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Family of linear transformations
In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that
Lorentz_transformation
There are many ways to derive the Lorentz transformations using a variety of physical principles, ranging from Maxwell's equations to Einstein's postulates
Derivations of the Lorentz transformations
Derivations_of_the_Lorentz_transformations
Development of linear transformations forming the Lorentz group
of Lorentz transformations comprises the development of linear transformations forming the Lorentz group or Poincaré group preserving the Lorentz interval
History of Lorentz transformations
History_of_Lorentz_transformations
Lie group of Lorentz transformations
In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for
Lorentz_group
Theory of interwoven space and time by Albert Einstein
two sets of coordinates in relative motion the Lorentz transformation replaces the Galilean transformation of Newtonian mechanics. Other effects include
Special_relativity
Linear transformation of spacetime coordinates
biquaternion Lorentz transformation is formulation of the Lorentz transformation using biquaternions. In special relativity, a Lorentz transformation is a real
Biquaternion Lorentz transformation
Biquaternion_Lorentz_transformation
Dutch physicist (1853–1928)
the Zeeman effect. He derived the Lorentz transformation of the special theory of relativity, as well as the Lorentz force, which describes the force acting
Hendrik_Lorentz
Mathematical model combining space and time
universe). However, space and time took on new meanings with the Lorentz transformation and special theory of relativity. In 1908, Hermann Minkowski presented
Spacetime
Physics principle that simultaneity depends on choice of reference frame
derive the time transformation for all orders in v/c, i.e., the complete Lorentz transformation. Poincaré obtained the full transformation earlier in 1905
Relativity_of_simultaneity
Rational function of the form (az + b)/(cz + d)
itself correspond to Lorentz transformations, by which Herglotz was able to classify the one-parameter Lorentz transformations into loxodromic, elliptic
Möbius_transformation
1887 investigation of the speed of light
extended by Joseph Larmor (1897), Lorentz (1904) and Henri Poincaré (1905), who developed the complete Lorentz transformation including time dilation in order
Michelson–Morley_experiment
Quantity in relativistic physics
equations in special relativity, and it arises in derivations of the Lorentz transformations. The name originates from its earlier appearance in Lorentzian
Lorentz_factor
Contraction of length in the direction of propagation in Minkowski space
own rest frame. It is also known as Lorentz contraction or Lorentz–FitzGerald contraction (after Hendrik Lorentz and George Francis FitzGerald) and is
Length_contraction
Mathematical transformation
dimension as in Minkowski space, so spherical wave transformations are connected to the Lorentz transformation of special relativity, and it turns out that
Spherical_wave_transformation
Expression in the theory of relativity
theory of physics, a Lorentz scalar is a scalar expression whose value is invariant under any Lorentz transformation. A Lorentz scalar may be generated
Lorentz_scalar
Graph of space and time in special relativity
particular Minkowski diagram illustrates the result of a Lorentz transformation. The Lorentz transformation relates two inertial frames of reference, where an
Spacetime_diagram
Group of flat spacetime symmetries
boosts, transformations connecting two uniformly moving bodies (K). The last two symmetries, J and K, together make the Lorentz group (see also Lorentz invariance);
Poincaré_group
French mathematician, physicist and engineer (1854–1912)
invariance of laws of physics under different transformations, and was the first to present the Lorentz transformations in their modern symmetrical form. Poincaré
Henri_Poincaré
Theoretical physics phenomenon
theoretical physics, the composition of two non-collinear Lorentz boosts results in a Lorentz transformation that is not a pure boost but is the composition of
Wigner_rotation
Method of teaching special relativity
relativity begin with the concept of velocity and a derivation of the Lorentz transformation. Other concepts such as time dilation, length contraction, the relativity
Bondi_k-calculus
Set of spacetime events, light-connected to a given event
partial differential equation Hypercone Light-cone coordinates Lorentz transformation Method of characteristics Minkowski diagram Monge cone Wave equation
Light_cone
Concept in physics and mathematics
the Lorentz transformations and Poincaré transformations; conversely, the group contraction in the classical limit c → ∞ of Poincaré transformations yields
Galilean_transformation
Vector in relativity
sometimes Lorentz vector) is an element of a four-dimensional vector space object with four components, which transform under Lorentz transformations with
Four-vector
Irish theoretical physicist (1857–1942)
Parallel to the development of Lorentz ether theory, Larmor published an approximation to the Lorentz transformations in the Philosophical Transactions
Joseph_Larmor
Topics referred to by the same term
known as the Lorentz distribution, Lorentzian function, or Cauchy–Lorentz distribution Lorentz lineshape (spectroscopy) Lorentz transformation Lorentzian
Lorentzian
to the direction of motion are unaffected by length contraction. Lorentz transformation x ′ = γ ( x − v t ) {\displaystyle x'=\gamma \left(x-vt\right)}
List of relativistic equations
List_of_relativistic_equations
Measured time difference as explained by relativity theory
as deduced by Einstein (1905) from the Lorentz transformation, when the source is running slow by the Lorentz factor. Hasselkamp, Mondry, and Scharmann
Time_dilation
Mathematical description of fermions
{\displaystyle \mathrm {SO} (1,3)} group (the Lorentz group without parity transformations). Under parity transformation the Weyl spinors transform into each other
Dirac_spinor
Force acting on charged particles in electric and magnetic fields
In electromagnetism, the Lorentz force is the force exerted on a charged particle by electric and magnetic fields. It determines how charged particles
Lorentz_force
Concept in physics
relativity (see History of Lorentz transformations and Lorentz ether theory). A more modern example of deriving the Lorentz transformation from electrodynamics
Postulates of special relativity
Postulates_of_special_relativity
Relativistic correction
is Lorentz-boosted relative to it, and a third boosted relative to the second, but non-colinear with the first boost, then the Lorentz transformation between
Thomas_precession
Concept in relativistic physics
particular, a Lorentz covariant scalar (e.g., the space-time interval) remains the same under Lorentz transformations and is said to be a Lorentz invariant
Lorentz_covariance
Relativistic quantum mechanical wave equation
{\text{SL}}(2,\mathbb {C} )} , which is a double cover of the Lorentz group. Under a Lorentz transformation, spacetime coordinates transform under the vector representation
Dirac_equation
Vector describing a wave; often its propagation direction
{u}}\right)} Taking the Lorentz transformation of the four-wavevector is one way to derive the relativistic Doppler effect. The Lorentz matrix is defined as
Wave_vector
Measure of relativistic velocity
corresponding velocity-addition formula. As we can see from the Lorentz transformation above, the Lorentz factor identifies with cosh w γ = 1 1 − v 2 / c 2 = 1
Rapidity
Relation of space and time in relativity theory
diameters." On this principle of relativity, he then wrote the Lorentz transformation in the modern form using rapidity. Edwin Bidwell Wilson and Gilbert
Hyperbolic_orthogonality
Defunct theory of electromagnetism
principle of relativity) Lorentz tried in 1899 and 1904 to expand his theory to all orders in v/c by introducing the Lorentz transformation. In addition, he assumed
Lorentz_ether_theory
Concept in relativity theory
the start and finish clocks. This is a matter of convention. The Lorentz transformation is defined such that the one-way speed of light will be measured
One-way_speed_of_light
Two interrelated physics theories by Albert Einstein
relativity is the replacement of the Galilean transformations of classical mechanics by the Lorentz transformations. (See Maxwell's equations of electromagnetism
Theory_of_relativity
Thought experiment in special relativity
mathematical terms, a Lorentz transformation can be separated into the product of a spatial rotation and a "proper" Lorentz transformation which involves no
Ladder_paradox
Speed of electromagnetic waves
accordingly ("local time"), which led to the formulation of the Lorentz transformation. Based on Lorentz's aether theory, Henri Poincaré (1900) showed that this
Speed_of_light
Representation of the symmetry group of spacetime in special relativity
The Lorentz group is a Lie group of symmetries of the spacetime of special relativity. This group can be realized as a collection of matrices, linear
Representation theory of the Lorentz group
Representation_theory_of_the_Lorentz_group
Mathematical description of spacetime used in relativity
dimension, the further transformations of translations in time and Lorentz boosts are added, and the group of all these transformations is called the Poincaré
Minkowski_spacetime
Hypothetical device in theoretical physics
velocity v, the time of arrival at B is given according to the Lorentz transformation (c is the speed of light): Δ t ′ = t 1 ′ − t 0 ′ = t 1 − v B / c
Tachyonic_antitelephone
Thought experiment in physics
revised the transformation of forces in moving reference frames to be consistent with Lorentz invariance. The details of these transformations are discussed
Moving magnet and conductor problem
Moving_magnet_and_conductor_problem
Algebra of 4D spacetime
x^{2}\\x^{1}+ix^{2}&&x^{0}-x^{3}\end{pmatrix}}} The restricted Lorentz transformations that preserve the direction of time and include rotations and boosts
Algebra_of_physical_space
correct Lorentz's preliminary transformation formulas, resulting in an exact set of equations that are now called the Lorentz transformations. A little
History_of_special_relativity
Relationship between relativity and pre-quantum electromagnetism
particular the electric and magnetic fields, are altered under a Lorentz transformation from one inertial frame of reference to another. It sheds light
Classical electromagnetism and special relativity
Classical_electromagnetism_and_special_relativity
Distinction between meanings of Euclidean space transformations
terms active transformation and passive transformation were first introduced in 1957 by Valentine Bargmann for describing Lorentz transformations in special
Active and passive transformation
Active_and_passive_transformation
Physics principle
Hendrik Lorentz discovered that Maxwell's equations were invariant only under a particular change of variables, the Lorentz transformations. In their
Principle_of_relativity
Physics concept expressed as E = mc²
of energy articles Electromagnetic mass Index of wave articles Lorentz transformation Length contraction Outline of energy Relativity of simultaneity
Mass–energy_equivalence
German-born theoretical physicist (1879–1955)
experimental equipment was donated by Geertruida de Haas-Lorentz, wife of de Haas and daughter of Lorentz, to the Ampère Museum in Lyon France in 1961 where
Albert_Einstein
Issue in science history
Alfred Bucherer had the relativity principle. Lorentz and Larmor had most of the Lorentz transformations, Poincaré had them all. Cohn and Bucherer rejected
Relativity_priority_dispute
Properties underlying modern physics
operators, and relates them to the Lie groups, and relativistic transformations in the Lorentz group and Poincaré group. The notational conventions used in
Symmetry_in_quantum_mechanics
Intrinsic quantum property of particles
under general Lorentz transformations, but we would immediately discover a major obstacle. Unlike SO(3), the group of Lorentz transformations SO(3,1) is
Spin_(physics)
Equation used in relativistic physics
can exceed the speed of light. Such formulas apply to successive Lorentz transformations, so they also relate different frames. Accompanying velocity addition
Velocity-addition_formula
Quaternions with complex number coefficients
biquaternion g satisfy g g ∗ = 1. {\displaystyle gg^{*}=1.} Then the Lorentz transformation associated with g is given by T ( q ) = g ∗ q g ¯ . {\displaystyle
Biquaternion
Physical phenomenon in electromagnetic field theory
explained in electromagnetic field theory due to Coulomb's law and Lorentz transformations. After Maxwell proposed the differential equation model of the
Relativistic_electromagnetism
Dual to the Dirac spinor
gamma matrix. The Lorentz group of special relativity is not compact, therefore spinor representations of Lorentz transformations are generally not unitary
Dirac_adjoint
Fundamental quantity in physics
in fact, hold in all frames. In 1875, Hendrik Lorentz (1853–1928) discovered Lorentz transformations, which left Maxwell's equations unchanged, allowing
Time_in_physics
Abstract coordinate system
to describe motion. Thus, Lorentz transformations and Galilean transformations may be viewed as coordinate transformations. An observational frame of
Frame_of_reference
German mathematician and physicist (1850–1919)
scored for violin and oboe. In 1887 Voigt formulated a form of the Lorentz transformation between a rest frame of reference and a frame moving with speed
Woldemar_Voigt
Property of a mass in motion
in two reference frames are related by the Lorentz transformation instead of the Galilean transformation. Consider, for example, one reference frame
Momentum
Fundamental concept of classical mechanics
measurements in another by a simple transformation — the Galilean transformation in Newtonian physics or the Lorentz transformation (combined with a translation)
Inertial_frame_of_reference
Low-velocity approximation of special relativity
possesses its own notion of elapsed time. The Galilean transformations are replaced by Lorentz transformations. In all inertial frames, all laws of physics are
Galilean_invariance
Thought experiment in special relativity
traveler's own perspective. Alternatively, Hans Thirring (1921) used the Lorentz transformation to show that relativity of simultaneity leads to desynchronization
Twin_paradox
Mathematical space used to study hyperbolic geometry
formulation of special relativity as an alternative to the use of Lorentz transformations to represent compositions of velocities (also called boosts – "boosts"
Gyrovector_space
Second order tensor in vector algebra
cross product matrix with a column vector. In special relativity, the Lorentz boost with speed v in the direction of a unit vector n can be expressed
Dyadics
Velocity differential over time, as described in Minkowski spacetime
differentiation of velocity with respect to time. However, because of the Lorentz transformation and time dilation, the concepts of time and distance become more
Acceleration (special relativity)
Acceleration_(special_relativity)
4D relativistic energy and momentum
because it is a Lorentz covariant vector. This means that it is easy to keep track of how it transforms under Lorentz transformations. Calculating the
Four-momentum
Effect in special relativity
appearance of the object at rest as seen by a moving observer. Since Lorentz transformations do not depend on the acceleration, the visual appearance of the
Terrell_rotation
Matrix representing the effect of scattering on a physical system
is said to be free (or non-interacting) if it transforms under Lorentz transformations as a tensor product, or direct product in physics parlance, of
S-matrix
Topics referred to by the same term
Hendrik Lorentz and Ludvig Lorenz Lorentz force, the force exerted on a charged particle in an electromagnetic field Lorentz transformation, the formula
Lorentz_(disambiguation)
Modified form of the Michelson–Morley experiment, testing special relativity
Combining the results of those three experiments, the complete Lorentz transformation can be derived. Improved variants of the Kennedy–Thorndike experiment
Kennedy–Thorndike_experiment
German mathematician and physicist (1864–1909)
isometries (or motions) in hyperbolic space can be related to Lorentz transformations, which included contributions of Wilhelm Killing (1880, 1885),
Hermann_Minkowski
Hypothetical FTL transportation by warping space
With regard to certain specific effects of special relativity, such as Lorentz contraction and time dilation, the Alcubierre metric has some apparently
Alcubierre_drive
Experiments probing the accuracy of special relativity's predictions
experiments conducted before 1904, Lorentz was forced to again expand his theory by introducing the complete Lorentz transformation. Henri Poincaré declared in
Tests_of_special_relativity
Boson with spin equal to zero
fields of spin-zero particles transform like a scalar under Lorentz transformation (i.e. are Lorentz invariant). A pseudoscalar boson is a scalar boson that
Scalar_boson
English mathematician, mathematical physicist (born 1931)
University Press. pp. 581–638. Terrell, James (1959). "Invisibility of the Lorentz Contraction". Physical Review. 116 (4): 1041–1045. Bibcode:1959PhRv..116
Roger_Penrose
Diagram of different points in spacetime
question. Causality Causal structure Conformal cyclic cosmology Weyl transformation Penrose, Roger (15 January 1963). "Asymptotic properties of fields and
Penrose_diagram
Obsolete postulated medium for the propagation of light
resulted in the formulation of the so-called Lorentz transformation by Joseph Larmor (1897, 1900) and Lorentz (1899, 1904), whereby (it was noted by Larmor)
Luminiferous_aether
Extension to the Standard Model
systems differing only by a particle Lorentz transformation. In special relativity, observer Lorentz transformations relate measurements made in reference
Standard-Model_Extension
Field-equations in general relativity
length Proper time Proper acceleration Relativistic mass Formulation Lorentz transformation Textbooks Phenomena Time dilation Mass–energy equivalence (E=mc2)
Einstein_field_equations
Compact astronomical body
few months after Schwarzschild, Johannes Droste, a student of Hendrik Lorentz, independently gave the same solution. At a certain radius from the centre
Black_hole
German mathematician
that work, he obtained the vector Lorentz transformation for arbitrary velocities (see History of Lorentz transformations#Herglotz (1911)). In 1916, he also
Gustav_Herglotz
Topics referred to by the same term
such as a real number Lorentz scalar, a quantity in the theory of relativity which is invariant under a Lorentz transformation Pseudoscalar, a quantity
Scalar
Topics referred to by the same term
mathematical theorems; called "the first artificial intelligence program" Lorentz transformation LT, a type of London bus LT (car), an early Swedish automobile LT
LT
Field theory of scalar fields
theory of scalar fields. A scalar field is invariant under any Lorentz transformation. The only fundamental scalar quantum field that has been observed
Scalar_field_theory
Experiment measuring the speed of light in moving water
however, Lorentz's transformations were strictly ad hoc, their only justification being that they seemed to work. Einstein showed how Lorentz's equations
Fizeau_experiment
Statement based on repeated empirical observations that describes some natural phenomenon
Galilean transformations) is the low-speed limit of special relativity (since the Galilean transformation is the low-speed approximation to the Lorentz transformation)
Scientific_law
Attraction of masses and energy
mechanics be reformulated to use the Lorentz transformation already applicable to light rather than the Galilean transformation adopted by Newton. Special relativity
Gravity
Theory of gravitation as curved spacetime
the Lorentz transformations asymptotic symmetry transformations, there are also additional transformations that are not Lorentz transformations but are
General_relativity
Relativistic wave description of fermions
symmetries are charge conjugation, parity transformation and time reversal; the continuous symmetry is Lorentz invariance. Charge conjugation plays an outsize
Majorana_equation
Lorentz transformation (Poincaré 1905). Sometimes this transformation is called the FitzGerald–Lorentz transformation or even the FitzGerald–Lorentz–Einstein
History of Maxwell's equations
History_of_Maxwell's_equations
Equations describing classical electromagnetism
fields are generated by electric charges and currents. Together with the Lorentz force law, they form the foundation of classical electromagnetism, classical
Maxwell's_equations
the Lorentz transformation (or Lorentz transformations) is named after the Dutch physicist Hendrik Lorentz. It was the result of attempts by Lorentz and
List_of_Dutch_discoveries
Feature of a system that is preserved under some transformation
transformations of spacetime or the way it is mathematically described. For example, both the Galilean invariance of Newtonian mechanics and Lorentz invariance
Symmetry_(physics)
Angular momentum in special and general relativity
four-vectors depend on the frame of reference used, and change under Lorentz transformations to other inertial frames or accelerated frames. Relativistic angular
Relativistic_angular_momentum
Extension of Poincaré spacetime symmetry
namely rotations, spatial translations, time-translations, and Lorentz transformations (also known as boosts). In addition to these symmetries, conformal
Conformal_symmetry
Setting of relativistic physics in geometric algebra
Identifications to express Lorentz transformation formulas in terms of complex quaternions It is easy to put these Lorentz transformation formulas in terms of
Spacetime_algebra
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