Born Coordinates

	Born Coordinates In relativistic physics, the Born coordinate chart is a coordinate chart for (part of) Minkowski spacetime, the flat spacetime of special relativity. It is often used to analyze the physical experience of observers who ride on a ring or disk rigidly rotating at relativistic speeds, so called Langevin observers. This chart is often attributed to Max Born, due to his 1909 work on the relativistic physics of a rotating body. For overview of the application of accelerations in flat spacetime, see Acceleration (special relativity) and proper reference frame (flat spacetime). From experience by inertial scenarios (i.e. measurements in inertial frames), Langevin observers synchronize their clocks by standard Einstein convention or by slow clock synchronization, respectively (both internal synchronizations). For a certain Langevin observer this method works perfectly. Within its immediate vicinity clocks are synchronized and light propagates isotropic in space. But the experience when ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Langevin Frame Cyl Desynchronization 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 ... {{Disambig ... [...More Info...] [...Related Items...] OR:** [Wikipedia] [Google] [Baidu]
picture info	Inertial Frame In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration. It is a frame in which an isolated physical object — an object with zero net force acting on it — is perceived to move with a constant velocity (it might be a zero velocity) or, equivalently, it is a frame of reference in which Newton's first law of motion holds. All inertial frames are in a state of constant, rectilinear motion with respect to one another; in other words, an accelerometer moving with any of them would detect zero acceleration. It has been observed that celestial objects which are far away from other objects and which are in uniform motion with respect to the cosmic microwave background radiation maintain such uniform motion. Measurements in one inertial frame can be converted to measurements in another by a si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Killing Vector In mathematics, a Killing vector field (often called a Killing field), named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo-Riemannian manifold) that preserves the metric. Killing fields are the infinitesimal generators of isometries; that is, flows generated by Killing fields are continuous isometries of the manifold. More simply, the flow generates a symmetry, in the sense that moving each point of an object the same distance in the direction of the Killing vector will not distort distances on the object. Definition Specifically, a vector field ''X'' is a Killing field if the Lie derivative with respect to ''X'' of the metric ''g'' vanishes: :\mathcal_ g = 0 \,. In terms of the Levi-Civita connection, this is :g\left(\nabla_Y X, Z\right) + g\left(Y, \nabla_Z X\right) = 0 \, for all vectors ''Y'' and ''Z''. In local coordinates, this amounts to the Killing equation :\nabla_\mu X_\nu + \nabla_ X_\mu = 0 \,. This condition is expressed i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Four-acceleration In the theory of relativity, four-acceleration is a four-vector (vector in four-dimensional spacetime) that is analogous to classical acceleration (a three-dimensional vector, see three-acceleration in special relativity). Four-acceleration has applications in areas such as the annihilation of antiprotons, resonance of strange particles and radiation of an accelerated charge. Four-acceleration in inertial coordinates In inertial coordinates in special relativity, four-acceleration \mathbf is defined as the rate of change in four-velocity \mathbf with respect to the particle's proper time along its worldline. We can say: \begin \mathbf = \frac &= \left(\gamma_u\dot\gamma_u c,\, \gamma_u^2\mathbf a + \gamma_u\dot\gamma_u\mathbf u\right) \\ &= \left( \gamma_u^4\frac,\, \gamma_u^2\mathbf + \gamma_u^4\frac\mathbf \right) \\ &= \left( \gamma_u^4\frac,\, \gamma_u^4\left(\mathbf + \frac\right) \right), \end where * \mathbf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Einstein Synchronisation Einstein synchronisation (or Poincaré–Einstein synchronisation) is a convention for synchronising clocks at different places by means of signal exchanges. This synchronisation method was used by telegraphers in the middle 19th century, but was popularized by Henri Poincaré and Albert Einstein, who applied it to light signals and recognized its fundamental role in relativity theory. Its principal value is for clocks within a single inertial frame. Einstein According to Albert Einstein's prescription from 1905, a light signal is sent at time \tau_1 from clock 1 to clock 2 and immediately back, e.g. by means of a mirror. Its arrival time back at clock 1 is \tau_2. This synchronisation convention sets clock 2 so that the time \tau_3 of signal reflection is defined to be \tau_3 = \tau_1 + \tfrac(\tau_2 - \tau_1) = \tfrac(\tau_1 + \tau_2). The same synchronisation is achieved by "slowly" transporting a third clock from clock 1 to clock 2, in the limit of vanishing transport velo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Helix A helix () is a shape like a corkscrew or spiral staircase. It is a type of smooth space curve with tangent lines at a constant angle to a fixed axis. Helices are important in biology, as the DNA molecule is formed as two intertwined helices, and many proteins have helical substructures, known as alpha helices. The word ''helix'' comes from the Greek word ''ἕλιξ'', "twisted, curved". A "filled-in" helix – for example, a "spiral" (helical) ramp – is a surface called '' helicoid''. Properties and types The ''pitch'' of a helix is the height of one complete helix turn Turn may refer to: Arts and entertainment Dance and sports * Turn (dance and gymnastics), rotation of the body * Turn (swimming), reversing direction at the end of a pool * Turn (professional wrestling), a transition between face and heel * Turn, ..., measured parallel to the axis of the helix. A double helix consists of two (typically congruent) helices with the same axis, differing by a tran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Langevin Frame Cyl Vorticity 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 ... {{Disambig ... [...More Info...] [...Related Items...] OR:** [Wikipedia] [Google] [Baidu]
	Paul Langevin Paul Langevin (; ; 23 January 1872 – 19 December 1946) was a French physicist who developed Langevin dynamics and the Langevin equation. He was one of the founders of the '' Comité de vigilance des intellectuels antifascistes'', an anti-fascist organization created after the 6 February 1934 far right riots. Being a public opponent of fascism in the 1930s resulted in his arrest and being held under house arrest by the Vichy government for most of World War II. Langevin was also president of the Human Rights League (LDH) from 1944 to 1946, having recently joined the French Communist Party. He was a doctoral student of Pierre Curie and later a lover of widowed Marie Curie. He is also known for his two US patents with Constantin Chilowsky in 1916 and 1917 involving ultrasonic submarine detection. He is entombed at the Panthéon. Life Langevin was born in Paris, and studied at the '' École de Physique et Chimie'' and the ''École Normale Supérieure''. He then went ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Spacelike Vector In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Although initially developed by mathematician Hermann Minkowski for Maxwell's equations of electromagnetism, the mathematical structure of Minkowski spacetime was shown to be implied by the postulates of special relativity. Minkowski space is closely associated with Einstein's theories of special relativity and general relativity and is the most common mathematical structure on which special relativity is formulated. While the individual components in Euclidean space and time may differ due to length contraction and time dilation, in Minkowski spacetime, all frames of reference will agree on the total distance in spacetime between events.This makes spacetime distance an invariant. Because ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]