|
Velocity-addition Formula
In relativistic physics, a velocity-addition formula is an equation that specifies how to combine the Velocity, velocities of objects in a way that is consistent with the requirement that no object's speed can exceed the speed of light. Such formulas apply to successive Lorentz transformations, so they also relate different frame of reference, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albert Einstein Head
Albert may refer to: Companies * Albert Computers, Inc., a computer manufacturer in the 1980s * Albert Czech Republic, a supermarket chain in the Czech Republic * Albert Heijn, a supermarket chain in the Netherlands * Albert Market, a street market in The Gambia * Albert Music, an Australian music company now known as Alberts ** Albert Productions, a record label * Albert (organisation), an environmental organisation concerning film and television productions Entertainment * Albert (1985 film), ''Albert'' (1985 film), a Czechoslovak film directed by František Vláčil * ''Albert'' (2015 film), a film by Karsten Kiilerich * Albert (2016 film), ''Albert'' (2016 film), an American TV movie * Albert (album), ''Albert'' (album), by Ed Hall, 1988 * Albert (short story), "Albert" (short story), by Leo Tolstoy * Albert (comics), a character in Marvel Comics * Albert (Discworld), Albert (''Discworld''), a character in Terry Pratchett's ''Discworld'' series * Albert, a character in Dario A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentz Aether Theory
What is now often called Lorentz ether theory (LET) has its roots in Hendrik Lorentz's "theory of electrons", which marked the end of the development of the classical aether theories at the end of the 19th and at the beginning of the 20th century. Lorentz's initial theory was created between 1892 and 1895 and was based on removing assumptions about aether motion. It explained the failure of the negative aether drift experiments to first order in ''v''/''c'' by introducing an auxiliary variable called "local time" for connecting systems at rest and in motion in the aether. In addition, the negative result of the Michelson–Morley experiment led to the introduction of the hypothesis of length contraction in 1892. However, other experiments also produced negative results and (guided by Henri Poincaré's principle of relativity) Lorentz tried in 1899 and 1904 to expand his theory to all orders in ''v''/''c'' by introducing the Lorentz transformation. In addition, he assumed that non-el ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polar Coordinates
In mathematics, the polar coordinate system specifies a given point (mathematics), point in a plane (mathematics), plane by using a distance and an angle as its two coordinate system, coordinates. These are *the point's distance from a reference point called the ''pole'', and *the point's direction from the pole relative to the direction of the ''polar axis'', a ray (geometry), ray drawn from the pole. The distance from the pole is called the ''radial coordinate'', ''radial distance'' or simply ''radius'', and the angle is called the ''angular coordinate'', ''polar angle'', or ''azimuth''. The pole is analogous to the origin in a Cartesian coordinate system. Polar coordinates are most appropriate in any context where the phenomenon being considered is inherently tied to direction and length from a center point in a plane, such as spirals. Planar physical systems with bodies moving around a central point, or phenomena originating from a central point, are often simpler and more in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentz Factor
The Lorentz factor or Lorentz term (also known as the gamma factor) is a dimensionless quantity expressing how much the measurements of time, length, and other physical properties change for an object while it moves. The expression appears in several equations in special relativity, and it arises in derivations of the Lorentz transformations. The name originates from its earlier appearance in Lorentz ether theory, Lorentzian electrodynamics – named after the Netherlands, Dutch physicist Hendrik Lorentz. It is generally denoted (the Greek lowercase letter gamma). Sometimes (especially in discussion of superluminal motion) the factor is written as (Greek uppercase-gamma) rather than . Definition The Lorentz factor is defined as \gamma = \frac = \frac = \frac , where: * is the relative velocity between inertial reference frames, * is the speed of light in vacuum, * is the ratio of to , * is coordinate time, * is the proper time for an observer (measuring time intervals in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivations Of The Lorentz Transformations
There are many ways to derive the Lorentz transformations using a variety of physical principles, ranging from Maxwell's equations to Einstein's postulates of special relativity, and mathematical tools, spanning from elementary algebra and hyperbolic functions, to linear algebra and group theory. This article provides a few of the easier ones to follow in the context of special relativity, for the simplest case of a Lorentz boost in standard configuration, i.e. two inertial frames moving relative to each other at constant (uniform) relative velocity less than the speed of light, and using Cartesian coordinates so that the ''x'' and ''x''′ axes are collinear. Lorentz transformation In the fundamental branches of modern physics, namely general relativity and its widely applicable subset special relativity, as well as relativistic quantum mechanics and relativistic quantum field theory, the Lorentz transformation is the transformation rule under which all four-vectors and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relativistic Mechanics
In physics, relativistic mechanics refers to mechanics compatible with special relativity (SR) and general relativity (GR). It provides a non- quantum mechanical description of a system of particles, or of a fluid, in cases where the velocities of moving objects are comparable to the speed of light ''c''. As a result, classical mechanics is extended correctly to particles traveling at high velocities and energies, and provides a consistent inclusion of electromagnetism with the mechanics of particles. This was not possible in Galilean relativity, where it would be permitted for particles and light to travel at ''any'' speed, including faster than light. The foundations of relativistic mechanics are the postulates of special relativity and general relativity. The unification of SR with quantum mechanics is relativistic quantum mechanics, while attempts for that of GR is quantum gravity, an unsolved problem in physics. As with classical mechanics, the subject can be divided into ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentz Transformation
In physics, the Lorentz transformations are a six-parameter family of Linear transformation, linear coordinate transformation, transformations from a Frame of Reference, coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity. The transformations are named after the Dutch physicist Hendrik Lorentz. The most common form of the transformation, parametrized by the real constant v, representing a velocity confined to the -direction, is expressed as \begin t' &= \gamma \left( t - \frac \right) \\ x' &= \gamma \left( x - v t \right)\\ y' &= y \\ z' &= z \end where and are the coordinates of an event in two frames with the spatial origins coinciding at , where the primed frame is seen from the unprimed frame as moving with speed along the -axis, where is the speed of light, and \gamma = \frac is the Lorentz factor. When speed is much smal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minkowski Spacetime
In physics, Minkowski space (or Minkowski spacetime) () is the main mathematical description of spacetime in the absence of gravitation. It combines inertial space and time manifolds into a four-dimensional model. The model helps show how a spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Mathematician Hermann Minkowski developed it from the work of Hendrik Lorentz, Henri Poincaré, and others said it "was grown on experimental physical grounds". Minkowski space is closely associated with Einstein's theories of special relativity and general relativity and is the most common mathematical structure by which special relativity is formalized. While the individual components in Euclidean space and time might differ due to length contraction and time dilation, in Minkowski spacetime, all frames of reference will agree on the total interval in spacetime between events.This makes spacetime distance an invarian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newtonian Mechanics
Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: # A body remains at rest, or in motion at a constant speed in a straight line, unless it is acted upon by a force. # At any instant of time, the net force on a body is equal to the body's acceleration multiplied by its mass or, equivalently, the rate at which the body's momentum is changing with time. # If two bodies exert forces on each other, these forces have the same magnitude but opposite directions. The three laws of motion were first stated by Isaac Newton in his '' Philosophiæ Naturalis Principia Mathematica'' (''Mathematical Principles of Natural Philosophy''), originally published in 1687. Newton used them to investigate and explain the motion of many physical objects and systems. In the time since Newton, new insights, especially around ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galilean Relativity
Galilean invariance or Galilean relativity states that the laws of motion are the same in all inertial frames of reference. Galileo Galilei first described this principle in 1632 in his ''Dialogue Concerning the Two Chief World Systems'' using the example of a ship travelling at constant velocity, without rocking, on a smooth sea; any observer below the deck would not be able to tell whether the ship was moving or stationary. Formulation Specifically, the term ''Galilean invariance'' today usually refers to this principle as applied to Newtonian mechanics, that is, Newton's laws of motion hold in all frames related to one another by a Galilean transformation. In other words, all frames related to one another by such a transformation are inertial (meaning, Newton's equation of motion is valid in these frames). In this context it is sometimes called ''Newtonian relativity''. Among the axioms from Newton's theory are: #There exists an '' absolute space'', in which Newton's laws ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galilean Transformation
In physics, a Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics. These transformations together with spatial rotations and translations in space and time form the inhomogeneous Galilean group (assumed throughout below). Without the translations in space and time the group is the homogeneous Galilean group. The Galilean group is the group of motions of Galilean relativity acting on the four dimensions of space and time, forming the Galilean geometry. This is the passive transformation point of view. In special relativity the homogeneous and inhomogeneous Galilean transformations are, respectively, replaced by the Lorentz transformations and Poincaré transformations; conversely, the group contraction in the classical limit of Poincaré transformations yields Galilean transformations. The equations below are only physically valid in a Newtonian fra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Absolute Space And Time
Absolute space and time is a concept in physics and philosophy about the properties of the universe. In physics, absolute space and time may be a preferred frame. Early concept A version of the concept of absolute space (in the sense of a preferred frame) can be seen in Aristotelian physics. Robert S. Westman writes that a "whiff" of absolute space can be observed in Copernicus's '' De revolutionibus orbium coelestium'', where Copernicus uses the concept of an immobile sphere of stars. Newton Originally introduced by Sir Isaac Newton in '' Philosophiæ Naturalis Principia Mathematica'', the concepts of absolute time and space provided a theoretical foundation that facilitated Newtonian mechanics. According to Newton, absolute time and space respectively are independent aspects of objective reality: Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, appar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
