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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 Einstein's theory of relativity, the path of an object moving relative to a particular frame of reference is defined by four coordinate functions x μ (τ), where μ is a spacetime index which takes the value 0 for the timelike component, and 1, 2, 3 for the spacelike coordinates.
The four-force is defined as the rate of change in the four-momentum of a particle with respect to the particle's proper time.Hence,: =. For a particle of constant invariant mass >, the four-momentum is given by the relation =, where = (,) is the four-velocity.
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.
The 3-space momentum = (,,) is conserved (not to be confused with the classic non-relativistic momentum ). Note that the invariant mass of a system of particles may be more than the sum of the particles' rest masses, since kinetic energy in the system center-of-mass frame and potential energy from forces between the particles contribute to the ...
Also known as vector current, it is used in the geometric context of four-dimensional spacetime, rather than separating time from three-dimensional space. Mathematically it is a four-vector and is Lorentz covariant. This article uses the summation convention for indices.
The company’s developing space brewing equipment, with a planned launch date later in 2025. For more CNN news and newsletters create an account at CNN.com Show comments
State vectors are defined with respect to some frame of reference, usually but not always an inertial reference frame. One of the more popular reference frames for the state vectors of bodies moving near Earth is the Earth-centered inertial (ECI) system defined as follows: [1]: 23 The origin is Earth's center of mass;
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