Kaluza–Klein Theory
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Kaluza–Klein Theory
In physics, Kaluza–Klein theory (KK theory) is a classical unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the common 4D of space and time and considered an important precursor to string theory. In their setup, the vacuum has the usual 3 dimensions of space and one dimension of time but with another microscopic extra spatial dimension in the shape of a tiny circle. Gunnar Nordström had an earlier, similar idea. But in that case, a fifth component was added to the electromagnetic vector potential, representing the Newtonian gravitational potential, and writing the Maxwell equations in five dimensions. The five-dimensional (5D) theory developed in three steps. The original hypothesis came from Theodor Kaluza, who sent his results to Albert Einstein in 1919 and published them in 1921. Kaluza presented a purely classical extension of general relativity to 5D, with a metric tensor of 15 components. Ten components are ...
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K Theory
In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is a cohomology theory known as topological K-theory. In algebra and algebraic geometry, it is referred to as algebraic K-theory. It is also a fundamental tool in the field of operator algebras. It can be seen as the study of certain kinds of invariants of large matrices. K-theory involves the construction of families of ''K''-functors that map from topological spaces or schemes, or to be even more general: any object of a homotopy category to associated rings; these rings reflect some aspects of the structure of the original spaces or schemes. As with functors to groups in algebraic topology, the reason for this functorial mapping is that it is easier to compute some topological properties from the mapped rings than from the original spaces or schemes. Examples of results gleaned from the K-theory approach include the Grothe ...
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Oskar Klein
Oskar Benjamin Klein (; 15 September 1894 – 5 February 1977) was a Swedish theoretical physics, theoretical physicist. Oskar Klein is known for his work on Kaluza–Klein theory, which is partially named after him. Biography Klein was born in Danderyd Municipality, Danderyd outside Stockholm, son of the chief rabbi of Stockholm, Gottlieb Klein from Humenné in Kingdom of Hungary, now Slovakia and Antonie (Toni) Levy. He became a student of Svante Arrhenius at the Nobel Institute at a young age and was on the way to Jean-Baptiste Perrin in France when World War I broke out and he was drafted into the military. From 1917, he worked a few years with Niels Bohr in the University of Copenhagen and received his doctoral degree at the University College of Stockholm (now Stockholm University) in 1921. In 1923, he received a professorship at University of Michigan in Ann Arbor, Michigan, Ann Arbor and moved there with his recently wedded wife, Gerda Koch from Denmark. Klein returned ...
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Carl H
Carl may refer to: *Carl, Georgia, city in USA *Carl, West Virginia, an unincorporated community *Carl (name), includes info about the name, variations of the name, and a list of people with the name *Carl², a TV series * "Carl", an episode of television series ''Aqua Teen Hunger Force'' * An informal nickname for a student or alum of Carleton College CARL may refer to: *Canadian Association of Research Libraries *Colorado Alliance of Research Libraries See also *Carle (other) *Charles *Carle, a surname *Karl (other) *Karle (other) Karle may refer to: Places * Karle (Svitavy District), a municipality and village in the Czech Republic * Karli, India, a town in Maharashtra, India ** Karla Caves, a complex of Buddhist cave shrines * Karle, Belgaum, a settlement in Belgaum ... {{disambig ja:カール zh:卡尔 ...
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Physical Review
''Physical Review'' is a peer-reviewed scientific journal. The journal was established in 1893 by Edward Nichols. It publishes original research as well as scientific and literature reviews on all aspects of physics. It is published by the American Physical Society (APS). The journal is in its third series, and is split in several sub-journals each covering a particular field of physics. It has a sister journal, '' Physical Review Letters'', which publishes shorter articles of broader interest. History ''Physical Review'' commenced publication in July 1893, organized by Cornell University professor Edward Nichols and helped by the new president of Cornell, J. Gould Schurman. The journal was managed and edited at Cornell in upstate New York from 1893 to 1913 by Nichols, Ernest Merritt, and Frederick Bedell. The 33 volumes published during this time constitute ''Physical Review Series I''. The American Physical Society (APS), founded in 1899, took over its publicati ...
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Brans–Dicke Theory
In physics, the Brans–Dicke theory of gravitation (sometimes called the Jordan–Brans–Dicke theory) is a competitor to Einstein's general theory of relativity. It is an example of a scalar–tensor theory, a gravitational theory in which the gravitational interaction is mediated by a scalar field as well as the tensor field of general relativity. The gravitational constant G is not presumed to be constant but instead 1 / G is replaced by a scalar field \phi which can vary from place to place and with time. The theory was developed in 1961 by Robert H. Dicke and Carl H. Brans building upon, among others, the earlier 1959 work of Pascual Jordan. At present, both Brans–Dicke theory and general relativity are generally held to be in agreement with observation. Brans–Dicke theory represents a minority viewpoint in physics. Comparison with general relativity Both Brans–Dicke theory and general relativity are examples of a class of relativistic classical field theories ...
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Paul Scherrer
Paul Hermann Scherrer (3 February 1890 – 25 September 1969) was a Swiss physicist. Born in St. Gallen, Switzerland, he studied at Göttingen, Germany, before becoming a lecturer there. Later, Scherrer became head of the Department of Physics at ETH Zurich. Early life and studies Paul Scherrer was born in St. Gallen. In 1908, he enrolled at the Swiss Federal Polytechnic (later known as ETH Zurich), changing course from Botany to Mathematics and Physics after two semesters. In 1912, Scherrer spent one semester at Königsberg University, then undertook further studies at the University of Göttingen, graduating from there with a doctorate on the Faraday effect in the hydrogen molecule. In 1916, while still working on his dissertation, he and his tutor, Peter Debye, developed the “Debye–Scherrer powder method”, a procedure using X-rays for the structural analysis of crystals. This made an important contribution to the development of the scattering techniques that are s ...
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Markus Fierz
Markus Eduard Fierz (20 June 1912 – 20 June 2006) was a Swiss physicist, particularly remembered for his formulation of spin–statistics theorem, and for his contributions to the development of quantum theory, particle physics, and statistical mechanics. He was awarded the Max Planck Medal in 1979 and the Albert Einstein Medal in 1989 for all his work. Biography Fierz's father Hans Eduard Fierz was a chemist with Geigy and later a professor at ETH Zurich, his mother was Linda Fierz-David. Fierz studied at the Realgymnasium in Zurich. In 1931 he began his studies in Göttingen, where he listened to the lectures of prolific academics including Hermann Weyl. In 1933 he returned to Zurich and studied physics at ETH under Wolfgang Pauli and Gregor Wentzel. In 1936 he earned a doctoral degree with his thesis on the infrared catastrophe in quantum electrodynamics. Afterward he went to Werner Heisenberg in Leipzig and in 1936 became an assistant to Wolfgang Pauli in Zurich. For his ha ...
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Wolfgang Pauli
Wolfgang Ernst Pauli ( ; ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and a pioneer of quantum mechanics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics "for the discovery of the Exclusion Principle, also called the Pauli exclusion principle, Pauli Principle". The discovery involved Spin (physics), spin theory, which is the basis of a theory of the Matter#Structure, structure of matter. To preserve the conservation of energy in beta decay, he posited the existence of a small neutral particle, dubbed the neutrino by Enrico Fermi. The neutrino was detected in 1956. Early life Pauli was born in Vienna to a chemist, (''né'' Wolf Pascheles, 1869–1955), and his wife, Bertha Camilla Schütz; his sister was Hertha Pauli, a writer and actress. Pauli's middle name was given in honor of his Godparent, godfather, physicist Ernst Mach. Pauli's paternal grandparents were from prominent Jewish families of ...
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Pascual Jordan
Ernst Pascual Jordan (; 18 October 1902 – 31 July 1980) was a German theoretical and mathematical physicist who made significant contributions to quantum mechanics and quantum field theory. He contributed much to the mathematical form of matrix mechanics, and developed canonical anticommutation relations for fermions. He introduced Jordan algebras in an effort to formalize quantum field theory; the algebras have since found numerous applications within mathematics. Jordan joined the Nazi Party in 1933, but did not follow the Deutsche Physik movement, which at the time rejected quantum physics developed by Albert Einstein and other Jewish physicists. After the Second World War, he entered politics for the conservative party CDU and served as a member of parliament from 1957 to 1961. Family history and education Jordan was born to Ernst Pasqual Jordan (1858–1924) and Eva Fischer. Ernst Jordan was a painter renowned for his portraits and landscapes. He was an associate p ...
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André Lichnerowicz
André Lichnerowicz (; January 21, 1915, Bourbon-l'Archambault – December 11, 1998, Paris) was a French differential geometer and mathematical physicist. He is considered the founder of modern Poisson geometry. Biography His grandfather Jan fought in the Polish resistance against the Prussians. Forced to flee Poland in 1860, he finally settled in France, where he married a woman from Auvergne, Justine Faure. Lichnerowicz's father, Jean, held agrégation in classics and was secretary of the Alliance française, while his mother, a descendant of paper makers, was one of the first women to earn the agrégation in mathematics. Lichnerowicz's paternal aunt, Jeanne, was a novelist and translator known under the pseudonym . André attended the Lycée Louis-le-Grand and then the École Normale Supérieure in Paris, gaining agrégation in 1936. After two years, he entered the Centre national de la recherche scientifique (CNRS) as one of the first researchers recruited by this instituti ...
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Princeton University
Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution. The institution moved to Newark, New Jersey, Newark in 1747 and then to its Mercer County, New Jersey, Mercer County campus in Princeton nine years later. It officially became a university in 1896 and was subsequently renamed Princeton University. The university is governed by the Trustees of Princeton University and has an endowment of $37.7 billion, the largest List of colleges and universities in the United States by endowment, endowment per student in the United States. Princeton provides undergraduate education, undergraduate and graduate education, graduate instruction in the hu ...
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Planck Units
In particle physics and physical cosmology, Planck units are a system of units of measurement defined exclusively in terms of four universal physical constants: ''Speed of light, c'', ''Gravitational constant, G'', ''Reduced Planck constant, ħ'', and Boltzmann constant, ''k''B (described further below). Expressing one of these physical constants in terms of Planck units yields a numerical value of 1 (number), 1. They are a system of natural units, defined using fundamental properties of Nature#Matter and energy, nature (specifically, properties of vacuum, free space) rather than properties of a chosen Prototype (metrology), prototype object. Originally proposed in 1899 by German physicist Max Planck, they are relevant in research on unified theories such as quantum gravity. The term Planck scale refers to quantities of space, time, energy and other units that are similar in magnitude to corresponding Planck units. This region may be characterized by particle energy, energies of ...
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