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Numerical relativity is the sub-field of general relativity which seeks to solve Einstein's equations through the use of numerical methods. Finite difference, finite element and pseudo-spectral methods are used to approximate the solution to the partial differential equations which arise. Novel techniques developed by numerical relativity ...
In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric vector [1] or spatial vector, [2] or – as here – simply a vector) is a geometric object that has both a magnitude (or length) and direction. A vector is what is needed to "carry" the point A to the point B; the Latin word vector means "one who carries ...
Fig 2-3 Different scales on the axes. The angle α between the x and x′ axes will be identical with that between the time axes ct and ct′. This follows from the second postulate of special relativity, which says that the speed of light is the same for all observers, regardless of their relative motion (see below). The angle α is given by [5]
Relativity links mass with energy, and energy with momentum. The equivalence between mass and energy, as expressed by the formula E = mc 2, is the most famous consequence of special relativity. In relativity, mass and energy are two different ways of describing one physical quantity.
In mathematical physics, spacetime algebra (STA) is the application of Clifford algebra Cl 1,3 (R), or equivalently the geometric algebra G(M 4) to physics. Spacetime algebra provides a "unified, coordinate-free formulation for all of relativistic physics, including the Dirac equation, Maxwell equation and General Relativity" and "reduces the mathematical divide between classical, quantum and ...
Its mathematics seemed difficult and fully understandable only by a small number of people. Around 1960, general relativity became central to physics and astronomy. New mathematical techniques to apply to general relativity streamlined calculations and made its concepts more easily visualized.
Bell's spaceship paradox is a thought experiment in special relativity. It was first described by E. Dewan and M. Beran in 1959 [1] but became more widely known after John Stewart Bell elaborated the idea further in 1976. [2] A delicate thread hangs between two spaceships initially at rest in the inertial frame S.
In the preface to Relativity: The Special and the General Theory, Einstein said "The present book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical ...