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Scalar Theories Of Gravitation
Scalar theories of gravitation are field theories of gravitation in which the gravitational field is described using a scalar field, which is required to satisfy some field equation. ''Note:'' This article focuses on relativistic classical field theories of gravitation. The best known relativistic classical field theory of gravitation, general relativity, is a tensor theory, in which the gravitational interaction is described using a tensor field. Newtonian gravity The prototypical scalar theory of gravitation is Newtonian gravitation. In this theory, the gravitational interaction is completely described by the potential \Phi, which is required to satisfy the Poisson equation (with the mass density acting as the source of the field). To wit: \Delta \Phi = 4 \pi G \rho, where * ''G'' is the gravitational constant and * \rho is the mass density. This field theory formulation leads directly to the familiar law of universal gravitation, F = m_1 m_2 G/r^2. Nordström's theori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitation
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak interaction. As a result, it has no significant influence at the level of subatomic particles. However, gravity is the most significant interaction between objects at the macroscopic scale, and it determines the motion of planets, stars, galaxies, and even light. On Earth, gravity gives weight to physical objects, and the Moon's gravity is responsible for sublunar tides in the oceans (the corresponding antipodal tide is caused by the inertia of the Earth and Moon orbiting one another). Gravity also has many important biological functions, helping to guide the growth of plants through the process of gravitropism and influencing the circul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perihelion
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two apsides in any elliptic orbit. The name for each apsis is created from the prefixes ''ap-'', ''apo-'' (), or ''peri-'' (), each referring to the farthest and closest point to the primary body the affixing necessary suffix that describes the primary body in the orbit. In this case, the suffix for Earth is ''-gee'', so the apsides' names are ''apogee'' and ''perigee''. For the Sun, its suffix is ''-helion'', so the names are ''aphelion'' and ''perihelion''. According to Newton's laws of motion, all periodic orbits are ellipses. The barycenter of the two bodies may lie well within the bigger body—e.g., the Earth–Moon barycenter is about 75% of the way from Earth's center to its surface. If, compared to the larger mass, the smaller mass is negligible (e.g., f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pascual Jordan
Ernst Pascual Jordan (; 18 October 1902 – 31 July 1980) was a German theoretical and mathematical physicist who made significant contributions to quantum mechanics and quantum field theory. He contributed much to the mathematical form of matrix mechanics, and developed canonical anticommutation relations for fermions. Jordan algebra is employed for and is still used in studying the mathematical and conceptual foundations of quantum theory, and has found other mathematical applications. Jordan joined the Nazi Party in 1933, but did not follow the Deutsche Physik movement, which at the time rejected quantum physics developed by Albert Einstein and other Jewish physicists. After the Second World War, he entered politics for the conservative party CDU and served as a member of parliament from 1957 to 1961. Family history Pascual Jordan's parents were Ernst Pasqual Jordan (1858-1924) and Eva Fischer. Ernst Jordan was a painter renowned for his portraits and landscapes. He was an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generally Covariant
In theoretical physics, general covariance, also known as diffeomorphism covariance or general invariance, consists of the invariance of the ''form'' of physical laws under arbitrary differentiable coordinate transformations. The essential idea is that coordinates do not exist ''a priori'' in nature, but are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws. While this concept is exhibited by general relativity, which describes the dynamics of spacetime, one should not expect it to hold in less fundamental theories. For matter fields taken to exist independently of the background, it is almost never the case that their equations of motion will take the same form in curved space that they do in flat space. Overview A physical law expressed in a generally covariant fashion takes the same mathematical form in all coordinate systems, and is usually expressed in terms of tensor fields. The classical (non-quantum) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffeomorphism
In mathematics, a diffeomorphism is an isomorphism of smooth manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function and its inverse are differentiable. Definition Given two manifolds M and N, a differentiable map f \colon M \rightarrow N is called a diffeomorphism if it is a bijection and its inverse f^ \colon N \rightarrow M is differentiable as well. If these functions are r times continuously differentiable, f is called a C^r-diffeomorphism. Two manifolds M and N are diffeomorphic (usually denoted M \simeq N) if there is a diffeomorphism f from M to N. They are C^r-diffeomorphic if there is an r times continuously differentiable bijective map between them whose inverse is also r times continuously differentiable. Diffeomorphisms of subsets of manifolds Given a subset X of a manifold M and a subset Y of a manifold N, a function f:X\to Y is said to be smooth if for all p in X there is a neighbor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetic Field
An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical counterpart to the quantized electromagnetic field tensor in quantum electrodynamics (a quantum field theory). The electromagnetic field propagates at the speed of light (in fact, this field can be identified ''as'' light) and interacts with charges and currents. Its quantum counterpart is one of the four fundamental forces of nature (the others are gravitation, weak interaction and strong interaction.) The field can be viewed as the combination of an electric field and a magnetic field. The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field. The way in which charges and currents interact with the electromagnetic field is des ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tangent Vector
In mathematics, a tangent vector is a vector that is tangent to a curve or surface at a given point. Tangent vectors are described in the differential geometry of curves in the context of curves in R''n''. More generally, tangent vectors are elements of a tangent space of a differentiable manifold. Tangent vectors can also be described in terms of germs. Formally, a tangent vector at the point x is a linear derivation of the algebra defined by the set of germs at x. Motivation Before proceeding to a general definition of the tangent vector, we discuss its use in calculus and its tensor properties. Calculus Let \mathbf(t) be a parametric smooth curve. The tangent vector is given by \mathbf'(t), where we have used a prime instead of the usual dot to indicate differentiation with respect to parameter . The unit tangent vector is given by \mathbf(t) = \frac\,. Example Given the curve \mathbf(t) = \left\ in \R^3, the unit tangent vector at t = 0 is given by \mathbf(0) = \frac = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Four-velocity
In physics, in particular in special relativity and general relativity, a four-velocity is a four-vector in four-dimensional spacetimeTechnically, the four-vector should be thought of as residing in the tangent space of a point in spacetime, spacetime itself being modeled as a smooth manifold. This distinction is significant in general relativity. that represents the relativistic counterpart of velocity, which is a three-dimensional vector in space. Physical events correspond to mathematical points in time and space, the set of all of them together forming a mathematical model of physical four-dimensional spacetime. The history of an object traces a curve in spacetime, called its world line. If the object has mass, so that its speed is necessarily less than the speed of light, the world line may be parametrized by the proper time of the object. The four-velocity is the rate of change of four-position with respect to the proper time along the curve. The velocity, in contrast, is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hole Argument
In general relativity, the hole argument is an apparent paradox that much troubled Albert Einstein while developing his famous field equations. Some philosophers of physics take the argument to raise a problem for '' manifold substantialism'', a doctrine that the manifold of events in spacetime is a "substance" which exists independently of the metric field defined on it or the matter within it. Other philosophers and physicists disagree with this interpretation, and view the argument as a confusion about gauge invariance and gauge fixing instead. Einstein's hole argument In a usual field equation, knowing the source of the field, and the boundary conditions, determines the field everywhere. For example, if we are given the current and charge density and appropriate boundary conditions, Maxwell's equations determine the electric and magnetic fields. They do not determine the vector potential though, because the vector potential depends on an arbitrary choice of gauge. Einstein n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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