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- ..., replacing rest mass with rest mass density <math>\mu_{0}</math> in terms of rest volume <math>V_{0}</math> produces the mass four-current <math>J^{\mu} ...[[#Weyl (1918-19)]]. Four-momentum density (c) played a role in the papers of [[#Einstein (1912-14)]] and [[#Lewis and Wilson (1912)]]. The material four ...17 KB (2,616 words) - 21:44, 29 October 2023
- ...ur-velocity and mass is four-momentum. It can be represented as a function of three-velocity <math>\mathbf{u}</math>: ...)'', velocity ''v=(p',x',y',z')'', acceleration ''(p”,x”,y”,z”)'' in terms of four components, obtaining the following relations:<ref group=M>Killing (18 ...13 KB (1,893 words) - 07:21, 25 May 2024
- ...s [[w:proper time]] <math>\tau</math>. It can be represented as a function of three-velocity <math>\mathbf{u}</math> and three-acceleration <math>\mathbf ...)'', velocity ''v=(p',x',y',z')'', acceleration ''(p”,x”,y”,z”)'' in terms of four components, obtaining the following relations:<ref group=M>Killing (18 ...11 KB (1,741 words) - 07:56, 19 May 2023
- ==History of three-acceleration transformation== The [[w:Acceleration (special relativity)|Lorentz transformation of three-acceleration]] is given by ...6 KB (969 words) - 09:08, 28 April 2024
- The [[w:Four-current]] is the four-dimensional analogue of the [[w:electric current density]] ...e electromagnetic potential <math>A^{\beta}</math>, or the four-divergence of the electromagnetic tensor <math>F^{\alpha\beta}</math>: ...20 KB (3,004 words) - 07:56, 19 May 2023
- ...be related to the four-current <math>J^\beta</math> or the four-divergence of the [[w:electromagnetic tensor]] <math>F^{\alpha\beta}</math> representing ..., [[#Silberstein (1911)]], and embedded in a generally covariant treatment of electromagnetism by [[#Kottler (1912)]] and [[#Einstein (1916)]]. ...22 KB (3,258 words) - 07:57, 19 May 2023
- ...he rate of change in the [[w:four-momentum]] <math>P^{\mu}=mU^{\mu}</math> of a particle with respect to the particle's [[w:proper time]] <math>\tau</mat :(b) function of three-force <math>\mathbf{f}</math> ...32 KB (5,229 words) - 07:56, 19 May 2023
- :(a) the rate of change in the four-momentum <math>P^{\mu}=mU^{\mu}</math> with respect to p :(b) function of three-force <math>\mathbf{f}</math> ...30 KB (4,879 words) - 07:57, 19 May 2023
- ==History of time dilation== [[w:Time dilation]] in special relativity is given by ...22 KB (3,441 words) - 07:39, 1 August 2024
- ...thbf{E}\cdot\mathbf{B}</math>. It can be expressed as the exterior product of the [[w:four-gradient]] and the [[w:electromagnetic four-potential]], produ ...presenting the inhomogeneous [[w:Maxwell equations]], while the divergence of <math>G^{\alpha\beta}</math> represents the homogeneous equations: ...49 KB (7,489 words) - 07:26, 27 October 2023
- {{center|Date of article creation: {{date|2023-11-09}}; Last edit: {{date|{{REVISIONYEAR}}-{ ...''human beings'', and that [[#Weyl (1918)]] explicitly discussed the aging of ''twins''. ...20 KB (3,093 words) - 23:33, 23 March 2024
- ...(2, C) is isomorphic to both the Lorentz group and the group of isometries of hyperbolic space. ...ion to surfaces of second degree and the invariance of the unit sphere. In relativity, ({{equationNote|6a}}) was first employed by [[#Herglotz1|Herglotz (1909/10 ...58 KB (8,301 words) - 21:43, 19 December 2024
- ...spatial rotations in terms of angle <math>\phi</math> and boosts in terms of hyperbolic angle <math>\eta</math>) is as follows:<ref>Synge (1972), pp. 13 with the special case of a Lorentz boost in the <math>x_1</math>-direction by setting: ...40 KB (5,928 words) - 08:47, 3 July 2023
- ...>, and <math>\vartheta</math> is equivalent to the Lobachevskian [[w:angle of parallelism]] <math>\Pi(\eta)=2\arctan(e^{-\eta})</math>: ...[[w:contact transformation]] in the plane (Laguerre geometry). In special relativity, it was first used by [[#Plummer|Plummer (1910)]], by [[#Gruner|Gruner (192 ...13 KB (1,835 words) - 21:30, 19 December 2024
- ...tes]], they have the general form (some authors alternatively add a factor of 2 or <math>\sqrt{2}</math>):<ref name=terng>Terng & Uhlenbeck (2000), p. 21 ...cally corresponds to the transformation of one parallelogram to other ones of same area, whose sides touch a hyperbola and both asymptotes. While equatio ...42 KB (6,019 words) - 21:44, 19 December 2024
- The '''history of Lorentz transformations''' comprises the development of [[w:linear map|linear transformations]] forming the [[w:Lorentz group|Loren ...ius group|Möbius group]] or [[w:projective special linear group|projective special linear group]], and the [[w:Spherical wave transformation#Transformation by ...4 KB (542 words) - 09:39, 11 September 2023
- ...iated [[w:bilinear form]] ''b(x,y)'', and the [[w:linear transformation]]s of ''q(x)'' and ''b(x,y)'' into ''q(x′)'' and ''b(x′,y′)'' using the [[w:trans ...tz interval is the invariant relation between axes and conjugate diameters of hyperbolas, illustrating Lorentz transformations between two inertial frame ...104 KB (15,302 words) - 21:20, 19 December 2024
- ...n space]] forming the [[w:orthogonal group]] O(n) if det '''g'''=±1 or the special orthogonal group SO(n) if det '''g'''=+1, the Lorentz interval becomes the ...being related to the dimension of time as well as the explicit formulation of Lorentz transformations with ''n=3'' was given by [[#Minkowski|Minkowski (1 ...17 KB (2,620 words) - 21:38, 19 December 2024
- The case of a Lorentz transformation without spatial rotation is called a [[w:Lorentz b ...[[w:Translation (geometry)|translation]] in the hyperbolic plane in terms of the hyperboloid model) is given by ...56 KB (8,367 words) - 21:40, 19 December 2024
- ...ta</math> the [[w:proper velocity]], <math>u'=c\tanh q</math> the velocity of another object, <math>u=c\tanh(q+\eta)</math> the [[w:velocity-addition for or in terms of <math>ct,x</math> as squeeze mapping in line with [[../Lorentz transformati ...56 KB (8,552 words) - 21:41, 19 December 2024
Page text matches
- The '''history of Lorentz transformations''' comprises the development of [[w:linear map|linear transformations]] forming the [[w:Lorentz group|Loren ...ius group|Möbius group]] or [[w:projective special linear group|projective special linear group]], and the [[w:Spherical wave transformation#Transformation by ...4 KB (542 words) - 09:39, 11 September 2023
- ==History of three-acceleration transformation== The [[w:Acceleration (special relativity)|Lorentz transformation of three-acceleration]] is given by ...6 KB (969 words) - 09:08, 28 April 2024
- ...>, and <math>\vartheta</math> is equivalent to the Lobachevskian [[w:angle of parallelism]] <math>\Pi(\eta)=2\arctan(e^{-\eta})</math>: ...[[w:contact transformation]] in the plane (Laguerre geometry). In special relativity, it was first used by [[#Plummer|Plummer (1910)]], by [[#Gruner|Gruner (192 ...13 KB (1,835 words) - 21:30, 19 December 2024
- ...s [[w:proper time]] <math>\tau</math>. It can be represented as a function of three-velocity <math>\mathbf{u}</math> and three-acceleration <math>\mathbf ...)'', velocity ''v=(p',x',y',z')'', acceleration ''(p”,x”,y”,z”)'' in terms of four components, obtaining the following relations:<ref group=M>Killing (18 ...11 KB (1,741 words) - 07:56, 19 May 2023
- ...ur-velocity and mass is four-momentum. It can be represented as a function of three-velocity <math>\mathbf{u}</math>: ...)'', velocity ''v=(p',x',y',z')'', acceleration ''(p”,x”,y”,z”)'' in terms of four components, obtaining the following relations:<ref group=M>Killing (18 ...13 KB (1,893 words) - 07:21, 25 May 2024
- ...n space]] forming the [[w:orthogonal group]] O(n) if det '''g'''=±1 or the special orthogonal group SO(n) if det '''g'''=+1, the Lorentz interval becomes the ...being related to the dimension of time as well as the explicit formulation of Lorentz transformations with ''n=3'' was given by [[#Minkowski|Minkowski (1 ...17 KB (2,620 words) - 21:38, 19 December 2024
- ..., replacing rest mass with rest mass density <math>\mu_{0}</math> in terms of rest volume <math>V_{0}</math> produces the mass four-current <math>J^{\mu} ...[[#Weyl (1918-19)]]. Four-momentum density (c) played a role in the papers of [[#Einstein (1912-14)]] and [[#Lewis and Wilson (1912)]]. The material four ...17 KB (2,616 words) - 21:44, 29 October 2023
- The [[w:Four-current]] is the four-dimensional analogue of the [[w:electric current density]] ...e electromagnetic potential <math>A^{\beta}</math>, or the four-divergence of the electromagnetic tensor <math>F^{\alpha\beta}</math>: ...20 KB (3,004 words) - 07:56, 19 May 2023
- ...ntz transformation (general)#math_Q1|E:general transformation '''(Q1)''']] of any quadratic form into itself can also be given using ''arbitrary'' parame ...1771) and Rodrigues (1840)]], which can be interpreted as the coefficients of [[w:quaternion]]s. Setting ''d=1'', the equations have the form: ...27 KB (3,991 words) - 21:27, 19 December 2024
- ...g^{\alpha\beta}</math> is the reciprocal of the metric tensor. In the case of vanishing pressure it becomes the [[w:dust solution]]: ...density in that fluid, providing an alternative way to formulate equations of motion. ...19 KB (3,094 words) - 07:58, 19 May 2023
- ...be related to the four-current <math>J^\beta</math> or the four-divergence of the [[w:electromagnetic tensor]] <math>F^{\alpha\beta}</math> representing ..., [[#Silberstein (1911)]], and embedded in a generally covariant treatment of electromagnetism by [[#Kottler (1912)]] and [[#Einstein (1916)]]. ...22 KB (3,258 words) - 07:57, 19 May 2023
- ...the skeletons may be [[#Study notes|filled out]] by participants (see page history) and new resources may be spun off. ...ules/LIGHTCONE/index.html The Light Cone - an illuminating introduction to relativity] ...7 KB (1,009 words) - 02:15, 20 January 2025
- ==History of time dilation== [[w:Time dilation]] in special relativity is given by ...22 KB (3,441 words) - 07:39, 1 August 2024
- ...he rate of change in the [[w:four-momentum]] <math>P^{\mu}=mU^{\mu}</math> of a particle with respect to the particle's [[w:proper time]] <math>\tau</mat :(b) function of three-force <math>\mathbf{f}</math> ...32 KB (5,229 words) - 07:56, 19 May 2023
- :(a) the rate of change in the four-momentum <math>P^{\mu}=mU^{\mu}</math> with respect to p :(b) function of three-force <math>\mathbf{f}</math> ...30 KB (4,879 words) - 07:57, 19 May 2023
- ...roup Con(1,p) of spacetime [[w:conformal transformation]]s in terms of [[w:special conformal transformation]]s and inversions producing the relation ...the group Con(1,3) is the most general one leaving invariant the equations of Maxwell's electrodynamics. ...40 KB (5,683 words) - 12:59, 19 August 2023
- ...[[w:stress–energy tensor]] due to the [[w:electromagnetic field]] in terms of the electromagnetic field tensor <math>F^{\mu\nu}</math>, Poynting vector < ...by relating the six components of the spatial part <math>X_{x}\dots</math> of the stress-energy tensor to the “relative stresses” <math>X_{x}^{\prime}\do ...44 KB (7,420 words) - 07:58, 19 May 2023
- ...(2, C) is isomorphic to both the Lorentz group and the group of isometries of hyperbolic space. ...ion to surfaces of second degree and the invariance of the unit sphere. In relativity, ({{equationNote|6a}}) was first employed by [[#Herglotz1|Herglotz (1909/10 ...58 KB (8,301 words) - 21:43, 19 December 2024
- {{center|Date of article creation: {{date|2023-11-09}}; Last edit: {{date|{{REVISIONYEAR}}-{ ...''human beings'', and that [[#Weyl (1918)]] explicitly discussed the aging of ''twins''. ...20 KB (3,093 words) - 23:33, 23 March 2024
- The case of a Lorentz transformation without spatial rotation is called a [[w:Lorentz b ...[[w:Translation (geometry)|translation]] in the hyperbolic plane in terms of the hyperboloid model) is given by ...56 KB (8,367 words) - 21:40, 19 December 2024