich at length, Debye and Studentkowski decided to visit Bacher in Berlin. Both discovered in their separate visits that, with encouragement from Gottingen, Bacher had finally settled on Heisenberg as Born’s successor in Gottingen. Because of this, Bacher had sent Munich’s request for Heisenberg back to Munich with a demand for the usual list of three or more names from which to choose. 9 Debye and Studentkowski could only object to the bureaucrat “that Heisenberg himself does not want to go [to Gottingen] and prefers Munich. . . . Another acceptable candidate will have to be found for Gottingen.” 10
On November 4, 1935, just as Heisenberg and Euler were completing their last contribution to positron theory, the nonlinear Lagrangian discussed in Chapter 17, the Munich faculty duly submitted to the Bavarian Culture Ministry (and ultimately to Bacher) the requested list of candidates for Sommerfeld’s chair. At the top was Heisenberg and, “far behind Heisenberg,” a list of practically all of Sommerfeld’s available former pupils and colleagues: Hund, Wentzel, Kronig, Stuckelberg, Fues, Sauter, Unsold, and Jordan. 11
Faced with renewed pressure from Debye and Studentkowski and the additional support of the dean of the Munich philosophy faculty, Leopold Kolbl, in which Sommerfeld’s institute was located, Bacher and the REM were now inclined to approve Munich’s choice. Chemist Dr. Rudolf Mentzel, the SS officer in charge of REM office W-II (office for military research), had already found another candidate for Gottingen — Richard Becker, a hapless theorist at the highly regarded Technische Hochschule (TH) Berlin (Berlin Technical College), who had run afoul of the local army ballistics professor. Upon complaints from the ballistics professor, Mentzel dispatched Becker to Gottingen without appeal. This move left the TH Berlin with the largest number of physics students but without a lecturer in theoretical physics —and it clearly demonstrated to German physicists the willful attitude of their masters. 12
But it also left an undeterred Heisenberg free at last to move to his beloved Munich.
The decision was postponed again. Old warriors Stark and Lenard, wielding their sharpest battle axe — “deutsche” physics — suddenly unleashed a public campaign to thwart Heisenberg’s appointment and to strengthen their own influence on REM policies. As Munich again settled on Heisenberg and as Heisenberg and Euler sent their latest positron theory to press in December 1935, Werner was forced again to deal with “ugly” things.
The “deutsche” physics campaign has been described in varying detail and perspective. 13 It was closely related to several significant changes in the Third Reich that took place at about the same time. The first was a major shift from internal policies to police-state tactics, as exemplified in June 1936 by the shift of domestic power from Hitler’s political interior minister, Wilhelm Frick, to his new Reich chief of police, Reichsftihrer-SS Heinrich Himmler. The second change concerned the beginning of overt preparations for war in the first four-year plan, which was aimed at achieving economic and military independence and selfsufficiency by 1939. Concurrent with these events, and following the second wave of dismissals in 1935, the Nazis escalated their suppression of any remaining opposition among non-Jewish Germans by practicing a new form of mental tyranny: accusing critics and opponents of simply thinking or acting “Jewish,” thus threatening them with the same persecutions as actual Jews faced. Himmler’s deputy, Reinhard Heydrich, spoke in 1935 of a “spiritualization” of the Nazi struggle for domestic control now that many of the Jews and overt political opponents had been ostracized — of a Kampf der Geister (struggle of the spirits) for the hearts and minds of those who remained. 14 Stark and Lenard, though not allied with the Himmler-Heydrich SS power bloc within the regime, eagerly joined the battle. 15
Stark and Lenard opened their ideological assault in December 1935 at the dedication of the new Philipp Lenard Institute for Physics in Heidelberg. In his laudation for the now retired Lenard, Stark — with his high-pitched voice and meanly contoured face — raved not only at Einstein and other Jewish physicists, who, in his view, had produced the ‘Jewish formalism” of the relativity and quantum theories, but at “their non-Jewish pupils and imitators” who were teaching and using such physics. 16 Lenard’s long struggle against Einstein and “Jewish” physics had, said Stark, only partially succeeded: “Now Einstein has disappeared from Germany; but unfortunately his German friends and supporters continue to act in his spirit.” Planck was still head of the Kaiser
Wilhelm Society; Laue was still a physics referee in the Berlin Academy; “and the theoretical formalist Heisenberg, spirit of Einstein’s spirit, is now even to be rewarded with a call to a chair.” Such a situation could not be tolerated in Nazi Germany. “May Lenard’s struggle against Einsteinism be a warning,” Stark bellowed. “And it is to be hoped that the responsible referees in the Culture Ministry allow themselves to be guided by Lenard in the filling of physics teaching chairs, including those for theoretical physics.”
These were ominous threats and serious accusations and demands. Of course, Stark and Lenard had raved earlier against “Jewish” physics and had even included Heisenberg’s name in their ravings, but now the situation was much more serious. With the “spiritualization” of the struggle, the SS in ascendance, and war on the distant horizon, the political orientation of non-Jews was of paramount concern to the regime, and to call a non-Jew the spirit of Einstein’s spirit was to call him an enemy of the Reich. Perhaps a parallel can be made with the demogogical blacklisting of liberals accused of being communists during the McCarthy era in the United States. To extract as much political gain as they could from their attack, Stark and Lenard turned to party ideologue Alfred Rosenberg, their ostensible patron in Hitler’s cabinet.
Among the many ruthless competitors for power in Hitler’s Third Reich, Rosenberg was no match for Himmler, Hess, Goring, or Goebbels. His primary claim to the title of party ideologue was his rambling anti-Semitic diatribe, The Saga of the Twentieth Century, which, like Hitler’s Mein Kampf, few had ever bothered to read. Although Hitler continued to keep him in his cabinet, by 1936 his star was already in decline as others rose in power and stature, but he still held one point of light in his crown — he was editor-in-chief of the official Nazi party newspaper, the Volkischer Beobachter (Volkisch Observer), or VB. Like official party organs in other totalitarian regimes — Pravda in the Soviet Union or Neues Deutschland in former East Germany — the VB exerted an influence beyond its estimated circulation in 1936 of 500,000. All party officials were required to subscribe to it; rank-and-file party members showed their support by buying the paper; ordinary citizens read the newspaper to learn the regime’s official line. 17 If an ideological subgroup could place an article in the VB, it would lend official approval to their position and influence regime bureaucrats to act on their behalf.
Soon after the Heidelberg meeting, Lenard complained to Rosenberg of the lack of due attention accorded “deutsche” physics in the VB. Rosenberg, willing to support the Nazi physicists only under pressure^
responded by inviting Lenard to name a science editor to the paper, which Lenard apparently never did. Instead, at the end of January 1936 an article appeared in the VB, entitled “Deutsche Physik und judische Physik” (“German physics and Jewish physics”). In February, a transcript of Stark’s Heidelberg speech calling Heisenberg the spirit of Einstein s spirit appeared in Rosenberg’s monthly magazine for the party faithful, the Nationalsozialistische Monatsbefte (National Socialist Monthlies)} 9,
Since the aim of Stark’s and Lenard’s political onslaught was control over university physics teaching, hence over the future of physics in Germany, an otherwise unknown Nazi physics student at the TH Berlin, Willi Menzel (not to be confused with Dr. Rudolf Mentzel), wrote the VB plea for the teaching of “deutsche” physics at German universities. 19 The young man was obviously well coached. Quoting at length from Stark’s unpublished Heidelberg address and from the unpublished foreword to Lenard’s forthcoming Deutsche Physik, Menzel tried, as did his mentors, to distinguish a supposedly overly speculative and mathematically abstruse (formalistic) “Jewish” physics from a solidly researched and experimentally grounded “German” physics. “Jewish” physics — the relativity and quantum theories — was not just wrong, it was bad — and it was bad because it was Jewish. For Heisenberg, Planck, Laue, and others who had worked at preserving decent physics at German universities — even if they did not preserve the teachers to teach it — Menzel’s closing cry in an official organ of the Nazi party must have been unsettling: “We young people today want to continue the struggle for a German physics, and we will succeed in making its name just as esteemed as German technology and scholarship have been for years.” “Jewish” physics was to be suppressed at German universities.
While Stark’s Heidelberg diatribe sank to personal attacks on individuals, Menzel’s assault focused on the teaching curriculum. He mentioned Heisenberg only once, in passing — as the founder of the formalistic matrix theory — and did not refer at all to Heisenberg’s Munich appointment. Menzel’s mentors probably reasoned that while a student could plead for curriculum, it would not do for him to complain about a professor, no matter what that professor’s position might be. Although the article was a clear setup, a stunned Heisenberg was unsure of its import and unsure whether or how he should respond. 20 At a meeting in February with Munich Dean Kolbl, which lasted until 1:30 A.M., Kolbl confirmed Werner’s suspicions: that the article “was expressly meant as an attack against me.” Because of bureaucratic opposition raised by the article, his appointment at Munich would have to be postponed for the
time being, he told his mother, “but I can wait; this complete idiocy cannot last forever.” 21
While waiting for the irritating idiocy to pass, Heisenberg was not idle. At about the same time as the Kolbl meeting, a befriended party district leader in Leipzig advised Heisenberg to protest the Menzel and Stark articles by visiting the Saxon Culture Ministry and by demanding an audience with the Reich Minister, which he did. 22 Rosenberg — or more likely an editorial staff member — agreed to print a response from Heisenberg in the party newspaper. The article appeared, together with a comment by Stark, in the February 28, 1936, issue of the V olkiscber' Beobachter and was so widely read that the New York Times took note. 23 On the same day, Dean Rudorf of the Leipzig science faculty directed a comprehensive letter to Studentkowski, urging him to active support of the physicists’ cause. 24
A now more worried Heisenberg wrote his mother of his apprehension about his future: “I have to have a lot of luck if anything more is to be made of my life.” 25 He had begun to personalize the attack even more than was warranted. Of course, the language and the intent of the articles implied a great personal danger for Heisenberg, but they were ultimately aimed not at him but at the physics profession as a whole, of which Heisenberg was being held up as a representative. Nor did his future success in life really depend on whether or not he succeeded Sommerfeld. He began to associate his own fortunes with the fortunes of his profession.
Heisenberg took the lead in responding to Menzel in the pages of the Volkiscber Beobachter. As he had in his Hannover address to the GDNA m 1934, Heisenberg offered party newspaper readers a carefully worded explanation of the nature and value of contemporary theoretical physics and of its importance to the education of young Germans. This time, however, he did not dare mention any Jewish physicists. The goal of physics, he wrote, is not only to observe nature but to understand it. Mathematics is often the most suitable way to formulate natural laws, but theoretical systems of concepts are more essential, and these often must be adapted as science progresses.
Relativity and quantum theory served Heisenberg as examples. Further research on these theories in particular, “from which perhaps the strongest influences on the structure of our entire spiritual life will arise, is one of the most important tasks for German youth,” Heisenberg proclaimed in the Nazi newspaper. “Evidently courage is not quite dead in the universities,” the New York Times editorialized. 26 But Stark’s
response, preceded by an introduction by Rosenberg himself, left no doubt that party orthodoxy stood squarely behind Stark’s reiterated demand: “The type of physics that Heisenberg defends ought no longer, as it has until now, exert a decisive influence on filling physics teaching chairs.” 27
Two days after the VB exchange, Studentkowski met with Dr. Mentzel, the REM official, to discuss Leipzig physics. A memo that Studentkowski wrote to himself after the meeting was to the point: “Professor Heisenberg remains in Leipzig. Professor Hund likewise remains in Leipzig.” 28 Despite his penchant for Nazi demagoguery, Studentkowski apparently had no use for “deutsche” physics and had cultivated friendly relations with leading Leipzig scientists who, because of their reputations, could perhaps work to his advantage in Saxon affairs. Lor whatever reason the Nazi bureaucrat supported the scientists, previous studies of this episode have overlooked the crucial role he played in the affair at this stage.
In a long reply on March 24, 1936, to Leipzig Dean Rudorf’s Lebruary 28 request for assistance, Studentkowski told of successful meetings with various bureaucrats involved in the affair. 29 Lirst, he wrote, he had managed to find “cover” for Heisenberg in the person of Dr. Lahr, head of the Saxon State Chancellery, who had direct access to the Reich plenipotentiary for Saxony. Heisenberg would not be molested as long as he remained in Saxony. Second, Studentkowski had made inroads with Alfred Rosenberg, who, as readers of the VB already knew, had backed Stark before declaring the entire controversy closed. 30
Most importantly, Studentkowski had Mentzel’s ear. Mentzel’s earlier conflict with Stark and the Stark-Lenard bid for control of physics appointments would, one might think, have made Mentzel eager to support the physicists. But Mentzel appeared more cautious to Studentkowski. “He does not at all approve unreservedly of Stark’s attacks, but he also has certain reservations about the present methods of theoretical physics, or better, about overreliance on them.” Stark’s and Lenard’s connections with Hess’s office in Munich through the Munich-based Nazi leagues for students and lecturers, in the person of Dr. Liihrer, probably gave Mentzel pause. Mentzel and the REM were then seeking improved relations with Hess, Hitler’s party deputy. 31 Perhaps, too, Mentzel, acting the impartial bureaucrat, sought to play both sides against each other to his own advantage. Lor whatever ulterior motive, he willingly granted an audience to Heisenberg — following proper bureaucratic procedures, of course — and asked Studentkowski to relay
the message. Studentkowski informed Rudorf: “Mentzel requests Heisenberg through me to visit him sometime, and to make an appointment as soon as possible.” Rudorf passed the letter to Heisenberg with his best wishes for an early meeting with the SS officer. 32
Heisenberg’s meeting with Mentzel, probably in early April 1936, was a turning point. According to a form letter sent by Heisenberg, Max Wien, and Hans Geiger to the entire German physics professorate shortly after the meeting, Mentzel, ostensibly speaking for Rust, had requested during the meeting a memorandum signed by “most” German university physicists describing their understanding of the relationship between experimental and theoretical physics. 33 This memorandum — in effect, a petition for theoretical physics — would provide Rust “a suitable means for his instruction, which will then enable him to alleviate the unpleasantly tense situation that has recently arisen.” In other words, Mentzel (and possibly Rust) was willing to move against Stark and Lenard, but only if he had the support, in writing, of the overwhelming majority of German physics professors. Heisenberg, Geiger, and Wien wrote a carefully worded memo and attached it to their letter, requesting its return to Heisenberg’s private address — with or without signature — by May 19, 1936. 34 Not surprisingly, Lenard and Stark were livid. 35
Geiger and Wien made ideal coauthors. Both were well-known, politically conservative experimentalists, at once sympathetic toward modern theory and acceptable to REM officials. 36 Wien’s cousin, Willy, had been close to Stark, and Geiger, the famous coinventor of the GeigerMuller counter, was being considered by Mentzel as a replacement either for Debye in Leipzig or for Nobelist Gustav Hertz in Berlin, who, being part Jewish, had resigned in the face of indignities. 37 Wien had already privately expressed some concern for theoretical physics and physics in general in the wake of the first round of dismissals. Encouraged by Debye, he had responded two years earlier by helping to formulate a memo on the declining state of German physics due to regime policies. 38 If that memo was ever actually submitted, it was almost certainly ignored. One SS Security Service (SD) officer assigned to the REM later recalled an office cabinet stuffed with similar memos.
Whether sent or not, the 1934 Wien memo served as the basis for the Heisenberg-Wien-Geiger petition of 1936, which, unlike its predecessor, enjoyed a huge success. Its cardinal point was utilitarian: Germany faced a critical situation regarding physics teaching and personnel that it could ill afford, especially as the four-year plan came into full swing. “The great demand for physicists in technology and the military is met by a
lack of suitable candidates. Empty teaching chairs are filled only with great difficulties, and the number of physics students in the beginning semesters is much too small. Moreover, read the memorandum, theory and experiment were both essential for scientific progress and for future technological gains. Public attacks on theory were only frightening students away and damaging Germany’s reputation abroad. Attacks against theory must cease in order to stimulate science and to maintain a useful physics profession in Germany.
These were arguments that few could refuse, and few did. Seventyfive physicists — nearly all German physics professors — signed the petition. Included were theorists and experimentalists, pure and applied physicists, party members and nonmembers. 40 It was an outpouring of support for physics and especially for Heisenberg and theoretical physics, support that had been building since 1933. After three years of hand-wringing, at last, it seemed, something could be done — even if that something were to point up the utility of physics to regime policies.
Rust received the momentous memorandum by October 1936 and handed it to his politically adept state secretary for evaluation. The secretary, thoroughly ignorant of physics, could only respond with a criticism of his weakling boss. 41 In the professors’ conflict, he wrote in a private memo, one side —Heisenberg’s —had sought help from the REM and had even referred to Rust by name in its cover letter and by title in its petition. If this were a purely scientific controversy, Rust should stay out of it; if it were political, which it was, then he, as culture minister, had even less reason “to mix in these things.”
Rust decided to leave matters to Mentzel, who by that time had already bested Stark on another front. The cabinet power shifts of 1936 had greatly reduced the influence of both Frick and Rosenberg, leaving Stark and Lenard without powerful supporters. But Stark ultimately did himself in through his foolish mismanagement of Research Association funds. The rabidly empirical physicist had heavily sponsored a speculative project based on an old Teutonic myth in an effort to extract gold from south German heaths. The scandal gave the REM an edge in forcing Stark’s resignation in November, and his replacement as head of the Research Association was none other than the indomitable Dr. Mentzel. 42 A visit from Munich Dean Kolbl to the Berlin REM in the same month brought welcome news, relayed to Heisenberg by Kolbl’s colleague Sommerfeld: “Kolbl reported to me from the Berlin ministry that you have won in your controversy with St[ark] and L[enard] both ‘scientifically’ and ‘morally.’” 43 Heisenberg would replace his mentor at last.
Closely following the twists and turns of Heisenberg’s political fortunes during 1936 was a sudden shift in the prospects for his physics. At the same time as he hit back at the professional assault with a successful memorandum of support, Heisenberg firmly believed that he had found an explanation for the appearance of high-energy cosmic-ray showers that would once again revolutionize quantum physics. The two achievements reinforced his optimism in both areas. Since laboratory accelerators had not yet reached high energies — that is, above about 10 8 electron volts (eV) — during the 1930s high-energy physics concentrated on cosmic-ray events. By 1936, every experiment on the absorption of cosmic rays in matter had seemed to indicate — mistakenly, as it turned out — a breakdown of quantum electrodynamics (QED) near a theoretically expected upper energy limit of about 137 MeV. 44 High-energy cosmic rays penetrated much farther through matter than they should have according to QED. This suggested that the particles simply stop radiating away their energy, thus slowing down, at that energy limit. Internally, QED contained no such limit and required particles to radiate at all energies, without any supposed breakdown. QED would thus not do for shower theories, since showers involved energies far above the supposed upper limit for validity of the theory. Experimental evidence seemed so strong that physicists greeted with frank disbelief the discovery by Weizsacker, Williams, and Landau in 1934 that no good theoretical reason existed to expect any breakdown. 45 Some incredulous physicists — notably Oppenheimer and Nordheim in the United States —even began introducing cutoffs into QED to match the theory to the data. 46
Heisenberg took a different tack, pushing existing theory to its limits to try to perceive what lay beyond. He caught his first glimpse of a new frontier in May 1936. Exactly one week after the stated May 19 deadline for receipt of the Heisenberg-Wien-Geiger petition at Heisenberg’s home address, Heisenberg reported to Pauli from his institute that an alternative to QED yielded new insights. 47 Italian physicist Enrico Fermi, then head of the internationally acclaimed nuclear research group in Rome, had recently formulated an alternative field theory to handle nuclear beta decay — the ejection of an electron and a neutrino from a radioactive nucleus as a neutron turns into a proton. (The emission of a positron, as a proton decayed into a neutron, and the distinction between neutrinos and antineutrinos were later discoveries.) When taken out of the nucleus and applied to the high-energy collision of a proton with a nucleus, the new held, Heisenberg discovered, produced an explosion of particles as soon as the particles approached closer than a
minimum length, about the size of an electron. “It thus appears to me,” he wrote, that one can understand the existence of cosmic-ray showers immediately from the Fermi /? theory.”
Nuclear beta decay involved an electron, which was also a primary player in quantum electrodynamics and the basic source of electric and magnetic fields. Although QED could account for the creation of an electron out of electromagnetic energy, it could not account for the decay of neutrons nor for the nonelectromagnetic nuclear force holding neutrons and protons together in a nucleus. These were not electromagnetic processes. Inspired by the discussion of Heisenberg’s neutron-proton nuclear theory, which Heisenberg had presented to Fermi and others at the 1933 Solvay Congress, Fermi had returned to Rome, where, in December 1933, he developed a theory of the neutron-proton force that relied on an entirely different field. 48 In form, however, it differed only slightly from Heisenberg’s nuclear theory, according to which the neutron-proton force arises from the virtual exchange of an electron (“virtual” because energy conservation is violated for an instant). Together, an electron and a proton constituted a neutron.
Unfortunately, Heisenberg’s exchange force violated energy and momentum conservation laws, unless one included the hypothetical massless “Pauli neutrinos” in the theory (the word neutrino is Italian for “little neutron”). Fermi showed that both Heisenberg’s force and conservation laws could be maintained if the neutron and proton exchange not just an electron but an electron and a neutrino.
Fermi constructed his theory in close analogy to QED, but it involved an entirely different type of field. Much as an electron and a positron are attracted to each other in QED by tossing back and forth a photon, the quantum of the electromagnetic field, so a neutron and a proton are attracted to each other in a nucleus by “playing catch” with an electron and a neutrino, the quanta of a new “Fermi field.” The free emission of such a field yielded the observed beta decay, just as the emission of light quanta could be observed as spectroscopic radiation.
In Fermi’s formulation of field theory, an analogy is made with Hamilton’s old formulation of classical mechanics, in which an energy function, the Hamiltonian, carries all the properties of the system. The analogy had been used earlier in Schrodinger’s formulation of the wave equation and in Dirac’s quantum perturbation theory. In the perturbation formulation of field theory, separate Hamiltonian functions (actually densities) are obtained for the matter and the field, while the interaction between the two — which gives forces — is treated as a small perturbation of the separate agreement. The perturbation is represented
by a Hamiltonian density, H int , containing wave functions representing the interacting matter and field quanta.
Fermi’s Hamiltonian density for the interaction, H int , may be written in modern relativistic form:
where (//>, y/ N , y/ e , and y/ v are the proton, neutron, electron, and neutrino wave functions, respectively; y^ is the 4X4 relativistic gamma matrix; f is a constant; and a bar over a wave function indicates the complex conjugate adjoint. (This version of the theory did not contain antineutrinos). The size of the coupling constant, f, represents the size of the interaction. Fermi made his constant analogous to its counterpart in QED, the so-called fine-structure constant, a = Inet/hc. In Fermi’s theory, f = 2ng/hc, where g is a constant, but unlike the dimensionless a, f has the dimension cm 2 .
Fermi’s field was widely studied in Leipzig and elsewhere as an explanation both for nuclear forces and for the observed properties of beta decay. 49 Heisenberg, who read Fermi’s first paper in Italian, was at first very excited by it. But his enthusiasm waned when he discovered in 1934 that the resulting nuclear force was much too weak to account for the size and range of the neutron-proton force in nuclei or even for the observed distribution of beta-decay energies. Indeed, during a four-part lecture series on nuclear physics, delivered in the spring of 1934 to Dirac’s institute in Cambridge, England, Heisenberg found the force to be as much as 10 10 too small. 50 Various ad hoc proposals were put forward to fix the Fermi force, and these were intensively studied in Leipzig and Zurich thereafter. All proved unsuccessful. The Fermi force — which was later relegated to only the weak interaction within protons and neutrons —remained an unsatisfactory account of the nuclear force and, at the time, even of beta decay. 51
Even worse, because of the size of the matter-field coupling constant, f , the self-energies of the neutron and proton — the calculated energy of
a proton or neutron sitting alone, surrounded by its Fermi field_
diverged even more rapidly to infinity than did QED; a discouraging situation, to be sure, but Werner thrived on challenges. Having exhausted positron theory and having turned to cosmic rays for clues on how to handle distances shorter than the size of an electron, Heisenberg reported to Pauli in May 1936, as the physicists’ memorandum circulated throughout Germany, a new and momentous discovery that could potentially revolutionize physics. In a perturbation expansion of Fermi’s
H int in analogy to QED, the contribution to the higher order terms diverged to infinity as they did in QED but in a fundamentally different way that accounted for one phenomenon that QED could not —the appearance of cosmic-ray showers.
A cosmic-ray shower arises when a high-speed particle hits a piece of matter, producing in the course of the collision numerous new particles. The creation of material particles had to be understood in field theory in a very fundamental way, as the transfer of energy from the collision to the field quanta excited by the collision, which are then detected as real (as opposed to virtual) particles in a cloud chamber or Geiger counter. In QED, the creation of a certain number of particles (electrons and
positrons) is represented by the corresponding order of interaction_
the octave of the harmonic vibration mode. For n number of particles, the cross section —essentially the probability —for exciting the nthorder interaction is proportional to (a)" = (V137)”. As n, the number of particles, increases, the probability rapidly decreases, since V137 is a small fraction. Large bursts of particles, such as those that had been detected by Geiger counters, or even small showers containing a handful of particles, would thus be extremely rare.
Not so for the Fermi field. Here, the analogous cross section for the creation of n particles depends on a parameter (A c /A)", where A is the wavelength of the incoming proton and A c is a critical minimum wavelength, equal to -ff. As the energy of the incoming proton increases, its wavelength decreases. For low-energy collisions, less than about 10 8 electron volts, A > A c , and from the parameter higher interactions involving the creation of any new particles are rare. But as soon as A < A c , the parameter increases — the interaction cross sections do not decrease but on the contrary grow ever larger, the larger the value of n. An instantaneous explosion of particles occurs within the minute area of collision, resulting in a shower of particles emanating from a single point. The number of particles produced when a proton hits a nucleus is governed only by the conservation of energy. 52
Heisenberg had hit upon a new and astounding property of Fermi’s beta-decay theory: when applied to cosmic rays, it could account for the observed creation of particles in a way that the reigning quantum electrodynamics could not. Despite his astonishment, Pauli responded with typical skepticism. He did not dispute Heisenberg’s new use of Fermi’s theory, but he doubted that it offered anything new. At very small distances, Fermi’s theory went to infinity even faster than did QED. This feature actually unleashed the particle explosion, but to Pauli it indicated the need for a new revolution in physics to handle high
energies, not the usefulness of alternative field theories. 53 Heisenberg actually agreed, but he believed that the Fermi formalism gave an important clue as to where to look for this revolution. He quickly submitted a manuscript on the subject in early June 1936 and took a copy with him to the annual Copenhagen physics conference later that month. 54
As he wrote in the paper and argued in Copenhagen, the clue to the future lay in the critical wavelength X c . Since it controlled the creation of showers of new particles, and in a way that he had expected from his positron work with Euler, Heisenberg saw in it a fundamental characteristic of the future theory. This theory would contain a new fundamental constant, a critical length l 0 = /l c , which would serve as the long-sought link between matter and fields and thereby remove the mathematical divergences that occurred in attaching fields to matter. The task for theorists now was to find a consistent way to introduce this new critical minimum length into physics and thus achieve the new theory. The result would be revolutionary. Indeed, he wrote (avoiding mention of Einstein’s name), “It must probably be connected with a fundamental alteration of the formalism [the mathematics], just as, for instance, the introduction of the constant c gave rise to a modification of prerelativistic physics.” 55
But the need for revolution — and the direction in which to look for it — was not easily accepted outside the Leipzig-Zurich axis. During the Copenhagen meeting, attended by numerous refugee physicists, Walter Heitler, then in Bristol, stunned the audience with his announcement of Anderson’s latest results on cosmic-ray absorption. 56 Despite theoretical arguments to the contrary, physicists were still convinced by cosmic-ray absorption data that QED was invalid for energies at which showers of new particles begin to appear. In May, as Heisenberg was busily submitting his Mentzel memo and uncovering the revolutionary shower properties of the Fermi field, Anderson was privately informing Bethe and Heitler in England and Oppenheimer at Berkeley of his new data on the energy loss of electrons. Unlike all his previous experiments, Anderson’s new cloud-chamber arrangement was no longer biased against large energy losses. His data suddenly agreed with, rather than contradicted, the theoretically predicted absorption of high-speed particles using quantum electrodynamics! “As you can see,” he wrote to Heitler, who passed it on to the Copenhagen meeting, “these data do not show any breakdown of the theoretical formulae for energies ~300 MeV. The experiments are not accurate and the numbers measured are small, but certainly no large disagreement appears.” 57 If QED did not break down, there was no need for the revolution that Heisenberg was espousing or
even for the introduction of any other field theory to account for high-energy experiments.
Anderson’s new experiments also clearly distinguished for the first time the two very different components of the primary cosmic rays at sea level: the “soft, easily absorbable, electron-photon component of the incoming rays; and the “hard,” long-ranged component. While the soft component now showed precise agreement with QED to energies far beyond the supposed breakdown of the theory, the hard component still offered problems and was set aside for the time being. It penetrated such large layers of lead blocks that Anderson surmised that either QED eventually did break down at some very high energy or these particles were of an entirely unknown composition.
Anderson’s new data on the soft electron-photon component of cosmic rays, which he published with his assistant, Seth Neddermeyer, arrived at the Physical Review just one day before Eleisenberg submitted his shower paper to the Zeitschrift fur Physik. 5S These two papers initiated two conflicting approaches to showers and their field-theoretic implications that were rivals into the war years and beyond. While Heisenberg’s explosions attracted seekers of a new and even more radical quantum revolution — mainly the leaders of the first revolution, Heisenberg, Pauli, and their remaining Central European collaborators —the Anderson-Neddermeyer paper confirmed the Bethe-Heitler theory of absorption for the soft component and catalyzed the calculation of “cascade” showers using QED. For the supporters of this rival account of high-energy particle creation — mainly Oppenheimer, Heitler, and their collaborators in England and the United States — no new revolution was necessary at all: QED would do just fine. Heisenberg and Oppenheimer, so similar and yet so different, would never reach agreement on this or other matters during the coming years.
According to the cascade theory — presented independently by Oppenheimer and his student, J. F. Carlson, and by Heitler and Dirac’s former Cambridge student, Indian physicist Homi Bhabha — a cosmicray shower is formed not by an instantaneous explosion but by a succession of well-understood, individual Bremsstrahlung (braking radiation) and pair-creation events as an incoming high-energy electron, positron, or photon bounces between atoms after hitting a thin piece of matter. 59
Yet until the Oppenheimer and Heitler groups published in early 1937 their detailed calculations of the formation of cascade showers, Heisenberg’s theory of “explosion” showers — the formation of a shower in a single event using Fermi’s alternative electron-neutrino field — remained
the most plausible account of showers, and his physics remained the most likely replacement for QED. After crudely manipulating the Fermi interaction to obtain the correct size of the nuclear force and the correct critical length for showers, Heisenberg bolstered his claims for the new physics with empirical predictions that were astonishingly consistent with available data. According to Heisenberg’s derivations, the critical energy for the creation of showers of particles would be about 100 MeV, and the cross section would be about 10 -26 cm 2 , both of which agreed well with observations. Moreover, a shower would occur in a single act (an explosion), not in a series of individual events (a cascade). This seemed to be confirmed by the sudden bursts of ionization occurring in Geiger counters and by Blackett’s photographs showing showers emerging from a single point in the cloud chamber. The showers themselves, Heisenberg predicted, would contain mostly electrons and slow Pauli neutrinos —the quanta of the Fermi field. The electrons produced would constitute Anderson’s observed soft component within the showers themselves. The created neutrinos would constitute the hard component, which, according to Heisenberg’s theory, could penetrate thick absorbers to produce further showers by induced beta decay. 60 Heisenberg’s Fermi explosion-shower theory seemed to cover every observation.
The empirical consequences, Heisenberg’s firsthand experience in struggling with the problems of quantum electrodynamics and Dirac’s positron theory, and especially the new vistas opened by the Fermi field convinced Heisenberg both of the need for a new physics and that he really had a grasp of it. Quantum electrodynamics had numerous problems from the very start and could not, in early 1936, account for the phenomenon of showers. 1 herefore, Heisenberg wrote to Pauli, “I truly believe that the connection between the Fermi theory and’ shower formation is a very central point in the theory of matter.” 61 In the politically charged atmosphere of 1936, Heisenberg’s work had an additional significance. It was an indication that, as Gerlach responded to one foreign critic, the scientific life here is absolutely not dead at all but is actually growing.” 62
The new theory could also serve as an object lesson on the productivity of the much-maligned theoretical physics. Between mountain outings and summer military camp, Werner wrote an article informing the educated German public of the potentially significant consequences of his new theory of showers. These, he emphasized, “are capable of experimental verification.” 63 Far from generating purely abstract mathematical formalisms, Heisenberg claimed that he had discovered nothing
less than a new universal constant whose “introduction requires a reformulation of the entire theory, as was the case for the constants b and c.” As any reader who had experienced an introduction to modern physics knew, these two constants were the basis of quantum theory and relativity theory, respectively. Further theoretical analyses of empirical data on cosmic rays —not mathematical manipulation —“promise the most important contributions to the fundamental physical questions.”
The political and cultural implications of the new physics may have encouraged Heisenberg’s more grandiose claims for it. However, there is no evidence that any of his German colleagues saw it that way, even while expressing their overwhelming support for his petition in defense of their profession. Even petition coauthor and cosmic-ray investigator Hans Geiger remained unconvinced of Heisenberg’s explosions. Geiger learned of explosions and their possible rival, cascades, not from Heisenberg but at a Zurich nuclear physics conference in July 1936, attended by Sommerfeld, Bhabha, Pauli, Schrodinger, and others. 64 He preferred cascades, both in theory and in experiment. Although the possibility of explosion showers remained open, Geiger explained in a public lecture as late as 1940, other cloud-chamber photographs taken by British physicist Blackett appeared to show a buildup of showers — despite the occurrence of bursts in Geiger’s own counters! 65 If the vivacity of German theoretical physics was to be demonstrated by Heisenberg’s new revolution, Geiger would not support the cause. Physics and politics had to be held separate at all costs.
While German scientists were less than enthusiastic about Heisenberg’s new theory, Pauli, a foreigner, once again became Heisenberg’s chief collaborator and critic. Their collaboration was not at all empirical— as Heisenberg’s public may have expected from his report — but it was thoroughly abstract and mathematical. As usual, the two sought to push their formalism to the breaking point and beyond. As a trick for doing so, Pauli resurrected Heisenberg’s 1930 lattice world, discussed in Chapter 14 — whereby Heisenberg had sliced up space into cubes formed by the size of an electron as a minimum length. Pauli brought it with him to the Copenhagen meeting in June 1936. 66 Using Pauli’s trick, Heisenberg and Pauli analyzed the relation of the fundamental length to showers and infinities in nonlinear, Fermi-like field theories, hoping to find a new theory that contained the length in a natural way. Pauli was skeptical that any consistent theory could arise in this way, but the possibility that an empirical proof for his still hypothetical neutrinos might appear from Fermi showers did not escape Pauli’s notice.
Heisenberg did not join Pauli’s effort until after completing his required eight weeks of military training in the summer of 1936. 67 Heisenberg was a corporal in a mountain infantry unit in Bavaria near the Austrian border. The rigorous training not only interrupted his work, but also forced the cancellation of a planned trip to the United States to attend the annual Ann Arbor summer school in physics and the elaborate tricentennial celebrations at Harvard University. Werner’s abrupt cancellation of his American trip to attend the military training camp made the New York Times. 68 The political situation in physics was too volatile to permit his absence from Germany, he explained to his former • colleague Samuel A. Goudsmit, then in Ann Arbor. 69 Apparently adherence to German military requirements came before foreign conferences — he could have found an excuse to dodge the military duty, had he so desired. The old Neupfadfinder seemed to welcome the physical challenges of military mountaineering and, he wrote his mother, the escape from responsibility: “I am physically healthy and I very much enjoy the duty itself. It is nice not to have to think for a change, but only to obey. . . . The duty agrees with me in every respect.” 70
Returning to work in Leipzig in October 1936, Heisenberg received a long letter from Pauli proving that the Fermi formalism led nowhere — with or without a hypothetical lattice world. 71 Both physicists reacted in familiar fashion. Pauli declared that manipulations of divergent field theories were similar to quantizing mechanical models in the early 1920s. Since both contained unobservables, he suggested that Heisenberg declare the eigenvalues of all field Hamiltonians to be fundamentally unobservable, then see what happens. 72 Applied to atomic models, it was in just this way that Heisenberg had formulated the breakthrough to quantum mechanics in 1925.
As in the twenties, Heisenberg wanted first to exhaust all latticeworld models, and he presented Pauli with various constructions for them to study and reject together. He revealed his plan to Max Born in November: “The showers are still occupying Pauli and me very much.
I am very anxious to know how the work there will proceed. Pauli continually tries to prove that wave quantization always diverges, even with a universal length; I privately believe that Pauli is right but temporarily maintain the opposite, and in this way we get to know the mathematical properties of a nonlinear quantum field theory, which are highly interesting.” 73 Six days later, Sommerfeld informed Heisenberg of his victory over Stark. Physics and politics, though running on separate tracks, ran along parallel lines for Heisenberg.
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