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Retarded Position
{{Unreferenced, date=April 2021 Einstein's equations admit gravity wave-like solutions. In the case of a moving point-like mass and in the linearized limit of a weak-gravity approximation these solutions of the Einstein equations are known as the Liénard–Wiechert gravitational potentials. Wave-like solutions (variations) in gravitational field at any point of space at some instant of time t are generated by the mass taken in the preceding (or retarded) instant of time s < t on its world-line at a vertex of the null cone connecting the mass and the field point. The position of the mass that generates the field is called the retarded position and the Liénard–Wiechert potentials are called the retarded potentials. Gravitational waves caused by acceleration of a mass appear to come from the position and direction of the mass at the time it was accelerated (the retarded time and position). The retarded time and the retarded position of the mass are a direct consequence of the finit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Einstein's Equations
In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Einstein in 1915 in the form of a tensor equation which related the local ' (expressed by the Einstein tensor) with the local energy, momentum and stress within that spacetime (expressed by the stress–energy tensor). Analogously to the way that electromagnetic fields are related to the distribution of charges and currents via Maxwell's equations, the EFE relate the spacetime geometry to the distribution of mass–energy, momentum and stress, that is, they determine the metric tensor of spacetime for a given arrangement of stress–energy–momentum in the spacetime. The relationship between the metric tensor and the Einstein tensor allows the EFE to be written as a set of nonlinear partial differential equations when used in this way. The solutions of the EFE ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linearized Limit
In mathematics, linearization is finding the linear approximation to a function at a given point. The linear approximation of a function is the first order Taylor expansion around the point of interest. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or discrete dynamical systems. This method is used in fields such as engineering, physics, economics, and ecology. Linearization of a function Linearizations of a function are lines—usually lines that can be used for purposes of calculation. Linearization is an effective method for approximating the output of a function y = f(x) at any x = a based on the value and slope of the function at x = b, given that f(x) is differentiable on , b/math> (or , a/math>) and that a is close to b. In short, linearization approximates the output of a function near x = a. For example, \sqrt = 2. However, what would ... [...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 there is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World-line
The world line (or worldline) of an object is the path that an object traces in 4-dimensional spacetime. It is an important concept in modern physics, and particularly theoretical physics. The concept of a "world line" is distinguished from concepts such as an "orbit" or a "trajectory" (e.g., a planet's ''orbit in space'' or the ''trajectory'' of a car on a road) by the ''time'' dimension, and typically encompasses a large area of spacetime wherein perceptually straight paths are recalculated to show their ( relatively) more absolute position states—to reveal the nature of special relativity or gravitational interactions. The idea of world lines originates in physics and was pioneered by Hermann Minkowski. The term is now most often used in relativity theories (i.e., special relativity and general relativity). Usage in physics In physics, a world line of an object (approximated as a point in space, e.g., a particle or observer) is the sequence of spacetime events corresp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Speed Of Gravity
In classical theories of gravitation, the changes in a gravitational field propagate. A change in the distribution of energy and momentum of matter results in subsequent alteration, at a distance, of the gravitational field which it produces. In the relativistic sense, the "speed of gravity" refers to the speed of a gravitational wave, which, as predicted by general relativity and confirmed by observation of the GW170817 neutron star merger, is the same speed as the speed of light (''c''). Introduction The speed of gravitational waves in the general theory of relativity is equal to the ''speed of light'' in a vacuum, . Within the theory of special relativity, the constant is not only about light; instead it is the highest possible speed for any interaction in nature. Formally, is a conversion factor for changing the unit of time to the unit of space. This makes it the only speed which does not depend either on the motion of an observer or a source of light and / or gravity. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liénard–Wiechert Potential
The Liénard–Wiechert potentials describe the classical electromagnetic effect of a moving electric point charge in terms of a vector potential and a scalar potential in the Lorenz gauge. Stemming directly from Maxwell's equations, these describe the complete, relativistically correct, time-varying electromagnetic field for a point charge in arbitrary motion, but are not corrected for quantum mechanical effects. Electromagnetic radiation in the form of waves can be obtained from these potentials. These expressions were developed in part by Alfred-Marie Liénard in 1898 and independently by Emil Wiechert in 1900. Equations Definition of Liénard–Wiechert potentials The retarded time is defined, in the context of distributions of charges and currents, as :t_r(\mathbf,\mathbf, t) = t - \frac, \mathbf - \mathbf_s, , where \mathbf is the observation point, and \mathbf_s is the observed point subject to the variations of source charges and currents. For a moving point charg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 simple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relativistic Aberration
Relativistic aberration is the relativistic version of aberration of light, including relativistic corrections that become significant for observers who move with velocities close to the speed of light. It is described by Einstein's special theory of relativity. Suppose, in the reference frame of the observer, the source is moving with speed v\, at an angle \theta_s\, relative to the vector from the observer to the source at the time when the light is emitted. Then the following formula, which was derived by Einstein in 1905 from the Lorentz transformation, describes the aberration of the light source, \theta_o\,, measured by the observer: :\cos \theta_o=\frac \, In this circumstance, the rays of light from the source which reach the observer are tilted towards the direction of the source's motion (relative to the observer). It is as if light emitted by a moving object is concentrated conically, towards its direction of motion; an effect called relativistic beaming. Also, light ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Faster Than Light
Faster-than-light (also FTL, superluminal or supercausal) travel and communication are the conjectural propagation of matter or information faster than the speed of light (). The special theory of relativity implies that only particles with zero rest mass (i.e., photons) may travel ''at'' the speed of light, and that nothing may travel faster. Particles whose speed exceeds that of light (tachyons) have been hypothesized, but their existence would violate causality and would imply time travel. The scientific consensus is that they do not exist. "Apparent" or "effective" FTL, on the other hand, depends on the hypothesis that unusually distorted regions of spacetime might permit matter to reach distant locations in less time than light could in normal ("undistorted") spacetime. As of the 21st century, according to current scientific theories, matter is required to travel at slower-than-light (also STL or subluminal) speed with respect to the locally distorted spacetime region. Appar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
