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Four-velocity, the Glossary

In physics, in particular in special relativity and general relativity, a four-velocity is a four-vector in four-dimensional spacetimeTechnically, the four-vector should be thought of as residing in the tangent space of a point in spacetime, spacetime itself being modeled as a smooth manifold.^[1]

44 relations: Algebra of physical space, Causal structure, Chain rule, Charge density, Congruence (general relativity), Coordinate time, Covariance and contravariance of vectors, Differentiable manifold, Differential of a function, Event (relativity), Four-acceleration, Four-current, Four-force, Four-gradient, Four-momentum, Four-vector, General relativity, Hyperboloid model, Index notation, Invariant mass, Lorentz factor, Lorentz transformation, Mass in special relativity, Metric signature, Metric tensor (general relativity), Minkowski space, Parametrization (geometry), Physics, Position (geometry), Proper time, Proper velocity, Rapidity, Representation theory of the Lorentz group, Row and column vectors, Spacetime, Special relativity, Speed of light, Tachyon, Tangent space, Theory of relativity, Time dilation, Vector space, Velocity, World line.
Four-vectors

Algebra of physical space

In physics, the algebra of physical space (APS) is the use of the Clifford or geometric algebra Cl3,0(R) of the three-dimensional Euclidean space as a model for (3+1)-dimensional spacetime, representing a point in spacetime via a paravector (3-dimensional vector plus a 1-dimensional scalar).

See Four-velocity and Algebra of physical space

Causal structure

In mathematical physics, the causal structure of a Lorentzian manifold describes the causal relationships between points in the manifold.

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Chain rule

In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions and in terms of the derivatives of and.

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Charge density

In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume.

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Congruence (general relativity)

In general relativity, a congruence (more properly, a congruence of curves) is the set of integral curves of a (nowhere vanishing) vector field in a four-dimensional Lorentzian manifold which is interpreted physically as a model of spacetime.

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Coordinate time

In the theory of relativity, it is convenient to express results in terms of a spacetime coordinate system relative to an implied observer.

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Covariance and contravariance of vectors

In physics, especially in multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities changes with a change of basis.

See Four-velocity and Covariance and contravariance of vectors

Differentiable manifold

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus.

See Four-velocity and Differentiable manifold

Differential of a function

In calculus, the differential represents the principal part of the change in a function y.

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Event (relativity)

In relativity, an event is anything that happens that has a specific time and place in spacetime.

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Four-acceleration

In the theory of relativity, four-acceleration is a four-vector (vector in four-dimensional spacetime) that is analogous to classical acceleration (a three-dimensional vector, see three-acceleration in special relativity). Four-velocity and four-acceleration are four-vectors.

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Four-current

In special and general relativity, the four-current (technically the four-current density) is the four-dimensional analogue of the current density, with units of charge per unit time per unit area. Four-velocity and four-current are four-vectors.

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Four-force

In the special theory of relativity, four-force is a four-vector that replaces the classical force. Four-velocity and four-force are four-vectors.

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Four-gradient

In differential geometry, the four-gradient (or 4-gradient) \boldsymbol is the four-vector analogue of the gradient \vec from vector calculus. Four-velocity and four-gradient are four-vectors.

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Four-momentum

In special relativity, four-momentum (also called momentum–energy or momenergy) is the generalization of the classical three-dimensional momentum to four-dimensional spacetime. Four-velocity and four-momentum are four-vectors.

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Four-vector

In special relativity, a four-vector (or 4-vector, sometimes Lorentz vector) is an object with four components, which transform in a specific way under Lorentz transformations. Four-velocity and four-vector are four-vectors.

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General relativity

General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics.

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Hyperboloid model

In geometry, the hyperboloid model, also known as the Minkowski model after Hermann Minkowski, is a model of n-dimensional hyperbolic geometry in which points are represented by points on the forward sheet S+ of a two-sheeted hyperboloid in (n+1)-dimensional Minkowski space or by the displacement vectors from the origin to those points, and m-planes are represented by the intersections of (m+1)-planes passing through the origin in Minkowski space with S+ or by wedge products of m vectors.

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Index notation

In mathematics and computer programming, index notation is used to specify the elements of an array of numbers.

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Invariant mass

The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system.

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Lorentz factor

The Lorentz factor or Lorentz term (also known as the gamma factor) is a quantity that expresses how much the measurements of time, length, and other physical properties change for an object while that object is moving.

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Lorentz transformation

In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former.

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Mass in special relativity

The word "mass" has two meanings in special relativity: invariant mass (also called rest mass) is an invariant quantity which is the same for all observers in all reference frames, while the relativistic mass is dependent on the velocity of the observer.

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Metric signature

In mathematics, the signature of a metric tensor g (or equivalently, a real quadratic form thought of as a real symmetric bilinear form on a finite-dimensional vector space) is the number (counted with multiplicity) of positive, negative and zero eigenvalues of the real symmetric matrix of the metric tensor with respect to a basis.

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Metric tensor (general relativity)

In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study.

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Minkowski space

In physics, Minkowski space (or Minkowski spacetime) is the main mathematical description of spacetime in the absence of gravitation.

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Parametrization (geometry)

In mathematics, and more specifically in geometry, parametrization (or parameterization; also parameterisation, parametrisation) is the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, defined by an implicit equation.

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Physics

Physics is the natural science of matter, involving the study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force.

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Position (geometry)

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space.

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Proper time

In relativity, proper time (from Latin, meaning own time) along a timelike world line is defined as the time as measured by a clock following that line.

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Proper velocity

In relativity, proper velocity (also known as celerity) w of an object relative to an observer is the ratio between observer-measured displacement vector \textbf and proper time elapsed on the clocks of the traveling object: It is an alternative to ordinary velocity, the distance per unit time where both distance and time are measured by the observer.

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Rapidity

Rapidity is a measure for relativistic velocity.

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Representation theory of the Lorentz group

The Lorentz group is a Lie group of symmetries of the spacetime of special relativity.

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Row and column vectors

In linear algebra, a column vector with elements is an m \times 1 matrix consisting of a single column of entries, for example, \boldsymbol.

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Spacetime

In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.

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Special relativity

In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between space and time.

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Speed of light

The speed of light in vacuum, commonly denoted, is a universal physical constant that is exactly equal to). According to the special theory of relativity, is the upper limit for the speed at which conventional matter or energy (and thus any signal carrying information) can travel through space.

See Four-velocity and Speed of light

References

[1] https://en.wikipedia.org/wiki/Four-velocity

Also known as 4-speed, 4-velocity, Four velocity, Four-speed, Velocity Four-Vector.

Four-velocity, the Glossary

Table of Contents

See also

Four-vectors

References