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A four-vector A is a vector with a "timelike" component and three "spacelike" components, and can be written in various equivalent notations: [3] = (,,,) = + + + = + = where A α is the magnitude component and E α is the basis vector component; note that both are necessary to make a vector, and that when A α is seen alone, it refers strictly to the components of the vector.
In differential geometry, the four-gradient (or 4-gradient) is the four-vector analogue of the gradient from vector calculus. In special relativity and in quantum mechanics , the four-gradient is used to define the properties and relations between the various physical four-vectors and tensors .
A category for 4-vectors, (and closely related 4-operators) which are mathematical objects used in the special theory of relativity. Pages in category "Four-vectors" The following 11 pages are in this category, out of 11 total.
In special relativity, four-momentum (also called momentum–energy or momenergy [1]) is the generalization of the classical three-dimensional momentum to four-dimensional spacetime. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime.
Four-tensors of this kind are usually known as four-vectors. Here the component x 0 = ct gives the displacement of a body in time (coordinate time t is multiplied by the speed of light c so that x 0 has dimensions of length). The remaining components of the four-displacement form the spatial displacement vector x = (x 1, x 2, x 3). [1]
4 Examples. 5 See also. ... four-force is a four-vector that replaces the classical ... and are 3-space vectors describing the velocity, the momentum of the ...
The prime examples of such four-vectors are the four-position and four-momentum of a particle, and for fields the electromagnetic tensor and stress–energy tensor. The fact that these objects transform according to the Lorentz transformation is what mathematically defines them as vectors and tensors; see tensor for a definition.
(For example, for a position vector of length meters, if all Cartesian basis vectors are changed from meters in length to meters in length, the length of the position vector remains unchanged at meters, although the vector components will all increase by a factor of ). The scalar product of a vector and a covector is invariant, because one has ...