Eugene Paul "E. P." Wigner (Hungarian: Wigner Jenő Pál; November 17, 1902 – January 1, 1995) was a HungarianAmerican theoretical physicist, engineer and mathematician. He received the Nobel Prize in Physics in 1963 "for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles".^{[1]}
A graduate of the Technical University of Berlin, Wigner worked as an assistant to Karl Weissenberg and Richard Becker at the Kaiser Wilhelm Institute in Berlin, and David Hilbert at the University of Göttingen. Wigner and Hermann Weyl were responsible for introducing group theory into physics, particularly the theory of symmetry in physics. Along the way he performed groundbreaking work in pure mathematics, in which he authored a number of mathematical theorems. In particular, Wigner's theorem is a cornerstone in the mathematical formulation of quantum mechanics. He is also known for his research into the structure of the atomic nucleus. In 1930, Princeton University recruited Wigner, along with John von Neumann, and he moved to the United States.
Wigner participated in a meeting with Leo Szilard and Albert Einstein that resulted in the EinsteinSzilard letter, which prompted President Franklin D. Roosevelt to initiate the Manhattan Project to develop atomic bombs. Wigner was afraid that the German nuclear weapon project would develop an atomic bomb first. During the Manhattan Project, he led a team whose task was to design nuclear reactors to convert uranium into weapons grade plutonium. At the time, reactors existed only on paper, and no reactor had yet gone critical. Wigner was disappointed that DuPont was given responsibility for the detailed design of the reactors, not just their construction. He became Director of Research and Development at the Clinton Laboratory (now the Oak Ridge National Laboratory) in early 1946, but became frustrated with bureaucratic interference by the Atomic Energy Commission, and returned to Princeton.
In the postwar period he served on a number of government bodies, including the National Bureau of Standards from 1947 to 1951, the mathematics panel of the National Research Council from 1951 to 1954, the physics panel of the National Science Foundation, and the influential General Advisory Committee of the Atomic Energy Commission from 1952 to 1957 and again from 1959 to 1964. In later life, he became more philosophical, and published The Unreasonable Effectiveness of Mathematics in the Natural Sciences, his bestknown work outside technical mathematics and physics.
Wigner Jenő Pál was born in Budapest, AustriaHungary on November 17, 1902, to middle class Jewish parents, Elisabeth (Einhorn) and Anthony Wigner, a leather tanner. He had an older sister, Bertha, known as Biri, and a younger sister Margit, known as Manci,^{[2]} who later married British theoretical physicist Paul Dirac.^{[3]} He was home schooled by a professional teacher until the age of 9, when he started school at the third grade. During this period, Wigner developed an interest in mathematical problems.^{[4]} At the age of 11, Wigner contracted what his doctors believed to be tuberculosis. His parents sent him to live for six weeks in a sanatorium in the Austrian mountains, before the doctors concluded that the diagnosis was mistaken.^{[5]}
Wigner's family was Jewish, but not religiously observant, and his Bar Mitzvah was a secular one. From 1915 through 1919, he studied at the secondary grammar school called Fasori Evangélikus Gimnázium, the school his father had attended. Religious education was compulsory, and he attended classes in Judaism taught by a rabbi.^{[6]} A fellow student was János von Neumann, who was a year behind Wigner. They both benefited from the instruction of the noted mathematics teacher László Rátz.^{[7]} In 1919, to escape the Béla Kun communist regime, the Wigner family briefly fled to Austria, returning to Hungary after Kun's downfall.^{[8]} Partly as a reaction to the prominence of Jews in the Kun regime, the family converted to Lutheranism.^{[9]} Wigner explained later in his life that his family decision to convert to Lutheranism "was not at heart a religious decision but an anticommunist one".^{[9]} On religious views, Wigner was an atheist.^{[10]}
After graduating from the secondary school in 1920, Wigner enrolled at the Budapest University of Technical Sciences, known as the Műegyetem. He was not happy with the courses on offer,^{[11]} and in 1921 enrolled at the Technische Hochschule Berlin (now Technical University of Berlin), where he studied chemical engineering.^{[12]} He also attended the Wednesday afternoon colloquia of the German Physical Society. These colloquia featured such luminaries as Max Planck, Max von Laue, Rudolf Ladenburg, Werner Heisenberg, Walther Nernst, Wolfgang Pauli, and Albert Einstein.^{[13]} Wigner also met the physicist Leó Szilárd, who at once became Wigner's closest friend.^{[14]} A third experience in Berlin was formative. Wigner worked at the Kaiser Wilhelm Institute for Physical Chemistry and Electrochemistry (now the Fritz Haber Institute), and there he met Michael Polanyi, who became, after László Rátz, Wigner's greatest teacher. Polanyi supervised Wigner's DSc thesis, Bildung und Zerfall von Molekülen ("Formation and Decay of Molecules").^{[15]}
Wigner returned to Budapest, where he went to work at his father's tannery, but in 1926, he accepted an offer from Karl Weissenberg at the Kaiser Wilhelm Institute in Berlin. Weissenberg wanted someone to assist him with his work on xray crystallography, and Polanyi had recommended Wigner. After six months as Weissenberg's assistant, Wigner went to work for Richard Becker for two semesters. Wigner explored quantum mechanics, studying the work of Erwin Schrödinger. He also delved into the group theory of Ferdinand Frobenius and Eduard Ritter von Weber.^{[16]}
Wigner received a request from Arnold Sommerfeld to work at the University of Göttingen as an assistant to the great mathematician David Hilbert. This proved a disappointment, as the aged Hilbert's abilities were failing, and his interests had shifted to logic. Wigner nonetheless studied independently.^{[17]} He laid the foundation for the theory of symmetries in quantum mechanics and in 1927 introduced what is now known as the Wigner Dmatrix.^{[18]} Wigner and Hermann Weyl were responsible for introducing group theory into quantum mechanics. The latter had written a standard text, Group Theory and Quantum Mechanics (1928), but it was not easy to understand, especially for younger physicists. Wigner's Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra (1931) made group theory accessible to a wider audience.^{[19]}
In these works, Wigner laid the foundation for the theory of symmetries in quantum mechanics.^{[20]} Wigner's theorem proved by Wigner in 1931, is a cornerstone of the mathematical formulation of quantum mechanics. The theorem specifies how physical symmetries such as rotations, translations, and CPT symmetry are represented on the Hilbert space of states. According to the theorem, any symmetry transformation is represented by a linear and unitary or antilinear and antiunitary transformation of Hilbert space. The representation of a symmetry group on a Hilbert space is either an ordinary representation or a projective representation.^{[21]}^{[22]}
In the late 1930s, Wigner extended his research into atomic nuclei. By 1929, his papers were drawing notice in the world of physics. In 1930, Princeton University recruited Wigner for a oneyear lectureship, at 7 times the salary that he had been drawing in Europe. Princeton recruited von Neumann at the same time. Jenő Pál Wigner and János von Neumann had collaborated on three papers together in 1928 and two in 1929. They anglicized their first names to "Eugene" and "John", respectively.^{[23]} When their year was up, Princeton offered a fiveyear contract as visiting professors for half the year. The Technische Hochschule responded with a teaching assignment for the other half of the year. This was very timely, since the Nazis soon rose to power in Germany.^{[24]} At Princeton in 1934, Wigner introduced his sister Manci to the physicist Paul Dirac, whom she married.^{[25]}
Princeton did not rehire Wigner when his contract ran out in 1936.^{[26]} Through Gregory Breit, Wigner found new employment at the University of Wisconsin. There he met his first wife, Amelia Frank, who was a physics student there. However she died unexpectedly in 1937, leaving Wigner distraught. He therefore accepted a 1938 offer from Princeton to return there.^{[27]} Wigner became a naturalized citizen of the United States on January 8, 1937, and he brought his parents to the United States.^{[28]}
Although he was a professed political amateur, on August 2, 1939, he participated in a meeting with Leó Szilárd and Albert Einstein that resulted in the Einstein–Szilárd letter, which prompted President Franklin D. Roosevelt to initiate the Manhattan Project to develop atomic bombs.^{[29]} Wigner was afraid that the German nuclear weapon project would develop an atomic bomb first, and even refused to have his fingerprints taken because they could be used to track him down if Germany won.^{[30]} "Thoughts of being murdered," he later recalled, "focus your mind wonderfully."^{[30]}
On June 4, 1941, Wigner married his second wife, Mary Annette Wheeler, a professor of physics at Vassar College, who had completed her Ph.D. at Yale University in 1932. After the war she taught physics on the faculty of Rutgers University's Douglass College in New Jersey until her retirement in 1964. They remained married until her death in November 1977.^{[31]}^{[32]} They had two children, David Wigner and Martha Wigner Upton.^{[33]}
During the Manhattan Project, Wigner led a team that included Alvin M. Weinberg, Katharine Way, Gale Young and Edward Creutz. The group's task was to design the production nuclear reactors that would convert uranium into weapons grade plutonium. At the time, reactors existed only on paper, and no reactor had yet gone critical. In July 1942, Wigner chose a conservative 100 MW design, with a graphite neutron moderator and water cooling.^{[34]} Wigner was present at a converted rackets court under the stands at the University of Chicago's abandoned Stagg Field on December 2, 1942, when the world's first atomic reactor, Chicago Pile One (CP1) achieved a controlled nuclear chain reaction.^{[35]}
Wigner was disappointed that DuPont was given responsibility for the detailed design of the reactors, not just their construction. He threatened to resign in February 1943, but was talked out of it by the head of the Metallurgical Laboratory, Arthur Compton, who sent him on vacation instead. As it turned out, a design decision by DuPont to give the reactor additional load tubes for more uranium saved the project when neutron poisoning became a problem.^{[36]} Without the additional tubes, the reactor could have been run at 35% power until the boron impurities in the graphite were burned up and enough plutonium produced to run the reactor at full power; but this would have set the project back a year.^{[37]} During the 1950s, he would even work for DuPont on the Savannah River Site.^{[36]} Wigner did not regret working on the Manhattan Project, and sometimes wished the atomic bomb had been ready a year earlier.^{[38]}
An important discovery Wigner made during the project was the Wigner effect. This is a swelling of the graphite moderator caused by the displacement of atoms by neutron radiation.^{[39]} The Wigner effect was a serious problem for the reactors at the Hanford Site in the immediate postwar period, and resulted in production cutbacks and a reactor being shut down entirely.^{[40]} It was eventually discovered that it could be overcome by controlled heating and annealing.^{[41]}
Through Manhattan project funding, Wigner and Leonard Eisenbud also developed an important general approach to nuclear reactions, the Wigner–Eisenbud Rmatrix theory, which was published in 1947.^{[42]}
Wigner accepted a position as the Director of Research and Development at the Clinton Laboratory (now the Oak Ridge National Laboratory) in Oak Ridge, Tennessee in early 1946. Because he did not want to be involved in administrative duties, he became codirector of the laboratory, with James Lum handling the administrative chores as executive director.^{[43]} When the newly created Atomic Energy Commission (AEC) took charge of the laboratory's operations at the start of 1947, Wigner feared that many of the technical decisions would be made in Washington.^{[44]} He also saw the Army's continuation of wartime security policies at the laboratory as a "meddlesome oversight", interfering with research.^{[45]} One such incident occurred in March 1947, when the AEC discovered that Wigner's scientists were conducting experiments with a critical mass of uranium235 when the Director of the Manhattan Project, Major General Leslie R. Groves, Jr., had forbidden such experiments in August 1946 after the death of Louis Slotin at the Los Alamos Laboratory. Wigner argued that Groves's order had been superseded, but was forced to terminate the experiments, which were completely different from the one that killed Slotin.^{[46]}
Feeling unsuited to a managerial role in such an environment, he left Oak Ridge in 1947 and returned to Princeton University,^{[47]} although he maintained a consulting role with the facility for many years.^{[44]} In the postwar period he served on a number of government bodies, including the National Bureau of Standards from 1947 to 1951, the mathematics panel of the National Research Council from 1951 to 1954, the physics panel of the National Science Foundation, and the influential General Advisory Committee of the Atomic Energy Commission from 1952 to 1957 and again from 1959 to 1964.^{[48]} He also contributed to civil defense.^{[49]}
Near the end of his life, Wigner's thoughts turned more philosophical. In 1960, he published a now classic article on the philosophy of mathematics and of physics, which has become his bestknown work outside technical mathematics and physics, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences".^{[50]} He argued that biology and cognition could be the origin of physical concepts, as we humans perceive them, and that the happy coincidence that mathematics and physics were so well matched, seemed to be "unreasonable" and hard to explain.^{[50]} His original paper has provoked and inspired many responses across a wide range of disciplines. These included Richard Hamming in Computer Science,^{[51]} Arthur Lesk in Molecular Biology,^{[52]} Peter Norvig in data mining,^{[53]} Max Tegmark in Physics,^{[54]} Ivor GrattanGuinness in Mathematics,^{[55]} and Vela Velupillai in Economics.^{[56]}
Wigner was awarded the Nobel Prize in Physics in 1963 "for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles".^{[1]} The prize was shared that year, with the other half of the award divided between Maria GoeppertMayer and J. Hans D. Jensen.^{[1]} Wigner professed that he had never considered the possibility that this might occur, and added: "I never expected to get my name in the newspapers without doing something wicked."^{[57]} He also won the Franklin Medal in 1950,^{[58]} the Enrico Fermi award in 1958,^{[59]} the Atoms for Peace Award in 1959,^{[60]} the Max Planck Medal in 1961,^{[61]} the National Medal of Science in 1969,^{[62]} the Albert Einstein Award in 1972,^{[63]} and the eponymous Wigner Medal in 1978.^{[64]} In 1968 he gave the Josiah Willard Gibbs lecture.^{[65]}^{[66]}
Mary died in November 1977. In 1979, Wigner married his third wife, Eileen ClarePatton (Pat) Hamilton, the widow of physicist Donald Ross Hamilton, the Dean of the Graduate School at Princeton University, who had died in 1972.^{[67]} In 1992, at the age of 90, he published his memoirs, The Recollections of Eugene P. Wigner with Andrew Szanton. In it, Wigner said: "The full meaning of life, the collective meaning of all human desires, is fundamentally a mystery beyond our grasp. As a young man, I chafed at this state of affairs. But by now I have made peace with it. I even feel a certain honor to be associated with such a mystery."^{[68]} In his collection of essays Symmetries and Reflections – Scientific Essays (1995), he commented: "It was not possible to formulate the laws of quantum mechanics in a fully consistent way without reference to consciousness."^{[69]}
Wigner died of pneumonia at the University Medical Center in Princeton, New Jersey on 1 January 1995.^{[70]} He was survived by his wife Eileen (died 2010) and children Erika, David and Martha, and his sisters Bertha and Margit.^{[63]}
Oak Ridge at that time was so terribly bureaucratized that I am sorry to say I could not stand it.
In mathematics, an Albert algebra is a 27dimensional exceptional Jordan algebra. They are named after Abraham Adrian Albert, who pioneered the study of nonassociative algebras, usually working over the real numbers. Over the real numbers, there are three such Jordan algebras up to isomorphism. One of them, which was first mentioned by Pascual Jordan, John von Neumann, and Eugene Wigner (1934) and studied by Albert (1934), is the set of 3×3 selfadjoint matrices over the octonions, equipped with the binary operation
where denotes matrix multiplication. Another is defined the same way, but using split octonions instead of octonions. The final is constructed from the nonsplit octonions using a different standard involution.
Over any algebraically closed field, there is just one Albert algebra, and its automorphism group G is the simple split group of type F4. (For example, the complexifications of the three Albert algebras over the real numbers are isomorphic Albert algebras over the complex numbers.) Because of this, for a general field F, the Albert algebras are classified by the Galois cohomology group H^{1}(F,G).
The Kantor–Koecher–Tits construction applied to an Albert algebra gives a form of the E7 Lie algebra. The split Albert algebra is used in a construction of a 56dimensional structurable algebra whose automorphism group has identity component the simplyconnected algebraic group of type E6.
The space of cohomological invariants of Albert algebras a field F (of characteristic not 2) with coefficients in Z/2Z is a free module over the cohomology ring of F with a basis 1, f_{3}, f_{5}, of degrees 0, 3, 5. The cohomological invariants with 3torsion coefficients have a basis 1, g_{3} of degrees 0, 3. The invariants f_{3} and g_{3} are the primary components of the Rost invariant.
Andrew SzantonAndrew Szanton (born in Washington, D.C. in 1963) is an American collaborative memoirist. During his career he has worked with a wide range of subjects including civil rights pioneer Charles Evers, Nobel Prize winning physicist Eugene Wigner, former cochairman of Goldman Sachs John Whitehead, former United States Senator Edward Brooke, founding director of Xerox PARC George Pake, eminent surgeon Dr. Charles Epps, head of the Missouri Botanical Garden Peter Raven, and former Boston mayor Raymond Flynn.
In 2015, Szanton began working with former New Jersey senator Bill Bradley, conducting interviews for Senator Bradley's oral history.
A successful ghostwriter and memoir coach commonly performs a range of tasks: mastering whatever published material is directly relevant to telling the life story; helping the memoir subject to gather and evaluate family letters, manuscripts and photos; interviewing family, friends, and colleagues; and perhaps most important of all, seeing the essential patterns of the life,
and helping the subject eloquently trace those patterns through their life, understanding the
ways that certain experiences of childhood and youth can shape the choices of the mature person. Mr Szanton has a website at: www.MemoirAuthor.com.
Andrew Szanton honed his approach to memoir writing for a number of years as an instructor at the Extension School of Harvard University.
A 1985 graduate of Princeton University, Andrew Szanton worked for several years as an oral historian for the Smithsonian Institution before becoming an author. It was through the Smithsonian that Szanton first encountered the HungarianAmerican Eugene Wigner, a famously modest man who had always resisted entreaties to write his memoirs. Reminded of his own mortality by the raft of old friends and colleagues dying, Dr. Wigner agreed to write his memoir, with Szanton assisting. The result was "The Recollections of Eugene P. Wigner".
"Have No Fear" with Charles Evers followed in 1997 and "Bridging the Divide" with Edward Brooke was published in 2007.
Memoir collaboration was once commonly the work of journalists or academics, working as a sideline. For example, a critic of popular music for a major newsmagazine might be hired to bring material to, and check the accuracy of, the rich but scattered spoken recollections of a pop star. The journalist critic was hired primarily for what he or she knew about the subject area, and for an ability to meet deadlines—not for any particular dedication to, or demonstrated skill at, the memoir form. The books that resulted were advertised as "By (the headliner) "as told to" the collaborator, as though the collaborator were merely a scribe.
Andrew Szanton is a writer who places memoir collaboration at the center of his art, and has few institutional connections. In 2015, he began working with Princeton. Memoir collaborators often bring to their work detailed knowledge from certain fields—Szanton is something of an expert in the early history of atomic weaponry and of the U.S. civil rights movement from 19631971. But Szanton stakes his claim to coauthorship less on any fund of relevant knowledge than on his mastery of the memoir form.
Szanton lives in Newton, Massachusetts with his wife Barbara. They have two children.
Einstein–Szilárd letterThe Einstein–Szilárd letter was a letter written by Leó Szilárd and signed by Albert Einstein that was sent to the United States President Franklin D. Roosevelt on August 2, 1939. Written by Szilárd in consultation with fellow Hungarian physicists Edward Teller and Eugene Wigner, the letter warned that Germany might develop atomic bombs and suggested that the United States should start its own nuclear program. It prompted action by Roosevelt, which eventually resulted in the Manhattan Project developing the first atomic bombs.
Fritz Haber Institute of the Max Planck SocietyThe Fritz Haber Institute of the Max Planck Society (FHI) is a science research institute located at the heart of the academic district of Dahlem, in Berlin, Germany.
The original Kaiser Wilhelm Institute for Physical Chemistry and Electrochemistry, founded in 1911, was incorporated in the Max Planck Society and simultaneously renamed for its first director, Fritz Haber, in 1953.
The research topics covered throughout the history of the institute include chemical kinetics and reaction dynamics, colloid chemistry, atomic physics, spectroscopy, surface chemistry and surface physics, chemical physics and molecular physics, theoretical chemistry, and materials science.During World War I and World War II, the research of the institute was directed more or less towards Germany's military needs.
To the illustrious past members of the Institute belong Herbert Freundlich, James Franck, Paul Friedlander, Rudolf Ladenburg, Michael Polanyi, Eugene Wigner, Ladislaus Farkas, Hartmut Kallmann, Otto Hahn, Robert Havemann, Karl Friedrich Bonhoeffer, Iwan N. Stranski, Ernst Ruska, Max von Laue, Gerhard Borrmann, Rudolf Brill, Kurt Moliere, Jochen Block, Heinz Gerischer, Rolf Hosemann, Kurt Ueberreiter, Alexander Bradshaw, Elmar Zeitler, and Gerhard Ertl.
Nobel Prize laureates affiliated with the institute include Max von Laue (1914), Fritz Haber (1918), James Franck (1925), Otto Hahn (1944), Eugene Wigner (1963), Ernst Ruska (1986), Gerhard Ertl (2007).
Gabor–Wigner transformThe Gabor transform, named after Dennis Gabor, and the Wigner distribution function, named after Eugene Wigner, are both tools for timefrequency analysis. Since the Gabor transform does not have high clarity, and the Wigner distribution function has a "cross term problem" (i.e. is nonlinear), a 2007 study by S. C. Pei and J. J. Ding proposed a new combination of the two transforms that has high clarity and no cross term problem.
Since the cross term does not appear in the Gabor transform, the time frequency distribution of the Gabor transform can be used as a filter to filter out the cross term in the output of the Wigner distribution function.
Group contractionIn theoretical physics, Eugene Wigner and Erdal İnönü have discussed the possibility to obtain from a given Lie group a different (nonisomorphic) Lie group by a group contraction with respect to a continuous subgroup of it. That amounts to a limiting operation on a parameter of the Lie algebra, altering the structure constants of this Lie algebra in a nontrivial singular manner, under suitable circumstances.For example, the Lie algebra of the 3D rotation group SO(3), [X1, X2] = X3, etc., may be rewritten by a change of variables Y1 = εX1, Y2 = εX2, Y3 = X3, as
[Y1, Y2] = ε2 Y3, [Y2, Y3] = Y1, [Y3, Y1] = Y2.The contraction limit ε → 0 trivializes the first commutator and thus yields the nonisomorphic algebra of the plane Euclidean group, E2 ~ ISO(2). (This is isomorphic to the cylindrical group, describing motions of a point on the surface of a cylinder. It is the little group, or stabilizer subgroup, of null fourvectors in Minkowski space.) Specifically, the translation generators Y1, Y2, now generate the Abelian normal subgroup of E2 (cf. Group extension), the parabolic Lorentz transformations.
Similar limits, of considerable application in physics (cf. Correspondence principles), contract
the de Sitter group SO(4, 1) ~ Sp(2, 2) to the Poincaré group ISO(3, 1), as the de Sitter radius diverges: R → ∞; or
the Poincaré group to the Galilei group, as the speed of light diverges: c → ∞; or
the Moyal bracket Lie algebra (equivalent to quantum commutators) to the Poisson bracket Lie algebra, in the classical limit as the Planck constant vanishes: ħ → 0.
Kramers theoremIn quantum mechanics, the Kramers degeneracy theorem states that for every energy eigenstate of a timereversal symmetric system with halfinteger total spin, there is at least one more eigenstate with the same energy. In other words, every energy level is at least doubly degenerate if it has halfinteger spin. The law is named for the Dutch physicist H. A. Kramers.
In theoretical physics, the time reversal symmetry is the symmetry of physical laws under a time reversal transformation:
If the Hamiltonian operator commutes with the timereversal operator, that is
then for every energy eigenstate , the time reversed state is also an eigenstate with the same energy. Of course, this time reversed state might be identical to the original state, but that is not possible in a halfinteger spin system since time reversal reverses all angular momenta, and reversing a halfinteger spin cannot yield the same state (the magnetic quantum number is never zero).
For instance, the energy levels of a system with an odd total number of fermions (such as electrons, protons and neutrons) remain at least doubly degenerate in the presence of purely electric fields (i.e. no magnetic fields). It was first discovered in 1930 by H. A. Kramers as a consequence of the Breit equation.
As shown by Eugene Wigner in 1932, it is a consequence of the time reversal invariance of electric fields, and follows from an application of the antiunitary Toperator to the wavefunction of an odd number of fermions. The theorem is valid for any configuration of static or timevarying electric fields.
For example: the hydrogen (H) atom contains one proton and one electron, so that the Kramers theorem does not apply. The lowest (hyperfine) energy level of H is nondegenerate. The deuterium (D) isotope on the other hand contains an extra neutron, so that the total number of fermions is three, and the theorem does apply. The ground state of D contains two hyperfine components, which are twofold and fourfold degenerate.
List of things named after Eugene WignerThe following is a list of things named after Hungarian physicist E. P. Wigner.
László RátzLászló Rátz, (born 9 April 1863 in Sopron, died 30 September 1930 in Budapest), was a Hungarian mathematics high school teacher best known for educating such people as John von Neumann and Nobel laureate Eugene Wigner. He was a legendary teacher of "BudapestFasori Evangélikus Gimnázium", the Budapest Lutheran Gymnasium, a famous secondary school in Budapest in Hungary.
Method of moments (probability theory)In probability theory, the method of moments is a way of proving convergence in distribution by proving convergence of a sequence of moment sequences. Suppose X is a random variable and that all of the moments
exist. Further suppose the probability distribution of X is completely determined by its moments, i.e., there is no other probability distribution with the same sequence of moments (cf. the problem of moments). If
for all values of k, then the sequence {X_{n}} converges to X in distribution.
The method of moments was introduced by Pafnuty Chebyshev for proving the central limit theorem; Chebyshev cited earlier contributions by IrénéeJules Bienaymé. More recently, it has been applied by Eugene Wigner to prove Wigner's semicircle law, and has since found numerous applications in the theory of random matrices.
Pocono ConferenceThe Pocono Conference of 30 March to 2 April 1948 was the second of three postwar conferences held to discuss quantum physics; arranged by Robert Oppenheimer for the National Academy of Sciences. It followed the Shelter Island Conference of 1947 and preceded the Oldstone Conference of 1949.
Held at the Pocono Manor Inn in the Pocono Mountains of Pennsylvania, midway between Scranton, Pennsylvania and the Delaware Water Gap, 28 physicists attended. New participants were Niels Bohr, Aage Bohr, Paul Dirac, Walter Heitler, Eugene Wigner and Gregor Wentzel; while Kramers, MacInnes, Nordsieck, Pauling and Van Vleck who were at the Shelter Island Conference were absent.Julian Schwinger gave a daylong presentation of his developments in quantum electrodynamics (QED), the last great fling of the old way of doing quantum mechanics. Richard Feynman offered his version of quantum electrodynamics, introducing Feynman diagrams for the first time; it was unfamiliar and noone followed it, so Feynman was motivated to go back to Cornell and write his work up for publication so others could see it in cold print. Schwinger and Feynman compared notes; and although neither could really understand the other’s approach, their arrival at the same answer helped to confirm the theory. And on his return to Princeton, Oppenheimer received a third version by SinItiro Tomonaga; his version of QED was somewhat simpler than Schwinger's.
Quasiempiricism in mathematicsQuasiempiricism in mathematics is the attempt in the philosophy of mathematics to direct philosophers' attention to mathematical practice, in particular, relations with physics, social sciences, and computational mathematics, rather than solely to issues in the foundations of mathematics. Of concern to this discussion are several topics: the relationship of empiricism (see Maddy) with mathematics, issues related to realism, the importance of culture, necessity of application, etc.
The Martians (scientists)"The Martians" was a term used to refer to a group of prominent Hungarian scientists of Jewish descent (mostly, but not exclusively, physicists and mathematicians) who emigrated to the United States in the early half of the 20th century. Leó Szilárd, who jokingly suggested that Hungary was a front for aliens from Mars, used this term. In an answer to the question of why there is no evidence of intelligent life beyond earth despite the high probability of it existing, Szilárd responded: "They are already here among us – they just call themselves Hungarians." This account is featured in György Marx's book The Martians.
Paul Erdős, Paul Halmos, Theodore von Kármán, John G. Kemeny, John von Neumann, George Pólya, Leó Szilárd, Edward Teller, and Eugene Wigner are included in this group.
Dennis Gabor (Gábor Dénes), Ervin Bauer, Róbert Bárány, George de Hevesy (Hevesy György Károly), Nicholas Kurti (Kürti Miklós), George Klein and perhaps his wife, Eva Klein as well, Michael Polanyi (Polányi Mihály) and Marcel Riesz are also sometimes named as 'Martians', though they did not emigrate to the United States.
However, others not of Jewish descent are often mentioned in connection with 'The Martians', including Loránd Eötvös, Kálmán Tihanyi, Zoltán Lajos Bay, Victor Szebehely, Albert SzentGyörgyi and Georg von Békésy, as well as Maria Telkes, the only woman.
Elizabeth Róna was an important Jewish Hungarian nuclear chemist who discovered UraniumY, and emigrated to the United States in 1941 to work on the Manhattan Project. She may be an overlooked Martian.
Unreasonable ineffectiveness of mathematicsThe unreasonable ineffectiveness of mathematics is a phrase that alludes to the article by physicist Eugene Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". This phrase is meant to suggest that mathematical analysis has not proved as valuable in other fields as it has in physics.
Wigner's classificationIn mathematics and theoretical physics, Wigner's classification
is a classification of the nonnegative (E ≥ 0) energy irreducible unitary representations of the Poincaré group which have sharp mass eigenvalues. (Since this group is noncompact, these unitary representations are infinitedimensional.)
It was introduced by Eugene Wigner, to classify particles and fields in physics—see the article particle physics and representation theory. It relies on the stabilizer subgroups of that group, dubbed the Wigner little groups of various mass states.
The Casimir invariants of the Poincaré group are C1 = PμPμ, where P is the 4momentum operator, and C2 = WαWα, where W is the Pauli–Lubanski pseudovector. The eigenvalues of these operators serve to label the representations. The first is associated with masssquared and the second with helicity or spin.
The physically relevant representations may thus be classified according to whether m > 0 ; m = 0 but P0 > 0; and m = 0 with Pμ = 0. Wigner found that massless particles are fundamentally different from massive particles.
For the first case, note that the eigenspace (see generalized eigenspaces of unbounded operators) associated with P =(m,0,0,0) is a representation of SO(3). In the ray interpretation, one can go over to Spin(3) instead. So, massive states are classified by an irreducible Spin(3) unitary representation that characterizes their spin, and a positive mass, m.
For the second case, look at the stabilizer of P =(k,0,0,k). This is the double cover of SE(2) (see unit ray representation). We have two cases, one where irreps are described by an integral multiple of 1/2 called the helicity, and the other called the "continuous spin" representation.
The last case describes the vacuum. The only finitedimensional unitary solution is the trivial representation called the vacuum.
Wigner MedalThe Wigner Medal is an award designed "to recognize outstanding contributions to the understanding of physics through Group Theory". The Wigner Medal is administered by The Group Theory and Fundamental Physics Foundation, a publicly supported organization. Donations are taxdeductible as provided pursuant to the provisions of Section 170 of the Internal Revenue Code, a federal code of the United States.
The award was first presented in 1978 to Eugene Wigner, and was first awarded at the Integrative Conference on Group Theory and Mathematical Physics.
Wigner effectThe Wigner effect (named for its discoverer, Eugene Wigner), also known as the discomposition effect or Wigner's Disease, is the dislocation of atoms in a solid caused by neutron radiation.
Any solid can display the Wigner effect. The effect is of most concern in neutron moderators, such as graphite, intended to reduce the speed of fast neutrons, thereby turning them into thermal neutrons capable of sustaining a nuclear chain reaction involving uranium235.
Wigner surmiseIn mathematical physics, the Wigner surmise is a statement about the probability distribution of the spaces between points in the spectra of nuclei of heavy atoms. It was proposed by Eugene Wigner in probability theory. The surmise was a result of Wigner's introduction of random matrices in the field of nuclear physics. The surmise consists of two postulates:
The Wigner–Seitz radius , named after Eugene Wigner and Frederick Seitz, is the radius of a sphere whose volume is equal to the mean volume per atom in a solid (for first group metals). In the more general case of metals having more valence electrons, is the radius of a sphere whose volume is equal to the volume per a free electron. This parameter is used frequently in condensed matter physics to describe the density of a system. Worth to mention, is calculated for bulk materials.
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