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125-492: Werner Karl Heisenberg ( / ˈ h aɪ z ən b ɜːr ɡ / ; German: [ˈvɛʁnɐ kaʁl ˈhaɪzn̩bɛʁk] ; 5 December 1901 – 1 February 1976) was a German theoretical physicist , one of the main pioneers of the theory of quantum mechanics , and a principal scientist in the Nazi nuclear weapons program during World War II . He published his Umdeutung paper in 1925, a major reinterpretation of old quantum theory . In

250-615: A Potsdam builder. His father Franz Sommerfeld (1820–1906) was a physician from a leading family in Königsberg , where Arnold's grandfather had resettled from the hinterland in 1822 for a career as Court Postal Secretary in the service of the Kingdom of Prussia . Sommerfeld was baptized a Christian in his family's Prussian Evangelical Protestant Church , and although not religious, he would never renounce his Christian faith . Sommerfeld studied mathematics and physical sciences at

375-435: A mathematical theory , in the sense that the word "theory" has a different meaning in mathematical terms. R i c = k g {\displaystyle \mathrm {Ric} =kg} The equations for an Einstein manifold , used in general relativity to describe the curvature of spacetime A physical theory involves one or more relationships between various measurable quantities. Archimedes realized that

500-565: A working hypothesis . Arnold Sommerfeld Arnold Johannes Wilhelm Sommerfeld , ForMemRS ( German: [ˈzɔmɐˌfɛlt] ; 5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics , and also educated and mentored many students for the new era of theoretical physics. He served as doctoral supervisor and postdoc supervisor to seven Nobel Prize winners and supervised at least 30 other famous physicists and chemists. Only J. J. Thomson's record of mentorship offers

625-474: A (quantum) field equation accurately describing electrons, Heisenberg put matter on the same footing as electromagnetism : as being described by relativistic quantum field equations which allowed the possibility of particle creation and destruction. ( Hermann Weyl had already described this in a 1929 letter to Albert Einstein .) Heisenberg's Umdeutung paper that established modern quantum mechanics has puzzled physicists and historians. His methods assume that

750-404: A certain economy and elegance (compare to mathematical beauty ), a notion sometimes called " Occam's razor " after the 13th-century English philosopher William of Occam (or Ockham), in which the simpler of two theories that describe the same matter just as adequately is preferred (but conceptual simplicity may mean mathematical complexity). They are also more likely to be accepted if they connect

875-626: A chain reaction. He explored various ways of obtaining isotope 92 U in its pure form, including uranium enrichment and an alternative layered method of normal uranium and a moderator in a machine. This machine, he noted, could be used in practical ways to fuel vehicles, ships and submarines. Heisenberg stressed the importance of the Army Weapons Office's financial and material support for this scientific endeavour. A second scientific conference followed. Lectures were heard on problems of modern physics with decisive importance for

1000-832: A colonel in the hussars . In October 1893, Sommerfeld went to the University of Göttingen , which was the center of mathematics in Germany. There, he became assistant to Theodor Liebisch , at the Mineralogical Institute, through a fortunate personal contact – Liebisch had been a professor at the University of Königsberg and a friend of the Sommerfeld family. In September 1894, Sommerfeld became Felix Klein 's assistant, which included taking comprehensive notes during Klein's lectures and writing them up for

1125-454: A comparable list of high-achieving students. He introduced the second quantum number , azimuthal quantum number , and the third quantum number, magnetic quantum number . He also introduced the fine-structure constant and pioneered X-ray wave theory. Sommerfeld was born in 1868 to a family with deep ancestral roots in Prussia . His mother Cäcilie Matthias (1839–1902) was the daughter of

1250-500: A form of protoscience and others are a form of pseudoscience . The falsification of the original theory sometimes leads to reformulation of the theory. "Thought" experiments are situations created in one's mind, asking a question akin to "suppose you are in this situation, assuming such is true, what would follow?". They are usually created to investigate phenomena that are not readily experienced in every-day situations. Famous examples of such thought experiments are Schrödinger's cat ,

1375-766: A good example. For instance: " phenomenologists " might employ ( semi- ) empirical formulas and heuristics to agree with experimental results, often without deep physical understanding . "Modelers" (also called "model-builders") often appear much like phenomenologists, but try to model speculative theories that have certain desirable features (rather than on experimental data), or apply the techniques of mathematical modeling to physics problems. Some attempt to create approximate theories, called effective theories , because fully developed theories may be regarded as unsolvable or too complicated . Other theorists may try to unify , formalise, reinterpret or generalise extant theories, or create completely new ones altogether. Sometimes

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1500-399: A location of many German scientific research facilities. To limit casualties and loss of equipment, many of these facilities were dispersed to other locations in the latter years of the war. The Kaiser-Wilhelm-Institut für Physik (KWIP, Kaiser Wilhelm Institute for Physics) had been bombed so it had mostly been moved in 1943 and 1944 to Hechingen and its neighbouring town of Haigerloch , on

1625-498: A new branch of mathematics: infinite, orthogonal series . Modern theoretical physics attempts to unify theories and explain phenomena in further attempts to understand the Universe , from the cosmological to the elementary particle scale. Where experimentation cannot be done, theoretical physics still tries to advance through the use of mathematical models. Mainstream theories (sometimes referred to as central theories ) are

1750-503: A picture of nature so much as a picture of our relationships with nature . ...Science no longer confronts nature as an objective observer, but sees itself as an actor in this interplay between man and nature. The scientific method of analysing, explaining and classifying has become conscious of its limitations, which arise out of the fact that by its intervention science alters and refashions the object of investigation. In other words, method and object can no longer be separated. Shortly after

1875-1048: A power and merge into a pacified Europe." Sommerfeld was awarded many honors in his lifetime, such as the Lorentz Medal , the Max-Planck Medal , the Oersted Medal , election to the Royal Society of London , the United States National Academy of Sciences , Academy of Sciences of the USSR , the Indian Academy of Sciences , and other academies including those in Berlin, Munich, Göttingen, and Vienna, as well as having conferred on him numerous honorary degrees from universities including Rostock, Aachen, Calcutta, and Athens. He

2000-521: A private music recital. Elisabeth was the daughter of a well-known Berlin economics professor, and her brother was the economist E. F. Schumacher , author of Small Is Beautiful . Heisenberg married her on 29 April. Fraternal twins Maria and Wolfgang were born in January 1938, whereupon Wolfgang Pauli congratulated Heisenberg on his "pair creation"—a wordplay on a process from elementary particle physics, pair production . They had five more children over

2125-636: A professor at a number of German universities. His attempt to be appointed as successor to Arnold Sommerfeld failed because of opposition by the Deutsche Physik movement. On 1 April 1935, the eminent theoretical physicist Sommerfeld, Heisenberg's doctoral advisor at the Ludwig-Maximilians-Universität München , achieved emeritus status. However, Sommerfeld stayed in his chair during the selection process for his successor, which took until 1 December 1939. The process

2250-498: A ship floats by displacing its mass of water, Pythagoras understood the relation between the length of a vibrating string and the musical tone it produces. Other examples include entropy as a measure of the uncertainty regarding the positions and motions of unseen particles and the quantum mechanical idea that ( action and) energy are not continuously variable. Theoretical physics consists of several different approaches. In this regard, theoretical particle physics forms

2375-559: A short return trip in April. In December, Heisenberg lectured in neutral Switzerland . The United States Office of Strategic Services sent agent Moe Berg to attend the lecture carrying a pistol, with orders to shoot Heisenberg if his lecture indicated that Germany was close to completing an atomic bomb. In January 1945, Heisenberg, with most of the rest of his staff, moved from the Kaiser-Wilhelm Institut für Physik to

2500-469: A wide range of phenomena. Testing the consequences of a theory is part of the scientific method . Physical theories can be grouped into three categories: mainstream theories , proposed theories and fringe theories . Theoretical physics began at least 2,300 years ago, under the Pre-socratic philosophy , and continued by Plato and Aristotle , whose views held sway for a millennium. During

2625-497: Is a model of physical events. It is judged by the extent to which its predictions agree with empirical observations. The quality of a physical theory is also judged on its ability to make new predictions which can be verified by new observations. A physical theory differs from a mathematical theorem in that while both are based on some form of axioms , judgment of mathematical applicability is not based on agreement with any experimental results. A physical theory similarly differs from

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2750-426: Is thought of as a charged particle on a spring, perturbed by an external force, like an external charge. The motion of the oscillating charge can be expressed as a Fourier series in the frequency of the oscillator. Heisenberg solved for the quantum behavior by two different methods. First, he treated the system with the virtual oscillator method, calculating the transitions between the levels that would be produced by

2875-595: The Reichserziehungsministerium (REM, Reich Ministry of Education) and started the formal German nuclear energy project under military auspices. The project had its first meeting on 16 September 1939. The meeting was organized by Kurt Diebner , advisor to the HWA, and held in Berlin. The invitees included Walther Bothe , Siegfried Flügge , Hans Geiger , Otto Hahn , Paul Harteck , Gerhard Hoffmann , Josef Mattauch and Georg Stetter . A second meeting

3000-620: The Albertina University of his native city, Königsberg , East Prussia . His dissertation advisor was the mathematician Ferdinand von Lindemann , and he also benefited from classes with mathematicians Adolf Hurwitz and David Hilbert and physicist Emil Wiechert . His participation in the student fraternity Deutsche Burschenschaft resulted in a dueling scar on his face. He received his Ph.D. on 24 October 1891 (age 22). After receiving his doctorate, Sommerfeld remained at Königsberg to work on his teaching diploma. He passed

3125-514: The Deutsche Physik supporters. One attack was published in Das Schwarze Korps , the newspaper of the SS , headed by Heinrich Himmler . In this, Heisenberg was called a "White Jew" who should be made to "disappear". These attacks were taken seriously, as Jews were violently attacked and incarcerated. Heisenberg fought back with an editorial and a letter to Himmler, in an attempt to resolve

3250-539: The EPR thought experiment , simple illustrations of time dilation , and so on. These usually lead to real experiments designed to verify that the conclusion (and therefore the assumptions) of the thought experiments are correct. The EPR thought experiment led to the Bell inequalities , which were then tested to various degrees of rigor , leading to the acceptance of the current formulation of quantum mechanics and probabilism as

3375-499: The Fourier transform of the classical sharp series orbits, by contrast, are equally spaced. But these results could be explained by a semi-classical virtual state model: the incoming radiation excites the valence, or outer, electron to a virtual state from which it decays. In a subsequent paper, Heisenberg showed that this virtual oscillator model could also explain the polarization of fluorescent radiation. These two successes, and

3500-565: The Kaiser-Wilhelm Institut für Physik to Hechingen and its neighboring town of Haigerloch , on the edge of the Black Forest , for the same reasons. From 18–26 October, he travelled to German-occupied Netherlands . In December 1943, Heisenberg visited German-occupied Poland . From 24 January to 4 February 1944, Heisenberg travelled to occupied Copenhagen, after the German army confiscated Bohr's Institute of Theoretical Physics . He made

3625-781: The Ludwig Maximilian University of Munich under Arnold Sommerfeld and Wilhelm Wien and at the Georg-August University of Göttingen with Max Born and James Franck and mathematics with David Hilbert . He received his doctorate in 1923 at Munich under Sommerfeld. In June 1922, Sommerfeld took Heisenberg to Göttingen to attend the Bohr Festival , because Sommerfeld had a sincere interest in his students and knew of Heisenberg's interest in Niels Bohr 's theories on atomic physics . At

3750-543: The Neupfadfinder , a German Scout association and part of the German Youth Movement . In August 1923 Robert Honsell and Heisenberg organized a trip to Finland with a Scout group of this association from Munich. Heisenberg enjoyed classical music and was an accomplished pianist. His interest in music led to meeting his future wife. In January 1937, Heisenberg met Elisabeth Schumacher (1914–1998) at

3875-641: The Nobel Prize in Physics ; Peter Debye , who had received the Nobel Prize in Chemistry in 1936; and Richard Becker . The Munich Faculty was firmly behind these candidates, with Heisenberg as their first choice. However, supporters of Deutsche Physik and elements in the REM had their own list of candidates, and the battle dragged on for over four years. During this time, Heisenberg came under vicious attack by

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4000-572: The Scientific Revolution gathered pace, the concepts of matter , energy, space, time and causality slowly began to acquire the form we know today, and other sciences spun off from the rubric of natural philosophy . Thus began the modern era of theory with the Copernican paradigm shift in astronomy, soon followed by Johannes Kepler 's expressions for planetary orbits, which summarized the meticulous observations of Tycho Brahe ;

4125-604: The Sommerfeld–Wilson quantization rules (1915), a generalization of Bohr's atomic model , introduction of the Sommerfeld fine-structure constant (1916), co-discovery with Walther Kossel of the Sommerfeld–Kossel displacement law (1919), and publishing Atombau und Spektrallinien (1919), which became the "bible" of atomic theory for the new generation of physicists who developed atomic and quantum physics. The book underwent 4 editions from 1919 to 1924, to incorporate

4250-630: The Umdeutung (reinterpretation) paper, was published in September 1925. He returned to Göttingen and, with Max Born and Pascual Jordan over a period of about six months, developed the matrix mechanics formulation of quantum mechanics . On 1 May 1926, Heisenberg began his appointment as a university lecturer and assistant to Bohr in Copenhagen. It was in Copenhagen, in 1927, that Heisenberg developed his uncertainty principle , while working on

4375-575: The University of Wisconsin–Madison . In 1927 Sommerfeld applied Fermi–Dirac statistics to the Drude model of electrons in metals – a model put forth by Paul Drude . The new theory solved many of the problems predicting thermal properties the original model had and became known as the Drude–Sommerfeld model . In 1928/1929, Sommerfeld traveled globally, with major stops in India, China, Japan, and

4500-553: The Uranverein by Robert Döpel and his wife Klara Döpel . On 4 June 1942, Heisenberg was summoned to report to Albert Speer , Germany's Minister of Armaments, on the prospects for converting the Uranverein's research toward developing nuclear weapons . During the meeting, Heisenberg told Speer that a bomb could not be built before 1945, because it would require significant monetary resources and number of personnel. After

4625-606: The atomic nucleus , ferromagnetism , cosmic rays , and subatomic particles . He was also instrumental in planning the first West German nuclear reactor at Karlsruhe , together with a research reactor in Munich , in 1957. Following World War II, he was appointed director of the Kaiser Wilhelm Institute for Physics , which soon thereafter was renamed the Max Planck Institute for Physics . He

4750-461: The two-fluid theory of electricity are two cases in this point. However, an exception to all the above is the wave–particle duality , a theory combining aspects of different, opposing models via the Bohr complementarity principle . Physical theories become accepted if they are able to make correct predictions and no (or few) incorrect ones. The theory should have, at least as a secondary objective,

4875-642: The "discovery and development of talents". Albert Einstein told Sommerfeld: "What I especially admire about you is that you have, as it were, pounded out of the soil such a large number of young talents." Sommerfeld's style as a professor and institute director did not put distance between him and his colleagues and students. He invited collaboration from them, and their ideas often influenced his own views in physics. He entertained them in his home and met with them in cafes before and after seminars and colloquia. Sommerfeld owned an alpine ski hut to which students were often invited for discussions of physics as demanding as

5000-429: The 19th century. Another important event in the 19th century was the discovery of electromagnetic theory , unifying the previously separate phenomena of electricity, magnetism and light. The pillars of modern physics , and perhaps the most revolutionary theories in the history of physics, have been relativity theory and quantum mechanics . Newtonian mechanics was subsumed under special relativity and Newton's gravity

5125-556: The Bavarian Alps. He recounted philosophical conversations with his fellow students and teachers about understanding the atom while receiving his scientific training in Munich, Göttingen and Copenhagen. Heisenberg later stated that "My mind was formed by studying philosophy, Plato and that sort of thing" and that "Modern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in

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5250-476: The Dutchmen Snell and Huygens. In the 18th and 19th centuries Joseph-Louis Lagrange , Leonhard Euler and William Rowan Hamilton would extend the theory of classical mechanics considerably. They picked up the interactive intertwining of mathematics and physics begun two millennia earlier by Pythagoras. Among the great conceptual achievements of the 19th and 20th centuries were the consolidation of

5375-587: The Earth ) or may be an alternative model that provides answers that are more accurate or that can be more widely applied. In the latter case, a correspondence principle will be required to recover the previously known result . Sometimes though, advances may proceed along different paths. For example, an essentially correct theory may need some conceptual or factual revisions; atomic theory , first postulated millennia ago (by several thinkers in Greece and India ) and

5500-571: The Institute. With this appointment at the KWIP, Heisenberg obtained his first professorship. Peter Debye was still director of the institute, but had gone on leave to the United States after he had refused to become a German citizen when the HWA took administrative control of the KWIP. Heisenberg still also had his department of physics at the University of Leipzig where work had been done for

5625-704: The KWIP under the HWA program, considerable personal and professional animosity developed between Diebner and Heisenberg's inner circle, which included Karl Wirtz and Carl Friedrich von Weizsäcker . At a scientific conference on 26–28 February 1942 at the Kaiser Wilhelm Institute for Physics, called by the Army Weapons Office, Heisenberg presented a lecture to Reich officials on energy acquisition from nuclear fission. The lecture, entitled "Die theoretischen Grundlagen für die Energiegewinnung aus der Uranspaltung" ("The theoretical basis for energy generation from uranium fission") was, as Heisenberg wrote after

5750-612: The Ludwig Maximilian University of Munich. Müller was not a theoretical physicist, had not published in a physics journal, and was not a member of the German Physical Society . His appointment was considered a travesty and detrimental to educating theoretical physicists. The three investigators who led the SS investigation of Heisenberg had training in physics. Indeed, Heisenberg had participated in

5875-596: The Mathematics Reading Room, as well as managing the reading room. Sommerfeld's Habilitationsschrift was completed under Klein, in 1895, which allowed Sommerfeld to become a Privatdozent at Göttingen. As a Privatdozent, Sommerfeld lectured on a wide range of mathematical and mathematical physics topics. His lectures on partial differential equations were first offered at Göttingen, and they evolved over his teaching career to become Volume VI of his textbook series Lectures on Theoretical Physics , under

6000-539: The Netherlands, then to Sweden. Meitner, and her nephew Otto Robert Frisch , correctly interpreted Hahn's and Strassmann's results as being nuclear fission . Frisch confirmed this experimentally on 13 January 1939. In June and July 1939, Heisenberg traveled to the United States visiting Samuel Abraham Goudsmit at the University of Michigan in Ann Arbor . However, Heisenberg refused an invitation to emigrate to

6125-506: The Second World War in a letter to Samuel Goudsmit , "adapted to the intelligence level of a Reich Minister", as is often done when presenting complex and cutting-edge scientific concepts to laymen. Heisenberg lectured on the enormous energy potential of nuclear fission, stating that 250 million electron volts could be released through the fission of an atomic nucleus. Heisenberg stressed that pure U-235 had to be obtained to achieve

6250-415: The United States. Sommerfeld was a great theoretician. Besides his invaluable contributions to quantum theory, he worked in other fields of physics, such as the classical theory of electromagnetism. For example, he proposed a solution to the problem of a radiating hertzian dipole over a conducting earth, which over the years led to many applications. His Sommerfeld identity and Sommerfeld integrals are to

6375-644: The United States. He did not see Goudsmit again until six years later, when Goudsmit was the chief scientific advisor to the American Operation Alsos at the close of World War II. The German nuclear weapons program , known as Uranverein , was formed on 1 September 1939, the day World War II began in Europe. The Heereswaffenamt (HWA, Army Ordnance Office) had squeezed the Reichsforschungsrat (RFR, Reich Research Council) out of

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6500-914: The University of Leipzig. He taught lectures that physicists like Edward Teller and Robert Oppenheimer would attend, who would later work on the Manhattan Project for the United States. During Heisenberg's tenure at Leipzig, the high quality of the doctoral students and post-graduate and research associates who studied and worked with him is clear from the acclaim many later earned. At various times they included Erich Bagge , Felix Bloch , Ugo Fano , Siegfried Flügge , William Vermillion Houston , Friedrich Hund , Robert S. Mulliken , Rudolf Peierls , George Placzek , Isidor Isaac Rabi , Fritz Sauter , John C. Slater , Edward Teller , John Hasbrouck van Vleck , Victor Frederick Weisskopf , Carl Friedrich von Weizsäcker , Gregor Wentzel , and Clarence Zener . In early 1929, Heisenberg and Pauli submitted

6625-602: The Uranverein project was placed under the leadership of the Reich Research Council, it focused on nuclear power production and thus maintained its kriegswichtig (importance for the war) status; funding therefore continued from the military. The nuclear power project was broken down into the following main areas: uranium and heavy water production, uranium isotope separation and the Uranmaschine (uranium machine, i.e., nuclear reactor ). The project

6750-514: The algebra of matrices with their multiplication did not enter the picture as they did in the matrix formulation of quantum mechanics. In 1928, Albert Einstein nominated Heisenberg, Born, and Jordan for the Nobel Prize in Physics . The announcement of the Nobel Prize in Physics for 1932 was delayed until November 1933. It was at that time announced that Heisenberg had won the Prize for 1932 "for

6875-419: The applications of relativity to problems in astronomy and cosmology respectively . All of these achievements depended on the theoretical physics as a moving force both to suggest experiments and to consolidate results — often by ingenious application of existing mathematics, or, as in the case of Descartes and Newton (with Leibniz ), by inventing new mathematics. Fourier's studies of heat conduction led to

7000-406: The appointment amounted to the "destruction of the Munich theoretical physics tradition". As for Sommerfeld's once patriotic views, he wrote to Einstein shortly after Hitler took power: "I can assure you that the misuse of the word ‘national’ by our rulers has thoroughly broken me of the habit of national feelings that was so pronounced in my case. I would now be willing to see Germany disappear as

7125-583: The art of lecturing. While at Göttingen, Sommerfeld met Johanna Höpfner, daughter of Ernst Höpfner, curator at Göttingen. In October 1897 Sommerfeld began the appointment to the Chair of Mathematics at the Bergakademie in Clausthal-Zellerfeld ; he was successor to Wilhelm Wien . This appointment provided enough income to eventually marry Johanna. At Klein's request, Sommerfeld took on

7250-514: The body of knowledge of both factual and scientific views and possess a usual scientific quality of the tests of repeatability, consistency with existing well-established science and experimentation. There do exist mainstream theories that are generally accepted theories based solely upon their effects explaining a wide variety of data, although the detection, explanation, and possible composition are subjects of debate. The proposed theories of physics are usually relatively new theories which deal with

7375-492: The continuing failure of the Bohr–Sommerfeld model to explain the outstanding problem of the anomalous Zeeman effect, led Heisenberg to use the virtual oscillator model to try to calculate spectral frequencies. The method proved too difficult to immediately apply to realistic problems, so Heisenberg turned to a simpler example, the anharmonic oscillator . The dipole oscillator consists of a simple harmonic oscillator , which

7500-555: The creation of quantum mechanics, the application of which has, inter alia , led to the discovery of the allotropic forms of hydrogen ". The development of quantum mechanics, and the apparently contradictory implications in regard to what is "real" had profound philosophical implications, including what scientific observations truly mean. In contrast to Albert Einstein and Louis de Broglie , who were realists who believed that particles had an objectively true momentum and position at all times (even if both could not be measured), Heisenberg

7625-458: The department of physics at the University of Leipzig ; he gave his inaugural lecture there on 1 February 1928. In his first paper published from Leipzig, Heisenberg used the Pauli exclusion principle to solve the mystery of ferromagnetism . At 25 years old, Heisenberg gained the title of the youngest full-time professor in Germany and professorial chair of the Institute for Theoretical Physics at

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7750-462: The detailed calculations are worked out by Aitchison and coauthors. In Copenhagen, Heisenberg and Hans Kramers collaborated on a paper on dispersion, or the scattering from atoms of radiation whose wavelength is larger than the atoms. They showed that the successful formula Kramers had developed earlier could not be based on Bohr orbits, because the transition frequencies are based on level spacings which are not constant. The frequencies which occur in

7875-452: The development of quantum mechanics, which was then in very rapid development. During his 32 years of teaching at Munich, Sommerfeld taught general and specialized courses, as well as holding seminars and colloquia. The general courses were on mechanics, mechanics of deformable bodies, electrodynamics, optics, thermodynamics and statistical mechanics, and partial differential equations in physics. They were held four hours per week, 13 weeks in

8000-487: The discovery of the neutron by James Chadwick in 1932, Heisenberg submitted the first of three papers on his neutron-proton model of the nucleus . After Adolf Hitler came to power in 1933, Heisenberg was attacked in the press as a "White Jew" (i.e. an Aryan who acts like a Jew). Supporters of Deutsche Physik , or German Physics (also known as Aryan Physics), launched vicious attacks against leading theoretical physicists, including Arnold Sommerfeld and Heisenberg. From

8125-504: The doctoral examination of one of them at the Universität Leipzig . The most influential of the three was Johannes Juilfs . During their investigation, they became supporters of Heisenberg as well as his position against the ideological policies of the Deutsche Physik movement in theoretical physics and academia. In mid-1936, Heisenberg presented his theory of cosmic-ray showers in two papers. Four more papers appeared in

8250-604: The early 1930s onward, the anti-Semitic and anti-theoretical physics movement Deutsche Physik had concerned itself with quantum mechanics and the theory of relativity . As applied in the university environment, political factors took priority over scholarly ability, even though its two most prominent supporters were the Nobel Laureates in Physics Philipp Lenard and Johannes Stark . There had been many failed attempts to have Heisenberg appointed as

8375-489: The early 20th century, theorists, such as Sommerfeld at Munich and Max Born at the University of Göttingen , with their early training in mathematics, turned this around so that mathematical physics, i.e., theoretical physics, became the prime mover, and experimental physics was used to verify or advance theory. After getting their doctorates with Sommerfeld, Wolfgang Pauli , Werner Heisenberg , and Walter Heitler became Born's assistants and made significant contributions to

8500-770: The edge of the Black Forest , which eventually became included in the French occupation zone. This allowed the American task force of the Alsos Mission to take into custody a large number of German scientists associated with nuclear research. Theoretical physicist The advancement of science generally depends on the interplay between experimental studies and theory . In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations. For example, while developing special relativity , Albert Einstein

8625-407: The event, Bohr was a guest lecturer and gave a series of comprehensive lectures on quantum atomic physics and Heisenberg met Bohr for the first time, which had a lasting effect on him. Heisenberg's doctoral thesis , the topic of which was suggested by Sommerfeld, was on turbulence ; the thesis discussed both the stability of laminar flow and the nature of turbulent flow . The problem of stability

8750-483: The existence of positive electrons, later to be named positrons . In 1932, from a cloud chamber photograph of cosmic rays , the American physicist Carl David Anderson identified a track as having been made by a positron . In mid-1933, Heisenberg presented his theory of the positron. His thinking on Dirac's theory and further development of the theory were set forth in two papers. The first, "Bemerkungen zur Diracschen Theorie des Positrons" ("Remarks on Dirac's theory of

8875-489: The external source. He then solved the same problem by treating the anharmonic potential term as a perturbation to the harmonic oscillator and using the perturbation methods that he and Born had developed. Both methods led to the same results for the first and the very complicated second-order correction terms. This suggested that behind the very complicated calculations lay a consistent scheme. So Heisenberg set out to formulate these results without any explicit dependence on

9000-690: The facilities in the Black Forest. The Alsos Mission was an Allied effort to determine if the Germans had an atomic bomb program and to exploit German atomic-related facilities, research, material resources, and scientific personnel for the benefit of the US. Personnel on this operation generally swept into areas which had just come under control of the Allied military forces, but sometimes they operated in areas still under control by German forces. Berlin had been

9125-500: The first of two papers laying the foundation for relativistic quantum field theory . Also in 1929, Heisenberg went on a lecture tour of China, Japan, India, and the United States. In the spring of 1929, he was a visiting lecturer at the University of Chicago , where he lectured on quantum mechanics. In 1928, the British mathematical physicist Paul Dirac had derived his relativistic wave equation of quantum mechanics, which implied

9250-416: The highest order, writing Principia Mathematica . In it contained a grand synthesis of the work of Copernicus, Galileo and Kepler; as well as Newton's theories of mechanics and gravitation, which held sway as worldviews until the early 20th century. Simultaneously, progress was also made in optics (in particular colour theory and the ancient science of geometrical optics ), courtesy of Newton, Descartes and

9375-455: The idea of energy (as well as its global conservation) by the inclusion of heat , electricity and magnetism , and then light . The laws of thermodynamics , and most importantly the introduction of the singular concept of entropy began to provide a macroscopic explanation for the properties of matter. Statistical mechanics (followed by statistical physics and Quantum statistical mechanics ) emerged as an offshoot of thermodynamics late in

9500-675: The late 1920s. In the aftermath of World War 2, more progress brought much renewed interest in QFT, which had since the early efforts, stagnated. The same period also saw fresh attacks on the problems of superconductivity and phase transitions, as well as the first applications of QFT in the area of theoretical condensed matter. The 1960s and 70s saw the formulation of the Standard model of particle physics using QFT and progress in condensed matter physics (theoretical foundations of superconductivity and critical phenomena , among others ), in parallel to

9625-748: The latest advances in quantum mechanics, before splitting into two volumes. In 1918, Sommerfeld succeeded Einstein as chair of the Deutsche Physikalische Gesellschaft (DPG). One of his accomplishments was the founding of a new journal. The scientific papers published in DPG journals became so voluminous, that in 1919 a committee of the DPG recommended the establishment of Zeitschrift für Physik for publication of original research articles, which commenced in 1920. Since any reputable scientist could have their article published without refereeing, time between submission and publication

9750-442: The letter to Heydrich, Himmler said Germany could not afford to lose or silence Heisenberg, as he would be useful for teaching a generation of scientists. To Heisenberg, Himmler said the letter came on the recommendation of his family and he cautioned Heisenberg to make a distinction between professional physics research results and the personal and political attitudes of the involved scientists. Wilhelm Müller replaced Sommerfeld at

9875-418: The mathematical foundations of quantum mechanics. On 23 February, Heisenberg wrote a letter to fellow physicist Wolfgang Pauli , in which he first described his new principle. In his paper on the principle, Heisenberg used the word " Ungenauigkeit " (imprecision), not uncertainty, to describe it. In 1927, Heisenberg was appointed ordentlicher Professor (professor ordinarius) of theoretical physics and head of

10000-463: The matter and regain his honour. At one point, Heisenberg's mother visited Himmler's mother. The two women knew each other, as Heisenberg's maternal grandfather and Himmler's father were rectors and members of a Bavarian hiking club. Eventually, Himmler settled the Heisenberg affair by sending two letters, one to SS Gruppenführer Reinhard Heydrich and one to Heisenberg, both on 21 July 1938. In

10125-637: The national defense and economy. The conference was attended by Bernhard Rust , the Reich Minister of Science, Education and National Culture. At the conference, Reich Minister Rust decided to take the nuclear project away from the Kaiser Wilhelm Society. The Reich Research Council was to take on the project. In April 1942 the army returned the Physics Institute to the Kaiser Wilhelm Society, naming Heisenberg as Director at

10250-465: The national exam in 1892 and then began a year of military service, which was done with the reserve regiment in Königsberg. He completed his obligatory military service in September 1893, and for the next eight years continued voluntary eight-week military service. With his turned up moustache, his physical build, his Prussian bearing, and the fencing scar on his face, he gave the impression of being

10375-413: The new Theoretical Physics Institute at the University of Munich . He was selected for these positions by Wilhelm Röntgen , Director of the Physics Institute at Munich, which was looked upon by Sommerfeld as being called to a "privileged sphere of action". Until the late 19th century and early 20th century, experimental physics in Germany was considered as having a higher status within the community. In

10500-461: The next 12 years: Barbara, Christine, Jochen , Martin and Verena. In 1939 he bought a summer home for his family in Urfeld am Walchensee , in southern Germany. One of Heisenberg's sons, Martin Heisenberg , became a neurobiologist at the University of Würzburg , while another son, Jochen Heisenberg , became a physics professor at the University of New Hampshire . From 1924 to 1927, Heisenberg

10625-484: The next two years. In December 1938, the German chemists Otto Hahn and Fritz Strassmann sent a manuscript to The Natural Sciences reporting they had detected the element barium after bombarding uranium with neutrons, leading Hahn to conclude that a bursting of the uranium nucleus had occurred; simultaneously, Hahn communicated these results to his friend Lise Meitner , who had in July of that year fled, first to

10750-444: The number of scientists working on applied nuclear fission diminished dramatically. Many of the scientists not working with the main institutes stopped working on nuclear fission and devoted their efforts to more pressing war-related work. In September 1942, Heisenberg submitted his first paper of a three-part series on the scattering matrix, or S-matrix , in elementary particle physics . The first two papers were published in 1943 and

10875-714: The ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language". In 1919 Heisenberg arrived in Munich as a member of the Freikorps to fight the Bavarian Soviet Republic established a year earlier. Five decades later he recalled those days as youthful fun, like "playing cops and robbers and so on; it was nothing serious at all"; his duties were restricted to "seizing bicycles or typewriters from 'red' administrative buildings", and guarding suspected "red" prisoners. From 1920 to 1923, he studied physics and mathematics at

11000-403: The paper, he recognized the formulation as one which could be transcribed and extended to the systematic language of matrices, which he had learned from his study under Jakob Rosanes at Breslau University . Born, with the help of his assistant and former student Pascual Jordan , began immediately to make the transcription and extension, and they submitted their results for publication; the paper

11125-425: The particle independently of the process of observation. As a final consequence, the natural laws formulated mathematically in quantum theory no longer deal with the elementary particles themselves but with our knowledge of them. Nor is it any longer possible to ask whether or not these particles exist in space and time objectively ... When we speak of the picture of nature in the exact science of our age, we do not mean

11250-506: The position of editor of Volume V of Enzyklopädie der mathematischen Wissenschaften ; it was a major undertaking which lasted from 1898 to 1926. In 1900, Sommerfeld started his appointment to the Chair of Applied Mechanics at the Königliche Technische Hochschule Aachen (later RWTH Aachen University ) as extraordinarius professor, which was arranged through Klein's efforts. At Aachen, he developed

11375-537: The positron") was published in 1934, and the second, "Folgerungen aus der Diracschen Theorie des Positrons" ("Consequences of Dirac's Theory of the Positron"), was published in 1936. In these papers Heisenberg was the first to reinterpret the Dirac equation as a "classical" field equation for any point particle of spin ħ/2, itself subject to quantization conditions involving anti- commutators . Thus reinterpreting it as

11500-511: The present day the most common way to solve this kind of problem. Also, as a mark of the prowess of Sommerfeld's school of theoretical physics and the rise of theoretical physics in the early 1900s, as of 1928, nearly one-third of the ordinarius professors of theoretical physics in the German-speaking world were students of Sommerfeld. On 1 April 1935 Sommerfeld achieved emeritus status. He remained as his own temporary replacement during

11625-419: The process of becoming established and some proposed theories. It can include speculative sciences. This includes physics fields and physical theories presented in accordance with known evidence, and a body of associated predictions have been made according to that theory. Some fringe theories go on to become a widely accepted part of physics. Other fringe theories end up being disproven. Some fringe theories are

11750-492: The reader is familiar with Kramers -Heisenberg transition probability calculations. The main new idea, non-commuting matrices , is justified only by a rejection of unobservable quantities. It introduces the non- commutative multiplication of matrices by physical reasoning, based on the correspondence principle , despite the fact that Heisenberg was not then familiar with the mathematical theory of matrices. The path leading to these results has been reconstructed by MacKinnon, and

11875-671: The research division of the Allgemeine Elektrizitäts-Gesellschaft (General Electric Company) and president of the Deutsche Physikalische Gesellschaft , made reference to this in their correspondence to officials in the Reich. In an attachment to Prandtl's 28 April 1941 letter to Reich Marshal Hermann Göring , Prandtl referred to the appointment as "sabotage" of necessary theoretical physics instruction. In an attachment to Ramsauer's 20 January 1942 letter to Reich Minister Bernhard Rust , Ramsauer concluded that

12000-607: The rise of medieval universities , the only acknowledged intellectual disciplines were the seven liberal arts of the Trivium like grammar , logic , and rhetoric and of the Quadrivium like arithmetic , geometry , music and astronomy . During the Middle Ages and Renaissance , the concept of experimental science, the counterpoint to theory, began with scholars such as Ibn al-Haytham and Francis Bacon . As

12125-609: The selection process for his successor, which took until 1 December 1939. The process was lengthy due to academic and political differences between the Munich Faculty's selection and that of both the Reichserziehungsministerium (REM; Reich Education Ministry) and the supporters of Deutsche Physik , which was anti-Semitic and had a bias against theoretical physics , especially including quantum mechanics . The appointment of Wilhelm Müller – who

12250-1369: The six-volume Lectures on Theoretical Physics . For a list of students, please see the list organized by type. Four of Sommerfeld's doctoral students, Werner Heisenberg , Wolfgang Pauli , Peter Debye , and Hans Bethe went on to win Nobel Prizes , while others, most notably, Walter Heitler , Rudolf Peierls , Karl Bechert , Hermann Brück , Paul Peter Ewald , Eugene Feenberg , Herbert Fröhlich , Erwin Fues , Ernst Guillemin , Helmut Hönl , Ludwig Hopf , Adolf Kratzer , Otto Laporte , Wilhelm Lenz , Karl Meissner , Rudolf Seeliger , Ernst C. Stückelberg , Heinrich Welker , Gregor Wentzel , Alfred Landé , and Léon Brillouin became famous in their own right. Three of Sommerfeld's postdoctoral supervisees, Linus Pauling , Isidor I. Rabi and Max von Laue , won Nobel Prizes, and ten others, William Allis , Edward Condon , Carl Eckart , Edwin C. Kemble , William V. Houston , Karl Herzfeld , Walther Kossel , Philip M. Morse , Howard Robertson , and Wojciech Rubinowicz went on to become famous in their own right. Walter Rogowski , an undergraduate student of Sommerfeld at RWTH Aachen , also went on to become famous in his own right. Max Born believed Sommerfeld's abilities included

12375-448: The sport. While at Munich, Sommerfeld came in contact with the special theory of relativity by Albert Einstein , which was not yet widely accepted. His mathematical contributions to the theory helped its acceptance by the skeptics. In 1914 he worked with Léon Brillouin on the propagation of electromagnetic waves in dispersive media. He became one of the founders of quantum mechanics ; some of his contributions included co-discovery of

12500-484: The study of physics which include scientific approaches, means for determining the validity of models and new types of reasoning used to arrive at the theory. However, some proposed theories include theories that have been around for decades and have eluded methods of discovery and testing. Proposed theories can include fringe theories in the process of becoming established (and, sometimes, gaining wider acceptance). Proposed theories usually have not been tested. In addition to

12625-436: The subsequent series of papers with Max Born and Pascual Jordan , during the same year, his matrix formulation of quantum mechanics was substantially elaborated. He is known for the uncertainty principle , which he published in 1927. Heisenberg was awarded the 1932 Nobel Prize in Physics "for the creation of quantum mechanics". Heisenberg also made contributions to the theories of the hydrodynamics of turbulent flows ,

12750-472: The theories like those listed below, there are also different interpretations of quantum mechanics , which may or may not be considered different theories since it is debatable whether they yield different predictions for physical experiments, even in principle. For example, AdS/CFT correspondence , Chern–Simons theory , graviton , magnetic monopole , string theory , theory of everything . Fringe theories include any new area of scientific endeavor in

12875-495: The theory of hydrodynamics , which would retain his interest for a long time. Later, at the University of Munich, Sommerfeld's students Ludwig Hopf and Werner Heisenberg would write their Ph.D. theses on this topic. For his contributions to the understanding of journal bearing lubrication during his time at Aachen, he was named as one of the 23 "Men of Tribology" by Duncan Dowson . From 1906, Sommerfeld established himself as ordinarius professor of physics and director of

13000-440: The third in 1944. The S-matrix described only the states of incident particles in a collision process, the states of those emerging from the collision, and stable bound states ; there would be no reference to the intervening states. This was the same precedent as he followed in 1925 in what turned out to be the foundation of the matrix formulation of quantum mechanics through only the use of observables. In February 1943, Heisenberg

13125-462: The title Partial Differential Equations in Physics . Lectures by Klein in 1895 and 1896 on rotating bodies led Klein and Sommerfeld to write a four-volume text Die Theorie des Kreisels – a 13-year collaboration, 1897–1910. The first two volumes were on theory, and the latter two were on applications in geophysics, astronomy, and technology. The association Sommerfeld had with Klein influenced Sommerfeld's turn of mind to be applied mathematics and in

13250-573: The virtual oscillator model. To do this, he replaced the Fourier expansions for the spatial coordinates with matrices, matrices which corresponded to the transition coefficients in the virtual oscillator method. He justified this replacement by an appeal to Bohr's correspondence principle and the Pauli doctrine that quantum mechanics must be limited to observables. On 9 July, Heisenberg gave Born this paper to review and submit for publication. When Born read

13375-539: The vision provided by pure mathematical systems can provide clues to how a physical system might be modeled; e.g., the notion, due to Riemann and others, that space itself might be curved. Theoretical problems that need computational investigation are often the concern of computational physics . Theoretical advances may consist in setting aside old, incorrect paradigms (e.g., aether theory of light propagation, caloric theory of heat, burning consisting of evolving phlogiston , or astronomical bodies revolving around

13500-456: The winter and 11 weeks in the summer, and were for students who had taken experimental physics courses from Röntgen and later by Wilhelm Wien. There was also a two-hour weekly presentation for the discussion of problems. The specialized courses were of topical interest and based on Sommerfeld's research interests; material from these courses appeared later in the scientific literature publications of Sommerfeld. The objective of these special lectures

13625-530: The works of these men (alongside Galileo's) can perhaps be considered to constitute the Scientific Revolution. The great push toward the modern concept of explanation started with Galileo , one of the few physicists who was both a consummate theoretician and a great experimentalist . The analytic geometry and mechanics of Descartes were incorporated into the calculus and mechanics of Isaac Newton , another theoretician/experimentalist of

13750-562: Was a Privatdozent at Göttingen , meaning he was qualified to teach and examine independently, without having a chair. From 17 September 1924 to 1 May 1925, under an International Education Board Rockefeller Foundation fellowship, Heisenberg went to do research with Niels Bohr , director of the Institute of Theoretical Physics at the University of Copenhagen . His seminal paper, " Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen " ("Quantum theoretical re-interpretation of kinematic and mechanical relations") also called

13875-406: Was an anti-realist, arguing that direct knowledge of what is "real" was beyond the scope of science. Writing in his book The Physicist's Conception of Nature, Heisenberg argued that ultimately we only can speak of the knowledge (numbers in tables) which describe something about particles but we can never have any "true" access to the particles themselves: We can no longer speak of the behaviour of

14000-640: Was appointed to the Chair for Theoretical Physics at the Friedrich-Wilhelms-Universität (today, the Humboldt-Universität zu Berlin ). In April, his election to the Preußische Akademie der Wissenschaften ( Prussian Academy of Sciences ) was approved. That same month, he moved his family to their retreat in Urfeld as Allied bombing increased in Berlin. In the summer, he dispatched the first of his staff at

14125-502: Was born in Würzburg , Germany, to Kaspar Ernst August Heisenberg , and his wife, Annie Wecklein. His father was a secondary school teacher of classical languages who became Germany's only ordentlicher Professor (ordinarius professor) of medieval and modern Greek studies in the university system. Heisenberg was raised and lived as a Lutheran Christian. In his late teenage years, Heisenberg read Plato's Timaeus while hiking in

14250-510: Was concerned with the Lorentz transformation which left Maxwell's equations invariant, but was apparently uninterested in the Michelson–Morley experiment on Earth 's drift through a luminiferous aether . Conversely, Einstein was awarded the Nobel Prize for explaining the photoelectric effect , previously an experimental result lacking a theoretical formulation. A physical theory

14375-686: Was director of the institute until it was moved to Munich in 1958. He then became director of the Max Planck Institute for Physics and Astrophysics from 1960 to 1970. Heisenberg was also president of the German Research Council , chairman of the Commission for Atomic Physics, chairman of the Nuclear Physics Working Group, and president of the Alexander von Humboldt Foundation . Werner Karl Heisenberg

14500-526: Was elected an Honorary member of the Optical Society in 1950. He was nominated for the Nobel Prize 84 times, more than any other physicist (including Otto Stern , who got nominated 82 times ), but he never received the award. Sommerfeld died on April 26, 1951, in Munich from injuries after a traffic accident while walking with his grandchildren. The accident occurred at the corner of Dietlindenstrasse and Biedersteiner Strasse near his house which

14625-422: Was given a kinematic explanation by general relativity . Quantum mechanics led to an understanding of blackbody radiation (which indeed, was an original motivation for the theory) and of anomalies in the specific heats of solids — and finally to an understanding of the internal structures of atoms and molecules . Quantum mechanics soon gave way to the formulation of quantum field theory (QFT), begun in

14750-467: Was held soon thereafter and included Heisenberg, Klaus Clusius , Robert Döpel and Carl Friedrich von Weizsäcker . The Kaiser-Wilhelm Institut für Physik (KWIP, Kaiser Wilhelm Institute for Physics) in Berlin-Dahlem , was placed under HWA authority, with Diebner as the administrative director, and the military control of the nuclear research commenced. During the period when Diebner administered

14875-463: Was investigated by the use of the Orr–Sommerfeld equation , a fourth-order linear differential equation for small disturbances from laminar flow. He briefly returned to this topic after World War II. At Göttingen, under Born, he completed his habilitation in 1924 with a Habilitationsschrift (habilitation thesis) on the anomalous Zeeman effect . In his youth he was a member and Scoutleader of

15000-553: Was lengthy due to academic and political differences between the Munich Faculty's selection and that of the Reich Education Ministry and the supporters of Deutsche Physik . In 1935, the Munich Faculty drew up a list of candidates to replace Sommerfeld as ordinarius professor of theoretical physics and head of the Institute for Theoretical Physics at the University of Munich. The three candidates had all been former students of Sommerfeld: Heisenberg, who had received

15125-513: Was not a theoretical physicist, had not published in a physics journal, and was not a member of the Deutsche Physikalische Gesellschaft – as a replacement for Sommerfeld, was considered such a travesty and detrimental to educating a new generation of physicists that both Ludwig Prandtl , director of the Kaiser Wilhelm Institut für Strömungsforschung ( Kaiser Wilhelm Institute for Flow Research ), and Carl Ramsauer , director of

15250-478: Was received for publication just 60 days after Heisenberg's paper. A follow-on paper was submitted for publication before the end of the year by all three authors. Up until this time, matrices were seldom used by physicists; they were considered to belong to the realm of pure mathematics . Gustav Mie had used them in a paper on electrodynamics in 1912 and Born had used them in his work on the lattice theory of crystals in 1921. While matrices were used in these cases,

15375-438: Was then essentially split up between a number of institutes, where the directors dominated the research and set their own research agendas. The point in 1942, when the army relinquished its control of the German nuclear weapons program, was the zenith of the project relative to the number of personnel. About 70 scientists worked for the program, with about 40 devoting more than half their time to nuclear fission research. After 1942,

15500-507: Was to grapple with current issues in theoretical physics and for Sommerfeld and the students to garner a systematic comprehension of the issue, independent of whether or not they were successful in solving the problem posed by the current issue. For the seminar and colloquium periods, students were assigned papers from the current literature and they then prepared an oral presentation. From 1942 to 1951, Sommerfeld worked on putting his lecture notes in order for publication. They were published as

15625-486: Was very rapid – as fast as two weeks. This greatly stimulated the scientific theoretical developments, especially that of quantum mechanics in Germany at that time, as this journal was the preferred publication vehicle for the new generation of quantum theorists with avant-garde views. In the winter semester of 1922/1923, Sommerfeld gave the Carl Schurz Memorial Professor of Physics lectures at

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