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Proper Velocity
In relativity, proper velocity (also known as celerity) w of an object relative to an observer is the ratio between observer-measured displacement vector \textbf and proper time elapsed on the clocks of the traveling object: :\textbf = \frac It is an alternative to ordinary velocity, the distance per unit time where both distance and time are measured by the observer. The two types of velocity, ordinary and proper, are very nearly equal at low speeds. However, at high speeds proper velocity retains many of the properties that velocity loses in relativity compared with Newtonian theory. For example, proper velocity equals momentum per unit mass at any speed, and therefore has no upper limit. At high speeds, as shown in the figure at right, it is proportional to an object's energy as well. Proper velocity w can be related to the ordinary velocity v via the Lorentz factor ''γ'': :\textbf = \frac\frac=\textbf \,\gamma(v) where ''t'' is coordinate time or "map time". For unidirec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The first laser was built in 1960 by Theodore H. Maiman at Hughes Research Laboratories, based on theoretical work by Charles Hard Townes and Arthur Leonard Schawlow. A laser differs from other sources of light in that it emits light which is ''coherent''. Spatial coherence allows a laser to be focused to a tight spot, enabling applications such as laser cutting and lithography. Spatial coherence also allows a laser beam to stay narrow over great distances (collimation), enabling applications such as laser pointers and lidar (light detection and ranging). Lasers can also have high temporal coherence, which allows them to emit light with a very narrow spectrum. Alternatively, temporal coherence can be used to produce ultrashort pulses of ligh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always move at the speed of light in vacuum, (or about ). The photon belongs to the class of bosons. As with other elementary particles, photons are best explained by quantum mechanics and exhibit wave–particle duality, their behavior featuring properties of both waves and particles. The modern photon concept originated during the first two decades of the 20th century with the work of Albert Einstein, who built upon the research of Max Planck. While trying to explain how matter and electromagnetic radiation could be in thermal equilibrium with one another, Planck proposed that the energy stored within a material object should be regarded as composed of an integer number of discrete, equal-sized parts. To explain the photoelectric effect, Eins ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brownian Motion
Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas). This pattern of motion typically consists of random fluctuations in a particle's position inside a fluid sub-domain, followed by a relocation to another sub-domain. Each relocation is followed by more fluctuations within the new closed volume. This pattern describes a fluid at thermal equilibrium, defined by a given temperature. Within such a fluid, there exists no preferential direction of flow (as in transport phenomena). More specifically, the fluid's overall linear and angular momenta remain null over time. The kinetic energies of the molecular Brownian motions, together with those of molecular rotations and vibrations, sum up to the caloric component of a fluid's internal energy (the equipartition theorem). This motion is named after the botanist Robert Brown, who first described the phenomenon in 1827, while looking throu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Velocity-addition Formula
In relativistic physics, a velocity-addition formula is a three-dimensional equation that relates the velocities of objects in different reference frames. Such formulas apply to successive Lorentz transformations, so they also relate different frames. Accompanying velocity addition is a kinematic effect known as Thomas precession, whereby successive non-collinear Lorentz boosts become equivalent to the composition of a rotation of the coordinate system and a boost. Standard applications of velocity-addition formulas include the Doppler shift, Doppler navigation, the aberration of light, and the dragging of light in moving water observed in the 1851 Fizeau experiment. The notation employs as velocity of a body within a Lorentz frame , and as velocity of a second frame , as measured in , and as the transformed velocity of the body within the second frame. History The speed of light in a fluid is slower than the speed of light in vacuum, and it changes if the fluid is moving al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Linear Collider
The International Linear Collider (ILC) is a proposed linear particle accelerator. It is planned to have a collision energy of 500 GeV initially, with the possibility for a later upgrade to 1000 GeV (1 TeV). Although early proposed locations for the ILC were Japan, Europe (CERN) and the USA (Fermilab), the Kitakami highland in the Iwate prefecture of northern Japan has been the focus of ILC design efforts since 2013. The Japanese government is willing to contribute half of the costs, according to the coordinator of study for detectors at the ILC. The ILC would collide electrons with positrons. It will be between 30 km and 50 km (19–31 mi) long, more than 10 times as long as the 50 GeV Stanford Linear Accelerator, the longest existing linear particle accelerator. The proposal is based on previous similar proposals from Europe, the U.S., and Japan. In a staged approach, the ILC could initially be constructed at 250 GeV, for use as a Higgs factory. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Large Electron–Positron Collider
The Large Electron–Positron Collider (LEP) was one of the largest particle accelerators ever constructed. It was built at CERN, a multi-national centre for research in nuclear and particle physics near Geneva, Switzerland. LEP collided electrons with positrons at energies that reached 209 GeV. It was a circular collider with a circumference of 27 kilometres built in a tunnel roughly 100 m (300 ft) underground and passing through Switzerland and France. LEP was used from 1989 until 2000. Around 2001 it was dismantled to make way for the Large Hadron Collider, which re-used the LEP tunnel. To date, LEP is the most powerful accelerator of leptons ever built. Collider background LEP was a circular lepton collider – the most powerful such ever built. For context, modern colliders can be generally categorized based on their shape (circular or linear) and on what types of particles they accelerate and collide (leptons or hadrons). Leptons are point particles and are r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolic Geometry
In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai– Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For any given line ''R'' and point ''P'' not on ''R'', in the plane containing both line ''R'' and point ''P'' there are at least two distinct lines through ''P'' that do not intersect ''R''. (Compare the above with Playfair's axiom, the modern version of Euclid's parallel postulate.) Hyperbolic plane geometry is also the geometry of pseudospherical surfaces, surfaces with a constant negative Gaussian curvature. Saddle surfaces have negative Gaussian curvature in at least some regions, where they locally resemble the hyperbolic plane. A modern use of hyperbolic geometry is in the theory of special relativity, particularly the Minkowski model. When geometers first realised they were working with something other than the standard Euclidean geometry, they described their geomet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gyrovector Space
A gyrovector space is a mathematical concept proposed by Abraham A. Ungar for studying hyperbolic geometry in analogy to the way vector spaces are used in Euclidean geometry.Abraham A. Ungar (2005), "Analytic Hyperbolic Geometry: Mathematical Foundations and Applications", Published by World Scientific, , Ungar introduced the concept of gyrovectors that have addition based on gyrogroups instead of vectors which have addition based on groups. Ungar developed his concept as a tool for the formulation of special relativity as an alternative to the use of Lorentz transformations to represent compositions of velocities (also called boosts – "boosts" are aspects of relative velocities, and should not be conflated with " translations"). This is achieved by introducing "gyro operators"; two 3d velocity vectors are used to construct an operator, which acts on another 3d velocity. Name Gyrogroups are weakly associative group-like structures. Ungar proposed the term gyrogr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
