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Vector in relativity
special relativity, a four-vector (or 4-vector, sometimes Lorentz vector) is an element of a four-dimensional vector space object with four components, which
Four-vector
Analogue of velocity in four-dimensional spacetime
particular in special relativity and general relativity, a four-velocity is a four-vector in four-dimensional spacetime that represents the relativistic counterpart
Four-velocity
4D relativistic energy and momentum
spacetime. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime. The contravariant four-momentum of a particle
Four-momentum
Relativistic vector field
An electromagnetic four-potential is a relativistic vector function from which the electromagnetic field can be derived. It combines both an electric
Electromagnetic four-potential
Electromagnetic_four-potential
Physical quantity that is a vector
the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity
Vector_quantity
4D analogue of electric current density
as vector current, it is used in the context of four-dimensional spacetime, rather than separating time from three-dimensional space. It is a four-vector
Four-current
Vector describing a wave; often its propagation direction
a wave four-vector can be defined, combining the (angular) wave vector and (angular) frequency. The terms wave vector and angular wave vector have distinct
Wave_vector
Broad concept generalizing scalars in mathematics and physics
In mathematics and physics, a vector is a generalization of a single number. It may denote a vector quantity, i.e., physical quantity that cannot be expressed
Vector (mathematics and physics)
Vector_(mathematics_and_physics)
Geometric object that has length and direction
physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude
Euclidean_vector
Mathematical description of spacetime used in relativity
to form a four-vector. The 3-space electric field, E, combines with the 3-space magnetic field, B, to create a tensor in the four-vector formalism. This
Minkowski_spacetime
Ways of writing certain laws of physics
electromagnetic four-potential is a covariant four-vector containing the electric potential (also called the scalar potential) ϕ and magnetic vector potential
Covariant formulation of classical electromagnetism
Covariant_formulation_of_classical_electromagnetism
Four-vector analogue of the gradient operation
In differential geometry, the four-gradient (or 4-gradient) ∂ {\displaystyle {\boldsymbol {\partial }}} is the four-vector analogue of the gradient ∇ →
Four-gradient
Family of linear transformations
transformation matrix is universal for all four-vectors, not just 4-dimensional spacetime coordinates. If A is any four-vector, then in tensor index notation A
Lorentz_transformation
Line integral of the electric field
potential and the magnetic vector potential. The electric potential and the magnetic vector potential together form a four-vector, so that the two kinds of
Electric_potential
Four-vector that is analogous to classical acceleration
four-acceleration is a four-vector (vector in four-dimensional spacetime) that is analogous to classical acceleration (a three-dimensional vector, see
Four-acceleration
Vector representing the position of a point with respect to a fixed origin
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.
Position_(geometry)
Model of optics describing light as geometric rays
perpendicular to the light's wavefronts (and is therefore collinear with the wave vector). A slightly more rigorous definition of a light ray follows from Fermat's
Geometrical_optics
Property of a mass in motion
object. It is a vector quantity, possessing a magnitude and a direction. If m is an object's mass and v is its velocity (also a vector quantity), then
Momentum
For instance, many times the time-based terms are placed first in the four-vectors, with the spatial terms following. Also, sometimes η is replaced with
List of relativistic equations
List_of_relativistic_equations
Topics referred to by the same term
An element of a k-dimensional vector space, especially a four-vector used in relativity to mean a quantity related to four-dimensional spacetime This disambiguation
K-vector
British electronic music producer (1969–2026)
Kraftwerk and Depeche Mode. As Vector Lovers, Wheeler released several singles and EPs, as well as four albums. Early Vector Lovers' releases were through
Vector_Lovers
Index of articles associated with the same name
In mathematics, vector multiplication may refer to one of several operations between two (or more) vectors. It may concern any of the following articles:
Vector_multiplication
4-dimensional analogue of force used in theories of relativity
of relativity, four-force is a four-vector that replaces the classical force. The four-force is defined as the rate of change in the four-momentum of a
Four-force
Physical acceleration experienced by an object
momentarily at rest, the proper acceleration 3-vector, combined with a zero time-component, yields the object's four-acceleration, which makes proper-acceleration's
Proper_acceleration
Scalar-valued bilinear function
example of a bilinear form that is not an inner product would be the four-vector product. The definition of a bilinear form can be extended to include
Bilinear_form
Millennium Prize Problem
four self-adjoint operators, P j , j = 0 , 1 , 2 , 3 {\displaystyle P_{j},j=0,1,2,3} , which transform under the homogeneous group as a four-vector,
Yang–Mills existence and mass gap
Yang–Mills_existence_and_mass_gap
Axiomatization of quantum field theory
Poincaré group (the inhomogeneous Lorentz group). Thus, a is a real Lorentz four-vector representing the change of spacetime origin x ↦ x − a, where x is in
Wightman_axioms
Theory of interwoven space and time by Albert Einstein
appear anywhere. A four dimensional space has four-dimensional vectors, or "four-vectors". The simplest example of a four-vector is the position of an
Special_relativity
Concept in relativistic physics
of the Lorentz group, these quantities are built out of scalars, four-vectors, four-tensors, and spinors. In particular, a Lorentz covariant scalar (e
Lorentz_covariance
Quantity in electromagnetism
In classical electromagnetism, magnetic vector potential (often denoted A) is the vector quantity defined so that its curl is equal to the magnetic field
Magnetic_vector_potential
Four-vector
The four-frequency of a massless particle, such as a photon, is a four-vector defined by N a = ( ν , ν n ^ ) {\displaystyle N^{a}=\left(\nu ,\nu {\hat
Four-frequency
Sports car produced from 1990 to 1993, based on the Vector W2
The Vector W8 is a sports car produced by American automobile manufacturer Vector Aeromotive Corporation from 1989 to 1993. It was designed by company
Vector_W8
Principle in theoretical physics
hypothesized that such symmetry should apply to the four-vectors of special relativity, that is, to the four-vector space coordinates X = X μ := ( X 0 , X 1 ,
Born_reciprocity
Algebraic structure in linear algebra
operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. Real vector spaces and complex vector spaces
Vector_space
Submachine gun
The KRISS Vector is a submachine gun developed by the American company KRISS USA, formerly Transformational Defense Industries (TDI). Civilian variants
KRISS_Vector
Multivariate derivative (mathematics)
In vector calculus, the gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued
Gradient
Situation or occurrence located at a specific point in space and time
which the event occurs. These four coordinates ( x → , t ) {\displaystyle ({\vec {x}},t)} together form a four-vector associated to the event. One of
Event_(relativity)
Vector used in astronomy
In classical mechanics, the Laplace–Runge–Lenz vector (LRL vector) is a vector used chiefly to describe the shape and orientation of the orbit of one
Laplace–Runge–Lenz_vector
Quantum field giving rise to gluons
In theoretical particle physics, the gluon field is a four-vector field characterizing the propagation of gluons in the strong interaction between quarks
Gluon_field
Computer graphics images defined by points, lines and curves
Vector graphics are a form of computer graphics in which visual images are created directly from geometric shapes defined on a Cartesian plane, such as
Vector_graphics
Creation of particle-antiparticle pair from a neutral boson
properties can be derived through the kinematics of the interaction. Using four vector notation, the conservation of energy–momentum before and after the interaction
Pair_production
Instructions for the x86 microprocessors
has a book on the topic of: X86 Assembly/AVX, AVX2, FMA3, FMA4 Advanced Vector Extensions (AVX, also known as Gesher New Instructions and then Sandy Bridge
Advanced_Vector_Extensions
Case in parallel computing
specialized supercomputers, typically have vector operations that simultaneously perform operations such as the following four additions (via SIMD or SPMD hardware):
Automatic_vectorization
Theory of motion and forces for objects close to the speed of light
is two vectors (one of these, the conventional angular momentum, being an axial vector). The relativistic four-velocity, that is the four-vector representing
Relativistic_mechanics
Computer processor which works on arrays of several numbers at once
one-dimensional arrays of data called vectors. When integrated as a hardware component the vector processor is often called a vector processing unit (VPU). This
Vector_processor
Abbreviation in the fields of special and general relativity
listed next. In special relativity, the vector basis can be restricted to being orthonormal, in which case all four-tensors transform under Lorentz transformations
Four-tensor
Nonlinear force experienced by a charged particle
slightly more general fields, the starting point is the exact equations, in four-vector notation: m d u μ d τ = R e [ f μ ] = R e [ f ^ μ ( x , u ) e − i k ν
Ponderomotive_force
Set of methods for supervised statistical learning
In machine learning, a support vector machine (SVM) or support vector network is a supervised max-margin model with associated learning algorithms that
Support_vector_machine
Mid-engine sports car produced by Vector Aeromotive as a successor to the W8
The Vector M12 is a sports car manufactured by Vector Aeromotive under parent company Megatech, and was the first car produced after the hostile takeover
Vector_M12
Use of coordinates for representing vectors
Vector notation In mathematics and physics, vector notation is a commonly used notation for representing vectors, which may be Euclidean vectors, or more
Vector_notation
Angular momentum in special and general relativity
coordinates combine into the four-position, and energy and momentum combine into the four-momentum. The components of these four-vectors depend on the frame of
Relativistic_angular_momentum
Hypothetical particle dual to the photon
singularity is to include a second four-vector potential, called dual photon, in addition to the usual four-vector potential, photon. Additionally, it
Dual_photon
1985 supercomputer model
The Cray-2 is a supercomputer with four vector processors made by Cray Research starting in 1985. At 1.9 GFLOPS peak performance, it was the fastest machine
Cray-2
Classical statement of gravity as force
{r_{2}-r_{1}} }{|\mathbf {r_{2}-r_{1}} |}}} is the unit vector from body 1 to body 2. It can be seen that the vector form of the equation is the same as the scalar
Newton's law of universal gravitation
Newton's_law_of_universal_gravitation
Type of conserved current
In particle physics, the axial current, also denoted the pseudo-vector or chiral current, is the conserved current associated to the chiral symmetry or
Axial_current
Measure of directional electromagnetic energy flux
In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area, per unit time) or
Poynting_vector
Quantum mechanical waves describing matter
approaches zero (rest) the de Broglie wavelength approaches infinity. Using four-vectors, the de Broglie relations form a single equation: P = ℏ K , {\displaystyle
Matter_wave
Hypothetical superpartner to the graviton
gravitino field is conventionally written as ψμα with μ = 0, 1, 2, 3 a four-vector index and α = 1, 2 a spinor index. For μ = 0 one would get negative norm
Gravitino
Vector of length one
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase
Unit_vector
Class of subatomic particle
particle that contributes to the phenomenon of mass via the Higgs mechanism Four vector bosons (spin = 1) that act as force carriers. These are the gauge bosons:
Boson
from the previous generations. It was a parallel vector processor and supported one to four vector processors. In 1994, the S-3000 family was complemented
HITAC_S-3000
Number of vectors in any basis of the vector space
In mathematics, the dimension of a vector space V is the cardinality (i.e., the number of vectors) of a basis of V over its base field. It is sometimes
Dimension_(vector_space)
Relativistic equation relating total energy to mass and momentum
(divided by c) and momentum are two components of a Minkowski four-vector, namely the four-momentum: P = ( E c , p ) {\displaystyle \mathbf {P} =\left({\frac
Energy–momentum_relation
Type of potential in electrodynamics
}=h_{\mu \nu }-{\frac {1}{2}}\eta _{\mu \nu }h} plays the role of the four-vector potential, the harmonic gauge h ~ μ ν , μ = 0 {\displaystyle {\tilde
Retarded_potential
Mathematical operation in linear algebra
represented by capital letters in bold, e.g. A; vectors in lowercase bold, e.g. a; and entries of vectors and matrices are italic (they are numbers from
Matrix_multiplication
1968 physics-related discovery
'} is the string constant, k i {\displaystyle k_{i}} are the tachyon four-vectors, g o {\displaystyle g_{o}} is the open string theory coupling constant
Veneziano_amplitude
Formulas about vectors in three-dimensional Euclidean space
The following are important identities in vector algebra. Identities that only involve the magnitude of a vector ‖ A ‖ {\displaystyle \|\mathbf {A} \|} and
Vector_algebra_relations
Theoretical physics phenomenon
scenario, there are two equivalent ways to transform four-vectors from A to B: Rotate the original four-vector x μ ′ = x μ R ( θ ) {\displaystyle x'_{\mu }=x_{\mu
Wigner_rotation
Type of audio synthesis
Wavestation. Vector synthesis provides movement in a sound by providing dynamic cross-fading between (usually) four sound sources. The four sound sources
Vector_synthesis
Facet of general relativity
momentum. The ADM energy and momentum together form an energy–momentum four-vector P μ = ( E A D M , P A D M i ) {\displaystyle P^{\mu }=(E_{\mathrm {ADM}
Mass_in_general_relativity
Facet of ballistics and aeronautics
Thrust vectoring, also known as thrust vector control (TVC), is the ability of an aircraft, rocket or other vehicle to manipulate the direction of the
Thrust_vectoring
Physical quantity that changes sign with improper rotation
physics and mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under continuous rigid transformations such as rotations
Pseudovector
Concept in air navigation
dead reckoning navigation. The wind triangle is a vector diagram, with three vectors. The air vector represents the motion of the aircraft through the
Wind_triangle
Mathematical decision making technique similar to Analytic Hierarchy Process
weighting each idealized limit vector by the weight of its control criterion and adding the resulting vectors for each of the four merits: Benefits (B), Opportunities
Analytic_network_process
Physical concept
the system, taking into account fields, gives an integral vector that is not a four-vector. The stress-energy tensor of electromagnetic field is part
Electromagnetic_mass
Concepts from linear algebra
algebra, an eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is a (nonzero) vector that has its direction unchanged (or reversed) by a given linear
Eigenvalues_and_eigenvectors
Biotechnology for gene delivery
A viral vector is a modified virus designed to deliver genetic material into cells. This process can be performed inside an organism or in cell culture
Viral_vector
Construct in theoretical physics
a cylinder. It is the little group, or stabilizer subgroup, of null four-vectors in Minkowski space.) Specifically, the translation generators Y1, Y2
Group_contraction
Quantum field theory equations
applications of the TBDE to QED, the two particles interact by way of four-vector potentials derived from the field theoretic electromagnetic interactions
Two-body_Dirac_equations
{\displaystyle \partial _{\mu }F^{\mu \nu }=4\pi j^{\nu },} transforms as a four-vector, that is, under the (1/2, 1/2) representation of the O(1,3) group. The
Covariance_group
German software company
Vector Informatik develops software tools and components for networking of electronic systems based on the serial bus systems CAN, LIN, FlexRay, MOST,
Vector_Informatik
Influence that can change motion of an object
magnitude and direction of a force are both important, force is a vector quantity (force vector). The SI unit of force is the newton (N), and force is often
Force
Rate of change of velocity
Like velocity, acceleration has a magnitude and a direction, making it a vector quantity. The SI unit for acceleration is metre per second squared (m⋅s−2
Acceleration
all four-vectors and tensors containing physical quantities transform from one frame of reference to another. The prime examples of such four-vectors are
Derivations of the Lorentz transformations
Derivations_of_the_Lorentz_transformations
Length in a vector space
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance
Norm_(mathematics)
Topological structure of 4D spacetime
relativity. This physical theory models gravitation as the curvature of a four dimensional Lorentzian manifold (a spacetime) and the concepts of topology
Spacetime_topology
Concept in special relativity
τ 2 {\displaystyle d^{2}=x^{2}+y^{2}+z^{2}+\tau ^{2}} Similarly its four vector may then be written as ( x 0 , x 1 , x 2 , x 3 ) {\displaystyle (x_{0}
Imaginary_time
Circulation density in a vector field
In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional
Curl_(mathematics)
Sum of directed areas in exterior algebra
mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors. Considering a scalar
Bivector
Properties underlying modern physics
in this article are as follows. Boldface indicates vectors, four vectors, matrices, and vectorial operators, while quantum states use bra–ket notation
Symmetry_in_quantum_mechanics
Principle in particle physics
charge invariance is embedded in the charge density – current density four-vector j μ = ( c ρ , j → ) {\displaystyle j^{\mu }=\left(c\rho ,{\vec {j}}\right)}
Charge_invariance
Relationship between relativity and pre-quantum electromagnetism
combine into the four-vector J α = ( c ρ , J x , J y , J z ) {\displaystyle J^{\alpha }=\left(c\rho ,J_{x},J_{y},J_{z}\right)} called the four-current. Using
Classical electromagnetism and special relativity
Classical_electromagnetism_and_special_relativity
Four-dimensional number system
its vector part. Even though every quaternion can be viewed as a vector in a four-dimensional vector space, it is common to refer to the vector part
Quaternion
Military light utility vehicle
The VECTOR (Versatile Expeditionary Commando Tactial Off Road) is a Dutch light all-terrain tactical vehicle, designed and developed by defence contractor
Versatile Expeditionary Commando Tactial Off Road
Versatile_Expeditionary_Commando_Tactial_Off_Road
in which the four-dimensions of Minkowski spacetime are commonly represented: as a four-vector with 4 real coordinates, as a four-vector with 3 real and
Formulations of special relativity
Formulations_of_special_relativity
Spacetime modeled by four pointwise-orthonormal vector fields
frame field (also called a tetrad or vierbein) is a set of four pointwise-orthonormal vector fields, one timelike and three spacelike, defined on a Lorentzian
Frame fields in general relativity
Frame_fields_in_general_relativity
Elements of a field, e.g. real numbers, in the context of linear algebra
define a vector space through the operation of scalar multiplication: a vector (denoted v) multiplied by a scalar (denoted a) produces another vector (av)
Scalar_(mathematics)
Geometric space with six dimensions
Every rotation in four dimensions can be achieved by multiplying by a pair of unit quaternions, one before and one after the vector. These quaternion
Six-dimensional_space
Vector on which a quadratic form is zero
In mathematics, given a vector space X with an associated quadratic form q, written (X, q), a null vector or isotropic vector is a non-zero element x
Null_vector
Analogies between Maxwell's and Einstein's field equations
transformations, the GEM equations are not. The fact that ρg and jg do not form a four-vector is the basis of this difference. Instead they are merely a part of the
Gravitoelectromagnetism
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