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Minkowski space, the Glossary

In physics, Minkowski space (or Minkowski spacetime) is the main mathematical description of spacetime in the absence of gravitation.^[1]

158 relations: Abuse of notation, Academic Press, Affine space, Albert Einstein, Alfred A. Knopf, Angular velocity, Annals of Mathematics, Basis (linear algebra), Bilinear form, Birkhäuser, Born coordinates, Cambridge University Press, Cartesian coordinate system, Cauchy–Schwarz inequality, Classical group, Conformal field theory, Cornelius Lanczos, Cotangent space, Course of Theoretical Physics, Covariance and contravariance of vectors, Curvature, Curved space, Curvilinear coordinates, De Sitter space, Definite quadratic form, Degenerate bilinear form, Differential form, Differential geometry, Directional derivative, Dot product, Dual basis, Dual space, Einstein field equations, Einstein notation, Electromagnetic tensor, Electron, Euclidean distance, Euclidean group, Euclidean space, Event (relativity), Exterior derivative, Flat (geometry), Four-dimensional space, Four-momentum, Four-vector, Four-velocity, Galilean transformation, General relativity, German language, Gravity, ... Expand index (108 more) »
Hermann Minkowski
Lorentzian manifolds
Minkowski spacetime

Abuse of notation

In mathematics, abuse of notation occurs when an author uses a mathematical notation in a way that is not entirely formally correct, but which might help simplify the exposition or suggest the correct intuition (while possibly minimizing errors and confusion at the same time).

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Academic Press

Academic Press (AP) is an academic book publisher founded in 1941.

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Affine space

In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments.

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Albert Einstein

Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who is widely held as one of the most influential scientists. Best known for developing the theory of relativity, Einstein also made important contributions to quantum mechanics. His mass–energy equivalence formula, which arises from relativity theory, has been called "the world's most famous equation".

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Alfred A. Knopf

Alfred A. Knopf, Inc. is an American publishing house that was founded by Blanche Knopf and Alfred A. Knopf Sr. in 1915.

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Angular velocity

In physics, angular velocity (symbol or \vec, the lowercase Greek letter omega), also known as angular frequency vector,(UP1) is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction.

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Annals of Mathematics

The Annals of Mathematics is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study.

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Basis (linear algebra)

In mathematics, a set of vectors in a vector space is called a basis (bases) if every element of may be written in a unique way as a finite linear combination of elements of.

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Bilinear form

In mathematics, a bilinear form is a bilinear map on a vector space (the elements of which are called vectors) over a field K (the elements of which are called scalars).

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Birkhäuser

Birkhäuser was a Swiss publisher founded in 1879 by Emil Birkhäuser.

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Born coordinates

In relativistic physics, the Born coordinate chart is a coordinate chart for (part of) Minkowski spacetime, the flat spacetime of special relativity.

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Cambridge University Press

Cambridge University Press is the university press of the University of Cambridge.

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Cartesian coordinate system

In geometry, a Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system.

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Cauchy–Schwarz inequality

The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) is an upper bound on the inner product between two vectors in an inner product space in terms of the product of the vector norms.

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Classical group

In mathematics, the classical groups are defined as the special linear groups over the reals \mathbb, the complex numbers \mathbb and the quaternions \mathbb together with special automorphism groups of symmetric or skew-symmetric bilinear forms and Hermitian or skew-Hermitian sesquilinear forms defined on real, complex and quaternionic finite-dimensional vector spaces.

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Conformal field theory

A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations.

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Cornelius Lanczos

Cornelius (Cornel) Lanczos (Lánczos Kornél,; born as Kornél Lőwy, until 1906: Löwy (Lőwy) Kornél; February 2, 1893 – June 25, 1974) was a Hungarian-Jewish, Hungarian-American and later Hungarian-Irish mathematician and physicist.

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Cotangent space

In differential geometry, the cotangent space is a vector space associated with a point x on a smooth (or differentiable) manifold \mathcal M; one can define a cotangent space for every point on a smooth manifold.

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Course of Theoretical Physics

The Course of Theoretical Physics is a ten-volume series of books covering theoretical physics that was initiated by Lev Landau and written in collaboration with his student Evgeny Lifshitz starting in the late 1930s.

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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.

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Curvature

In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane.

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Curved space

Curved space often refers to a spatial geometry which is not "flat", where a flat space has zero curvature, as described by Euclidean geometry.

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Curvilinear coordinates

In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved.

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De Sitter space

In mathematical physics, n-dimensional de Sitter space (often denoted dSn) is a maximally symmetric Lorentzian manifold with constant positive scalar curvature. Minkowski space and de Sitter space are exact solutions in general relativity and Minkowski spacetime.

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Definite quadratic form

In mathematics, a definite quadratic form is a quadratic form over some real vector space that has the same sign (always positive or always negative) for every non-zero vector of.

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Degenerate bilinear form

In mathematics, specifically linear algebra, a degenerate bilinear form on a vector space V is a bilinear form such that the map from V to V∗ (the dual space of V&hairsp) given by is not an isomorphism.

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Differential form

In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds.

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Differential geometry

Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.

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Directional derivative

A directional derivative is a concept in multivariable calculus that measures the rate at which a function changes in a particular direction at a given point.

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Dot product

In mathematics, the dot product or scalar productThe term scalar product means literally "product with a scalar as a result".

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Dual basis

In linear algebra, given a vector space V with a basis B of vectors indexed by an index set I (the cardinality of I is the dimension of V), the dual set of B is a set B^* of vectors in the dual space V^* with the same index set I such that B and B^* form a biorthogonal system.

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Dual space

In mathematics, any vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear forms on V, together with the vector space structure of pointwise addition and scalar multiplication by constants.

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Einstein field equations

In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. Minkowski space and Einstein field equations are equations of physics.

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Einstein notation

In mathematics, especially the usage of linear algebra in mathematical physics and differential geometry, Einstein notation (also known as the Einstein summation convention or Einstein summation notation) is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving brevity.

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Electromagnetic tensor

In electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field in spacetime. Minkowski space and electromagnetic tensor are Minkowski spacetime.

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Electron

The electron (or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge.

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Euclidean distance

In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them.

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Euclidean group

In mathematics, a Euclidean group is the group of (Euclidean) isometries of a Euclidean space \mathbb^n; that is, the transformations of that space that preserve the Euclidean distance between any two points (also called Euclidean transformations).

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Euclidean space

Euclidean space is the fundamental space of geometry, intended to represent physical space.

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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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Exterior derivative

On a differentiable manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree.

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Flat (geometry)

In geometry, a flat or affine subspace is a subset of an affine space that is itself an affine space (of equal or lower dimension).

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Four-dimensional space

Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Minkowski space and Four-dimensional space are special relativity.

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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.

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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. Minkowski space and four-vector are Minkowski spacetime.

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Four-velocity

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.

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Galilean transformation

In physics, a Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics.

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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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German language

German (Standard High German: Deutsch) is a West Germanic language in the Indo-European language family, mainly spoken in Western and Central Europe. It is the most widely spoken and official or co-official language in Germany, Austria, Switzerland, Liechtenstein, and the Italian province of South Tyrol.

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Gravity

In physics, gravity is a fundamental interaction which causes mutual attraction between all things that have mass.

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Hendrik Lorentz

Hendrik Antoon Lorentz (18 July 1853 – 4 February 1928) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect.

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Henri Poincaré

Jules Henri Poincaré (29 April 185417 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.

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Hermann Minkowski

Hermann Minkowski (22 June 1864 – 12 January 1909) was a mathematician and professor at the University of Königsberg, the University of Zürich, and the University of Göttingen, described variously as German, Polish, or Lithuanian-German, or Russian.

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Hyperbolic geometry

In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry.

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Hyperbolic orthogonality

In geometry, the relation of hyperbolic orthogonality between two lines separated by the asymptotes of a hyperbola is a concept used in special relativity to define simultaneous events. Minkowski space and hyperbolic orthogonality are Minkowski spacetime.

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Hyperbolic quaternion

In abstract algebra, the algebra of hyperbolic quaternions is a nonassociative algebra over the real numbers with elements of the form where the squares of i, j, and k are +1 and distinct elements of multiply with the anti-commutative property. Minkowski space and hyperbolic quaternion are Minkowski spacetime.

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Hyperbolic space

In mathematics, hyperbolic space of dimension n is the unique simply connected, n-dimensional Riemannian manifold of constant sectional curvature equal to −1.

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Hyperboloid

In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal axes.

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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. Minkowski space and hyperboloid model are Minkowski spacetime.

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Hyperplane

In geometry, a hyperplane is a generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension.

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Hyperspace

In science fiction, hyperspace (also known as nulspace, subspace, overspace, jumpspace and similar terms) is a concept relating to higher dimensions as well as parallel universes and a faster-than-light (FTL) method of interstellar travel.

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Imaginary unit

The imaginary unit or unit imaginary number is a solution to the quadratic equation Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition and multiplication.

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Inclusion map

In mathematics, if A is a subset of B, then the inclusion map is the function \iota that sends each element x of A to x, treated as an element of B: \iota: A\rightarrow B, \qquad \iota(x).

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Induced metric

In mathematics and theoretical physics, the induced metric is the metric tensor defined on a submanifold that is induced from the metric tensor on a manifold into which the submanifold is embedded, through the pullback.

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Inertial frame of reference

In classical physics and special relativity, an inertial frame of reference (also called inertial space, or Galilean reference frame) is a stationary or uniformly moving frame of reference.

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Inner product space

In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product.

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Introduction to the mathematics of general relativity

The mathematics of general relativity is complicated.

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Invariant (physics)

In theoretical physics, an invariant is an observable of a physical system which remains unchanged under some transformation.

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Isometry group

In mathematics, the isometry group of a metric space is the set of all bijective isometries (that is, bijective, distance-preserving maps) from the metric space onto itself, with the function composition as group operation.

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Jacobian matrix and determinant

In vector calculus, the Jacobian matrix of a vector-valued function of several variables is the matrix of all its first-order partial derivatives.

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Johns Hopkins University Press

Johns Hopkins University Press (also referred to as JHU Press or JHUP) is the publishing division of Johns Hopkins University.

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Kernel (linear algebra)

In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the part of the domain which is mapped to the zero vector of the co-domain; the kernel is always a linear subspace of the domain.

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Length contraction

Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. Minkowski space and length contraction are special relativity.

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Light cone

In special and general relativity, a light cone (or "null cone") is the path that a flash of light, emanating from a single event (localized to a single point in space and a single moment in time) and traveling in all directions, would take through spacetime. Minkowski space and light cone are Lorentzian manifolds.

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Light-cone coordinates

In physics, particularly special relativity, light-cone coordinates, introduced by Paul Dirac and also known as Dirac coordinates, are a special coordinate system where two coordinate axes combine both space and time, while all the others are spatial.

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Line element

In geometry, the line element or length element can be informally thought of as a line segment associated with an infinitesimal displacement vector in a metric space. Minkowski space and line element are special relativity.

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Linear form

In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear mapIn some texts the roles are reversed and vectors are defined as linear maps from covectors to scalars from a vector space to its field of scalars (often, the real numbers or the complex numbers).

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Linear independence

In the theory of vector spaces, a set of vectors is said to be if there exists no nontrivial linear combination of the vectors that equals the zero vector.

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Local reference frame

In theoretical physics, a local reference frame (local frame) refers to a coordinate system or frame of reference that is only expected to function over a small region or a restricted region of space or spacetime.

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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. Minkowski space and Lorentz transformation are special relativity.

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M-theory

M-theory is a theory in physics that unifies all consistent versions of superstring theory.

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Magnetic moment

In electromagnetism, the magnetic moment or magnetic dipole moment is the combination of strength and orientation of a magnet or other object or system that exerts a magnetic field.

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Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

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Matrix (mathematics)

In mathematics, a matrix (matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object.

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Matter wave

Matter waves are a central part of the theory of quantum mechanics, being half of wave–particle duality.

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Maxwell's equations

Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, electric and magnetic circuits. Minkowski space and Maxwell's equations are equations of physics.

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McGraw Hill Education

McGraw Hill is an American publishing company for educational content, software, and services for pre-K through postgraduate education.

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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 space

In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points.

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Metric tensor

In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows defining distances and angles there.

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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 distance

The Minkowski distance or Minkowski metric is a metric in a normed vector space which can be considered as a generalization of both the Euclidean distance and the Manhattan distance. Minkowski space and Minkowski distance are Hermann Minkowski.

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Minkowski plane

In mathematics, a Minkowski plane (named after Hermann Minkowski) is one of the Benz planes (the others being Möbius plane and Laguerre plane).

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Nash embedding theorems

The Nash embedding theorems (or imbedding theorems), named after John Forbes Nash Jr., state that every Riemannian manifold can be isometrically embedded into some Euclidean space.

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Non-Euclidean geometry

In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry.

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Null vector

In mathematics, given a vector space X with an associated quadratic form q, written, a null vector or isotropic vector is a non-zero element x of X for which.

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One-form (differential geometry)

In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section of the cotangent bundle.

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Orientation (geometry)

In geometry, the orientation, attitude, bearing, direction, or angular position of an object – such as a line, plane or rigid body – is part of the description of how it is placed in the space it occupies.

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Orthogonality

In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity.

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Orthogonality (mathematics)

In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity to the linear algebra of bilinear forms.

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Orthonormal basis

In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other.

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Orthonormality

In linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal unit vectors.

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Oxford University Press

Oxford University Press (OUP) is the publishing house of the University of Oxford.

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Parallel transport

In differential geometry, parallel transport (or parallel translation) is a way of transporting geometrical data along smooth curves in a manifold.

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Partially ordered set

In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other.

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Pauli–Lubanski pseudovector

In physics, the Pauli–Lubanski pseudovector is an operator defined from the momentum and angular momentum, used in the quantum-relativistic description of angular momentum.

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PhilPapers

PhilPapers is an interactive academic database of journal articles in philosophy.

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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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Poincaré disk model

In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which all points are inside the unit disk, and straight lines are either circular arcs contained within the disk that are orthogonal to the unit circle or diameters of the unit circle.

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Poincaré group

The Poincaré group, named after Henri Poincaré (1906), was first defined by Hermann Minkowski (1908) as the isometry group of Minkowski spacetime.

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Poincaré half-plane model

In non-Euclidean geometry, the Poincaré half-plane model is the upper half-plane, denoted below as H.

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Polarization identity

In linear algebra, a branch of mathematics, the polarization identity is any one of a family of formulas that express the inner product of two vectors in terms of the norm of a normed vector space.

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Postulates of special relativity

Albert Einstein derived the theory of special relativity in 1905, from principle now called the postulates of special relativity. Minkowski space and postulates of special relativity are special relativity.

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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. Minkowski space and proper time are Minkowski spacetime.

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Pseudo-Euclidean space

In mathematics and theoretical physics, a pseudo-Euclidean space of signature is a finite-dimensional ''n''-space together with a non-degenerate quadratic form. Minkowski space and pseudo-Euclidean space are Lorentzian manifolds.

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Pseudo-Riemannian manifold

In mathematical physics, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. Minkowski space and pseudo-Riemannian manifold are Lorentzian manifolds.

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Pseudoscalar

In linear algebra, a pseudoscalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion while a true scalar does not.

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Pullback (differential geometry)

Let \phi:M\to N be a smooth map between smooth manifolds M and N. Then there is an associated linear map from the space of 1-forms on N (the linear space of sections of the cotangent bundle) to the space of 1-forms on M. This linear map is known as the pullback (by \phi), and is frequently denoted by \phi^*.

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Pushforward (differential)

In differential geometry, pushforward is a linear approximation of smooth maps (formulating manifold) on tangent spaces.

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Pythagorean theorem

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.

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Quadratic form

In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial).

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Raising and lowering indices

In mathematics and mathematical physics, raising and lowering indices are operations on tensors which change their type.

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Random House Webster's Unabridged Dictionary

Random House Webster's Unabridged Dictionary is a large American dictionary, first published in 1966 as The Random House Dictionary of the English Language: The Unabridged Edition.

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Real number

In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.

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Reflection (mathematics)

In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection.

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Relativistic mechanics

In physics, relativistic mechanics refers to mechanics compatible with special relativity (SR) and general relativity (GR).

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Relativity of simultaneity

In physics, the relativity of simultaneity is the concept that distant simultaneity – whether two spatially separated events occur at the same time – is not absolute, but depends on the observer's reference frame. Minkowski space and relativity of simultaneity are special relativity.

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Riemannian geometry

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an inner product on the tangent space at each point that varies smoothly from point to point).

See Minkowski space and Riemannian geometry

Riemannian manifold

In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature are defined.

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Riesz representation theorem

The Riesz representation theorem, sometimes called the Riesz–Fréchet representation theorem after Frigyes Riesz and Maurice René Fréchet, establishes an important connection between a Hilbert space and its continuous dual space.

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Rotation matrix

In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space.

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Space

Space is a three-dimensional continuum containing positions and directions. Minkowski space and Space are geometry.

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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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Spacetime diagram

A spacetime diagram is a graphical illustration of locations in space at various times, especially in the special theory of relativity. Minkowski space and spacetime diagram are geometry and special relativity.

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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. Minkowski space and speed of light are special relativity.

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Sphere

A sphere (from Greek) is a geometrical object that is a three-dimensional analogue to a two-dimensional circle.

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Spin (physics)

Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms.

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Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Stereographic projection

In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the pole or center of projection), onto a plane (the projection plane) perpendicular to the diameter through the point.

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Steven Weinberg

Steven Weinberg (May 3, 1933 – July 23, 2021) was an American theoretical physicist and Nobel laureate in physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles.

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String theory

In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings.

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Submanifold

In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S \rightarrow M satisfies certain properties.

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Sylvester's law of inertia

Sylvester's law of inertia is a theorem in matrix algebra about certain properties of the coefficient matrix of a real quadratic form that remain invariant under a change of basis.

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Symmetric bilinear form

In mathematics, a symmetric bilinear form on a vector space is a bilinear map from two copies of the vector space to the field of scalars such that the order of the two vectors does not affect the value of the map.

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Tangent space

In mathematics, the tangent space of a manifold is a generalization of to curves in two-dimensional space and to surfaces in three-dimensional space in higher dimensions.

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Tensor

In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space.

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Tensor product

In mathematics, the tensor product V \otimes W of two vector spaces and (over the same field) is a vector space to which is associated a bilinear map V\times W \rightarrow V\otimes W that maps a pair (v,w),\ v\in V, w\in W to an element of V \otimes W denoted.

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The Monist

The Monist: An International Quarterly Journal of General Philosophical Inquiry is a quarterly peer-reviewed academic journal in the field of philosophy.

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Time

Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, and into the future.

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Time dilation

Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them (special relativity), or a difference in gravitational potential between their locations (general relativity). Minkowski space and time dilation are special relativity.

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Transitive relation

In mathematics, a binary relation on a set is transitive if, for all elements,, in, whenever relates to and to, then also relates to.

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Translation (geometry)

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction.

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Transpose of a linear map

In linear algebra, the transpose of a linear map between two vector spaces, defined over the same field, is an induced map between the dual spaces of the two vector spaces.

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Unit vector

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.

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Vector field

In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space \mathbb^n.

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Vector space

In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', can be added together and multiplied ("scaled") by numbers called ''scalars''.

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World line

The world line (or worldline) of an object is the path that an object traces in 4-dimensional spacetime. Minkowski space and world line are Minkowski spacetime.

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References

[1] https://en.wikipedia.org/wiki/Minkowski_space

Also known as 4-dimensional spacetime, Flat spacetime, Four-dimensional spacetime, Geometry of special relativity, Lightlike, Lightlike separation, Lm distance, Locally flat spacetime, Minkowski Metric, Minkowski inner product, Minkowski metric tensor, Minkowski metrics, Minkowski signature, Minkowski space-time, Minkowski spacetime, Minkowski tensor, Minkowskian, Minkowskian geometry, Minowski space, Null vector (Minkowski space), One timelike dimension, Spacelike vector, Timelike vector.

, Hendrik Lorentz, Henri Poincaré, Hermann Minkowski, Hyperbolic geometry, Hyperbolic orthogonality, Hyperbolic quaternion, Hyperbolic space, Hyperboloid, Hyperboloid model, Hyperplane, Hyperspace, Imaginary unit, Inclusion map, Induced metric, Inertial frame of reference, Inner product space, Introduction to the mathematics of general relativity, Invariant (physics), Isometry group, Jacobian matrix and determinant, Johns Hopkins University Press, Kernel (linear algebra), Length contraction, Light cone, Light-cone coordinates, Line element, Linear form, Linear independence, Local reference frame, Lorentz transformation, M-theory, Magnetic moment, Manifold, Matrix (mathematics), Matter wave, Maxwell's equations, McGraw Hill Education, Metric signature, Metric space, Metric tensor, Metric tensor (general relativity), Minkowski distance, Minkowski plane, Nash embedding theorems, Non-Euclidean geometry, Null vector, One-form (differential geometry), Orientation (geometry), Orthogonality, Orthogonality (mathematics), Orthonormal basis, Orthonormality, Oxford University Press, Parallel transport, Partially ordered set, Pauli–Lubanski pseudovector, PhilPapers, Physics, Poincaré disk model, Poincaré group, Poincaré half-plane model, Polarization identity, Postulates of special relativity, Proper time, Pseudo-Euclidean space, Pseudo-Riemannian manifold, Pseudoscalar, Pullback (differential geometry), Pushforward (differential), Pythagorean theorem, Quadratic form, Raising and lowering indices, Random House Webster's Unabridged Dictionary, Real number, Reflection (mathematics), Relativistic mechanics, Relativity of simultaneity, Riemannian geometry, Riemannian manifold, Riesz representation theorem, Rotation matrix, Space, Spacetime, Spacetime diagram, Special relativity, Speed of light, Sphere, Spin (physics), Springer Science+Business Media, Stereographic projection, Steven Weinberg, String theory, Submanifold, Sylvester's law of inertia, Symmetric bilinear form, Tangent space, Tensor, Tensor product, The Monist, Time, Time dilation, Transitive relation, Translation (geometry), Transpose of a linear map, Unit vector, Vector field, Vector space, World line.

Minkowski space, the Glossary

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