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Ehrenfest Paradox
The Ehrenfest paradox concerns the rotation of a "rigid" disc in the theory of relativity. In its original 1909 formulation as presented by Paul Ehrenfest in relation to the concept of Born rigidity within special relativity, it discusses an ideally rigid cylinder that is made to rotate about its axis of symmetry. The radius ''R'' as seen in the laboratory frame is always perpendicular to its motion and should therefore be equal to its value R0 when stationary. However, the circumference (2''R'') should appear Lorentz-contracted to a smaller value than at rest, by the usual factor γ. This leads to the contradiction that ''R'' = ''R''0 ''and'' ''R'' < ''R''0. The has been deepened further by |
Theory Of Relativity
The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to the forces of nature. It applies to the cosmological and astrophysical realm, including astronomy. The theory transformed theoretical physics and astronomy during the 20th century, superseding a 200-year-old theory of mechanics created primarily by Isaac Newton. It introduced concepts including 4-dimensional spacetime as a unified entity of space and time, relativity of simultaneity, kinematic and gravitational time dilation, and length contraction. In the field of physics, relativity improved the science of elementary particles and their fundamental interactions, along with ushering in the nuclear age. With relativity, cosmology and astro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neutron-star Oscillations
Asteroseismology studies the internal structure of the Sun and other stars using oscillations. These can be studied by interpreting the temporal frequency spectrum acquired through observations. In the same way, the more extreme neutron stars might be studied and hopefully give us a better understanding of neutron-star interiors, and help in determining the equation of state for matter at nuclear densities. Scientists also hope to prove, or discard, the existence of so-called quark stars, or strange stars, through these studies. Fundamental information can be obtained of the General Relativity Theory by observing the gravitational radiation from oscillating neutron stars. Types of oscillations The modes of oscillations are divided into subgroups, each with different characteristic behavior. First they are divided into toroidal and spherical modes, with the latter further divided into radial and non-radial modes. Spherical modes are oscillations in the radial direction while to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theodor Kaluza
Theodor Franz Eduard Kaluza (; 9 November 1885 – 19 January 1954) was a German mathematician and physicist known for the Kaluza–Klein theory, involving field equations in five-dimensional space-time. His idea that fundamental forces can be unified by introducing additional dimensions re-emerged much later in string theory. Life Kaluza was born to a Roman Catholic family from the town of Ratibor (present-day Racibórz in Poland) in the German Empire's Prussian Province of Silesia. Kaluza himself was born in Wilhelmsthal (a village that was incorporated into Oppeln (present-day Opole) in 1899). He spent his youth in Königsberg, where his father, Max Kaluza, was a professor of the English language. He entered the University of Königsberg to study mathematics and gained his doctorate with a thesis on Tschirnhaus transformations. Kaluza was primarily a mathematician but began studying relativity. In April 1919 Kaluza noticed that when he solved Albert Einstein's equatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elasticity (physics)
In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to ''plasticity'', in which the object fails to do so and instead remains in its deformed state. The physical reasons for elastic behavior can be quite different for different materials. In metal A metal (from Greek μÎταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typi ...s, the Crystal structure, atomic lattice changes size and shape when forces are applied (energy is added to the system). When forces are removed, the lattice goes b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Max Planck
Max Karl Ernst Ludwig Planck (, ; 23 April 1858 – 4 October 1947) was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial contributions to theoretical physics, but his fame as a physicist rests primarily on his role as the originator of quantum theory, which revolutionized human understanding of atomic and subatomic processes. In 1948, the German scientific institution Kaiser Wilhelm Society (of which Planck was twice president) was renamed Max Planck Society (MPG). The MPG now includes 83 institutions representing a wide range of scientific directions. Life and career Planck came from a traditional, intellectual family. His paternal great-grandfather and grandfather were both theology professors in Göttingen; his father was a law professor at the University of Kiel and Munich. One of his uncles was also a judge. Planck was born in 1858 in Kiel, Holstein, to Johann Julius Wilhel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Herglotz–Noether Theorem
Born rigidity is a concept in special relativity. It is one answer to the question of what, in special relativity, corresponds to the rigid body of non-relativistic classical mechanics. The concept was introduced by Max Born (1909),Born (1909b) who gave a detailed description of the case of constant proper acceleration which he called hyperbolic motion. When subsequent authors such as Paul Ehrenfest (1909) tried to incorporate rotational motions as well, it became clear that Born rigidity is a very restrictive sense of rigidity, leading to the Herglotz–Noether theorem, according to which there are severe restrictions on rotational Born rigid motions. It was formulated by Gustav Herglotz (1909, who classified all forms of rotational motions)Herglotz (1909) and in a less general way by Fritz Noether (1909).Noether (1909) As a result, Born (1910)Born (1910) and others gave alternative, less restrictive definitions of rigidity. Definition Born rigidity is satisfied if the orthogonal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fritz Noether
Fritz Alexander Ernst Noether (7 October 1884 – 10 September 1941) was a Jewish German mathematician who emigrated from Nazi Germany to the Soviet Union. He was later executed by the NKVD. Biography Fritz Noether's father Max Noether was a mathematician and professor in Erlangen. The notable mathematician Emmy Noether was his elder sister. He had two sons, Herman D. Noether and Gottfried E. Noether. His eldest son Herman was a chemist. Gottfried was an American statistician and educator, and wrote a brief biography of his father. Fritz Noether was also an able mathematician. Not allowed to work in Nazi Germany for being a Jew, he moved to the Soviet Union, where he was appointed to a professorship at the Tomsk State University. In November 1937, during the Great Purge, he was arrested at his home in Tomsk by the NKVD. On 23 October 1938, Noether was sentenced to 25 years of imprisonment on charges of espionage and sabotage. He served time in different pris ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gustav Herglotz
Gustav Herglotz (2 February 1881 – 22 March 1953) was a German Bohemian physicist best known for his works on the theory of relativity and seismology. Biography Gustav Ferdinand Joseph Wenzel Herglotz was born in Volary num. 28 to a public notary Gustav Herglotz (also a Doctor of Law) and his wife Maria née Wachtel. The family were Sudeten Germans. He studied mathematics and astronomy at the University of Vienna in 1899, and attended lectures by Ludwig Boltzmann. In this time of study, he had a friendship with his colleagues Paul Ehrenfest, Hans Hahn and Heinrich Tietze. In 1900 he went to the LMU Munich and achieved his Doctorate in 1902 under Hugo von Seeliger. Afterwards, he went to the University of Göttingen, where he habilitated under Felix Klein. In 1904 he became Privatdozent for Astronomy and Mathematics there, and in 1907 Professor extraordinarius. In 1908 he became Professor extraordinarius in Vienna, and in 1909 at the University of Leipzig. From 1925 (until b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Max Born
Max Born (; 11 December 1882 – 5 January 1970) was a German physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 1930s. Born won the 1954 Nobel Prize in Physics for his "fundamental research in quantum mechanics, especially in the statistical interpretation of the wave function". Born entered the University of Göttingen in 1904, where he met the three renowned mathematicians Felix Klein, David Hilbert, and Hermann Minkowski. He wrote his PhD thesis on the subject of "Stability of Elastica in a Plane and Space", winning the university's Philosophy Faculty Prize. In 1905, he began researching special relativity with Minkowski, and subsequently wrote his habilitation thesis on the Thomson model of the atom. A chance meeting with Fritz Haber in Berlin in 1918 led to discussion of how an ionic compound is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Langevin Frame Cyl Desynchronization
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Langevin may refer to: * Langevin (surname) * 5290 Langevin, an asteroid * Langevin (crater) on the Moon See also * Institut Laue–Langevin, scientific facility in Grenoble, France * Office of the Prime Minister and Privy Council, a government office building in Ottawa, Canada formerly called Langevin Block * Physics and mathematics (named for Paul Langevin): ** Langevin's function (and its relation to Brillouin's) ** Langevin dynamics ** Langevin equation In physics, a Langevin equation (named after Paul Langevin) is a stochastic differential equation describing how a system evolves when subjected to a combination of deterministic and fluctuating ("random") forces. The dependent variables in a Lange ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Øyvind Grøn
Øyvind Grøn (born 11 March 1944) is a Norwegian physicist. Biography Grøn was born in Oslo, and is a twin. He took the cand. real. degree at the University of Oslo in 1973, majoring in meteorology. He followed up with the PhD degree in 1990 with a thesis on repulsive gravitation. He started his academic career as a research assistant at the University of Oslo, and has also been a lecturer there. He was appointed as a professor at Oslo University College in 1994, having been an associate professor since 1985. He has also been professor II at the University of Oslo since 1994. Scientific contributions Rotating reference frames Grøn has conducted research within the areas of general relativity, cosmology and classical electromagnetism. He has thrown new light on themes like the twin paradox, the physics in a rotating reference system ( Ehrenfest paradox) and repulsive gravitation associated with vacuum energy. Together with Erik Eriksen at the University of Oslo he has al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reductio Ad Absurdum
In logic, (Latin for "reduction to absurdity"), also known as (Latin for "argument to absurdity") or ''apagogical arguments'', is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction. This argument form traces back to Ancient Greek philosophy and has been used throughout history in both formal mathematical and philosophical reasoning, as well as in debate. Examples The "absurd" conclusion of a ''reductio ad absurdum'' argument can take a range of forms, as these examples show: * The Earth cannot be flat; otherwise, since Earth assumed to be finite in extent, we would find people falling off the edge. * There is no smallest positive rational number because, if there were, then it could be divided by two to get a smaller one. The first example argues that denial of the premise would result in a ridiculous conclusion, against the evidence of our senses. The second example is a mathematical proof ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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