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Acceleration (special Relativity)
Accelerations in special relativity (SR) follow, as in Newtonian Mechanics, by differentiation of velocity with respect to time. Because of the Lorentz transformation and time dilation, the concepts of time and distance become more complex, which also leads to more complex definitions of "acceleration". SR as the theory of flat Minkowski spacetime remains valid in the presence of accelerations, because general relativity (GR) is only required when there is curvature of spacetime caused by the energy–momentum tensor (which is mainly determined by mass). However, since the amount of spacetime curvature is not particularly high on Earth or its vicinity, SR remains valid for most practical purposes, such as experiments in particle accelerators. One can derive transformation formulas for ordinary accelerations in three spatial dimensions (three-acceleration or coordinate acceleration) as measured in an external inertial frame of reference, as well as for the special case of proper ac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the orientation of the ''net'' force acting on that object. The magnitude of an object's acceleration, as described by Newton's Second Law, is the combined effect of two causes: * the net balance of all external forces acting onto that object — magnitude is directly proportional to this net resulting force; * that object's mass, depending on the materials out of which it is made — magnitude is inversely proportional to the object's mass. The SI unit for acceleration is metre per second squared (, \mathrm). For example, when a vehicle starts from a standstill (zero velocity, in an inertial frame of reference) and travels in a straight line at increasing speeds, it is accelerating in the direction of travel. If the vehicle turns, an a ... [...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 * \mathb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hendrik Antoon Lorentz
Hendrik Antoon Lorentz (; 18 July 1853 – 4 February 1928) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect. He also derived the Lorentz transformation underpinning Albert Einstein's special theory of relativity, as well as the Lorentz force, which describes the combined electric and magnetic forces acting on a charged particle in an electromagnetic field. Lorentz was also responsible for the Lorentz oscillator model, a classical model used to describe the anomalous dispersion observed in dielectric materials when the driving frequency of the electric field was near the resonant frequency, resulting in abnormal refractive indices. According to the biography published by the Nobel Foundation, "It may well be said that Lorentz was regarded by all theoretical physicists as the world's leading spirit, who completed what was left unfinished by his predecessors and prepared ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolfgang Pauli
Wolfgang Ernst Pauli (; ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics for his "decisive contribution through his discovery of a new law of Nature, the exclusion principle or Pauli principle". The discovery involved spin theory, which is the basis of a theory of the structure of matter. Early years Pauli was born in Vienna to a chemist, Wolfgang Joseph Pauli (''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 godfather, physicist Ernst Mach. Pauli's paternal grandparents were from prominent families of Prague; his great-grandfather was the publisher Wolf Pascheles. Pauli's mother, Bertha Schütz, was raised in her mother's Roman Catholic religion; Pauli was raised as a Roman Cathol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Max Von Laue
Max Theodor Felix von Laue (; 9 October 1879 – 24 April 1960) was a German physicist who received the Nobel Prize in Physics in 1914 for his discovery of the diffraction of X-rays by crystals. In addition to his scientific endeavors with contributions in optics, crystallography, quantum theory, superconductivity, and the theory of relativity, Laue had a number of administrative positions which advanced and guided German scientific research and development during four decades. A strong objector to Nazism, he was instrumental in re-establishing and organizing German science after World War II. Biography Early years Laue was born in Pfaffendorf, now part of Koblenz, Germany, to Julius Laue and Minna Zerrenner. In 1898, after passing his ''Abitur'' in Strassburg, he began his compulsory year of military service, after which in 1899 he started to study mathematics, physics, and chemistry at the University of Strassburg, the University of Göttingen, and the Ludwig Maximilian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rindler Coordinates
In relativistic physics, the coordinates of a ''hyperbolically accelerated reference frame'' constitute an important and useful coordinate chart representing part of flat Minkowski spacetime. In special relativity, a uniformly accelerating particle undergoes hyperbolic motion, for which a uniformly accelerating frame of reference in which it is at rest can be chosen as its proper reference frame. The phenomena in this hyperbolically accelerated frame can be compared to effects arising in a homogeneous gravitational field. For general overview of accelerations in flat spacetime, see Acceleration (special relativity) and Proper reference frame (flat spacetime). In this article, the speed of light is defined by , the inertial coordinates are , and the hyperbolic coordinates are . These hyperbolic coordinates can be separated into two main variants depending on the accelerated observer's position: If the observer is located at time at position (with as the constant proper acceler ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Field
In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenomena, and is measured in newtons per kilogram (N/kg). Equivalently, it is measured in meters per second squared (m/s2). In its original concept, gravity was a force between point masses. Following Isaac Newton, Pierre-Simon Laplace attempted to model gravity as some kind of radiation field or fluid, and since the 19th century, explanations for gravity have usually been taught in terms of a field model, rather than a point attraction. In a field model, rather than two particles attracting each other, the particles distort spacetime via their mass, and this distortion is what is perceived and measured as a "force". In such a model one states that matter moves in certain ways in response to the curvature of spacetime, and that ther ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proper Reference Frame (flat Spacetime)
A proper reference frame in the theory of relativity is a particular form of accelerated reference frame, that is, a reference frame in which an accelerated observer can be considered as being at rest. It can describe phenomena in curved spacetime, as well as in "flat" Minkowski spacetime in which the spacetime curvature caused by the energy–momentum tensor can be disregarded. Since this article considers only flat spacetime—and uses the definition that special relativity is the theory of flat spacetime while general relativity is a theory of gravitation in terms of curved spacetime—it is consequently concerned with accelerated frames in special relativity. (For the representation of accelerations in inertial frames, see the article Acceleration (special relativity), where concepts such as three-acceleration, four-acceleration, proper acceleration, hyperbolic motion etc. are defined and related to each other.) A fundamental property of such a frame is the employment of the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-inertial Reference Frame
A non-inertial reference frame is a frame of reference that undergoes acceleration with respect to an inertial frame. An accelerometer at rest in a non-inertial frame will, in general, detect a non-zero acceleration. While the laws of motion are the same in all inertial frames, in non-inertial frames, they vary from frame to frame depending on the acceleration. In classical mechanics the motion of bodies in non-inertial reference frames is modeled by introducing additional forces ( d'Alembert forces) to inertial reference frames in order to account for the inertia effects that are appearing in this situation. Because in principle they don't belong to the modeling of an inertial frame in terms of Newton's second law such inertial effects are called fictitious forces. They might be called inertial forces or pseudo forces, too. Common examples of this include the Coriolis force and the centrifugal force. In general, the expression for any fictitious force can be derived from the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circular Motion
In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. The equations of motion describe the movement of the center of mass of a body. In circular motion, the distance between the body and a fixed point on the surface remains the same. Examples of circular motion include: an artificial satellite orbiting the Earth at a constant height, a ceiling fan's blades rotating around a hub, a stone which is tied to a rope and is being swung in circles, a car turning through a curve in a race track, an electron moving perpendicular to a uniform magnetic field, and a gear turning inside a mechanism. Since the object's velocity vector is constantly changing direction, the moving object is undergoing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolic Motion (relativity)
Hyperbolic motion is the motion of an object with constant proper acceleration in special relativity. It is called hyperbolic motion because the equation describing the path of the object through spacetime is a hyperbola, as can be seen when graphed on a Minkowski diagram whose coordinates represent a suitable inertial (non-accelerated) frame. This motion has several interesting features, among them that it is possible to outrun a photon if given a sufficient head start, as may be concluded from the diagram. History Hermann Minkowski (1908) showed the relation between a point on a worldline and the magnitude of four-acceleration and a "curvature hyperbola" (german: Krümmungshyperbel). In the context of Born rigidity, Max Born (1909) subsequently coined the term "hyperbolic motion" (german: Hyperbelbewegung) for the case of constant magnitude of four-acceleration, then provided a detailed description for charged particles in hyperbolic motion, and introduced the corresponding ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
