Energy momentum pseudotensor
Main article: Stress-energy-momentum pseudotensor In the theory of general relativity, a stress-energy-momentum pseudotensor, such as the Landau-Lifshitz pseudotensor, is an extension of the non-gravitational stress-energy tensor which incorporates the energy-momentum of gravity. It allows the energy-momentum of a system of gravitating matter to be defined. In particular it allows the total ofGeneral Relativity includes a dynamical spacetime, so it is difficult to see how to identify the conserved energy and momentum. Noether's theorem Noether's theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. The action of a physical system is an integral of a so-called Lagrangian function, from which the system's behavior can be determined by the principle of least action. This seminal theorem was proved by Emmy Noether in allows these quantities to be determined from a Lagrangian The Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics known as Lagrangian mechanics. In classical mechanics, the Lagrangian is defined as the kinetic energy, T, of the with translation invariance In geometry, a translation "slides" an object by a a: Ta = p + a, but general covariance In theoretical physics, general covariance is 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 makes translation invariance into something of a gauge symmetry Though 'gauge' in gauge symmetry means 'measure', gauge symmetries in theoretical physics are symmetries depending on parameter functions. In particular, a gauge symmetry of a Lagrangian L is defined as a differential operator on some vector bundle E taking its values in the linear space of symmetries of L. Therefore, a gauge symmetry of L depends. The energy and momentum derived within General relativity by Noether's presecriptions do not make a real tensor for this reason.
Einstein argued that this is true for fundamental reasons, because the gravitational field could be made to vanish by a choice of coordinates. He maintained that the noncovariante energy momentum pseudotensor was in fact the best description of the energy momentum distribution in a gravitational field. This approach has been echoed by Lev Landau Landau was born on January 22, 1908 to a Jewish family in Baku, in what was then Tsarist Russia. Recognized very early as a child prodigy in mathematics, Landau was quoted as saying in later life that he scarcely remembered a time when he was not familiar with calculus. Landau graduated at 13 from gymnasium. His parents regarded him too young to and Evgeny Lifshitz Evgeny Mikhailovich Lifshitz was a leading Soviet physicist from a Jewish origin and the brother of Ilya Mikhailovich Lifshitz, and others, and has become standard.
The use of non-covariant objects like pseudotensors was heavily criticized in 1917 by Erwin Schrodinger Erwin Rudolf Josef Alexander Schrödinger was an Austrian theoretical physicist who achieved fame for his contributions to quantum mechanics, especially the Schrödinger equation, for which he received the Nobel Prize in 1933. In 1935, after extensive correspondence with personal friend Albert Einstein, he proposed the Schrödinger's cat thought and others.
<<Table of Contents Albert Einstein was an ethnically Jewish, German-born theoretical physicist. He is best known for his theories of special relativity and general relativity. Einstein received the 1921 Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect.". He is often | Next>> | Show All>>
