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In general relativity, four-dimensional vectors, or four-vectors, are required. These four dimensions are length, height, width and time. A "point" in this context would be an event, as it has both a location and a time. Similar to vectors, tensors in relativity require four dimensions. One example is the Riemann curvature tensor.
:English translations: "Does the Inertia of a Body Depend Upon Its Energy Content?". Translation by George Barker Jeffery and Wilfrid Perrett in The Principle of Relativity, London: Methuen and Company, Ltd. (1923). :Used the newly formulated theory of special relativity to introduce the mass energy formula. One of the Annus Mirabilis papers.
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 contrast to all other modern theories of fundamental interactions, general relativity is a classical theory: it does not include the effects of quantum physics. The quest for a quantum version of general relativity addresses one of the most fundamental open questions in physics.
The term "theory of relativity" was based on the expression "relative theory" (German: Relativtheorie) used in 1906 by Planck, who emphasized how the theory uses the principle of relativity. In the discussion section of the same paper, Alfred Bucherer used for the first time the expression "theory of relativity" ( German : Relativitätstheorie ).
In special relativity, Newton's second law does not hold in the form F = ma, but it does if it is expressed as F = d p d t {\displaystyle \mathbf {F} ={\frac {d\mathbf {p} }{dt}}} where p = γ( v ) m 0 v is the momentum as defined above and m 0 is the invariant mass .
The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature. The weak form, known for centuries, relates to masses of any composition in free fall taking the same trajectories and landing at identical times.
The model does not explain gravitation, although physical confirmation of a theoretical particle known as a graviton would account for it to a degree. Though it addresses strong and electroweak interactions, the Standard Model does not consistently explain the canonical theory of gravitation, general relativity, in terms of quantum field theory.