@prefix rdf: . @prefix dbr: . @prefix owl: . dbr:Wigner_rotation rdf:type owl:Thing . @prefix dbo: . dbr:Wigner_rotation rdf:type dbo:MusicalWork . @prefix rdfs: . dbr:Wigner_rotation rdfs:label "Wigner rotation"@en ; rdfs:comment "In 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 a boost and a rotation. This rotation is called Thomas rotation, Thomas\u2013Wigner rotation or Wigner rotation. The rotation was discovered and proved by Ludwik Silberstein in his 1914 book 'Relativity', rediscovered by Llewellyn Thomas in 1926, and rederived by Wigner in 1939. Wigner acknowledged Silberstein. If a sequence of non-collinear boosts returns an object to its initial velocity, then the sequence of Wigner rotations can combine to produce a net rotation called the Thomas precession."@en ; owl:differentFrom dbr:Thomas_precession . @prefix foaf: . dbr:Wigner_rotation foaf:depiction , , , , , , , . @prefix dcterms: . @prefix dbc: . dbr:Wigner_rotation dcterms:subject dbc:Coordinate_systems , dbc:Mathematical_physics , dbc:Theory_of_relativity , dbc:Theoretical_physics , dbc:Special_relativity ; dbo:wikiPageID 24293838 ; dbo:wikiPageRevisionID 1114517950 ; dbo:wikiPageWikiLink dbr:Rotation_matrix , , dbr:Orthogonal_matrix , dbr:Addison-Wesley_Publishing_Company , dbr:Axis-angle_representation , dbr:Binary_operation , dbr:Cambridge_University_Press , dbc:Coordinate_systems , , dbr:Llewellyn_Thomas , dbr:Matrix_similarity , , dbr:Herbert_Goldstein , dbr:Velocity_addition_formula , dbr:Journal_of_Mathematical_Physics , dbr:Cross_product , dbr:Velocity-addition_formula , dbr:Right-hand_rule , , dbr:Rapidity , dbr:Rotational_motion , dbr:Thomas_precession , dbr:Lobachevsky_geometry , dbr:Representation_theory_of_the_Lorentz_group , dbr:Bargmann-Michel-Telegdi_equation , dbr:Commutation_relation , dbr:Hyperbolic_triangle , dbr:Cyclic_permutation , dbr:Twin_paradox , dbr:Theoretical_physics , dbr:Column_vector , dbr:Nonlinear , , , , dbr:Matrix_transpose , dbr:Group_commutator , dbc:Mathematical_physics , dbr:Block_matrix , , dbr:Parallelogram_law , dbr:Commutator , dbc:Theoretical_physics , dbr:Symmetric_matrix , dbr:Lorentz_factor , dbc:Theory_of_relativity , dbr:Euclidean_plane , , dbr:Unit_vector , dbr:Collinear , dbr:Ludwik_Silberstein , dbr:Lorentz_boost , , , dbr:Active_transformation , , dbr:Lorentz_group , dbr:Annals_of_Mathematics , dbr:Commutative_property , , dbr:Associative_property , dbr:Lorentz_transformation , dbr:Spacetime_diagram , dbc:Special_relativity , dbr:Vector_addition ; dbo:wikiPageExternalLink , , , . @prefix ns8: . dbr:Wigner_rotation dbo:wikiPageExternalLink ns8:On , . @prefix ns9: . dbr:Wigner_rotation dbo:wikiPageExternalLink ns9:e7a88a5d0617b5adbefcedccb5e52a12725de6bf . @prefix ns10: . dbr:Wigner_rotation dbo:wikiPageExternalLink ns10:quantumtheoryoff00stev , . @prefix wikidata: . dbr:Wigner_rotation owl:sameAs wikidata:Q25303636 , . @prefix yago-res: . dbr:Wigner_rotation owl:sameAs yago-res:Wigner_rotation , . @prefix dbp: . @prefix dbt: . dbr:Wigner_rotation dbp:wikiPageUsesTemplate dbt:Citation , dbt:Reflist , dbt:Harvtxt , dbt:Mvar , dbt:Spacetime , dbt:Main , , dbt:Relativity , dbt:Quote , dbt:Cite_web , dbt:Math , dbt:Cite_journal , dbt:Cite_book , dbt:Distinguish , dbt:EquationRef , dbt:NumBlk , dbt:Abs ; dbo:thumbnail ; dbp:text "The decomposition process described can be carried through on the product of two pure Lorentz transformations to obtain explicitly the rotation of the coordinate axes resulting from the two successive \"boosts\". In general, the algebra involved is quite forbidding, more than enough, usually, to discourage any actual demonstration of the rotation matrix"@en ; dbo:abstract "In 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 a boost and a rotation. This rotation is called Thomas rotation, Thomas\u2013Wigner rotation or Wigner rotation. The rotation was discovered and proved by Ludwik Silberstein in his 1914 book 'Relativity', rediscovered by Llewellyn Thomas in 1926, and rederived by Wigner in 1939. Wigner acknowledged Silberstein. If a sequence of non-collinear boosts returns an object to its initial velocity, then the sequence of Wigner rotations can combine to produce a net rotation called the Thomas precession. There are still ongoing discussions about the correct form of equations for the Thomas rotation in different reference systems with contradicting results. Goldstein: The spatial rotation resulting from the successive application of two non-collinear Lorentz transformations have been declared every bit as paradoxical as the more frequently discussed apparent violations of common sense, such as the twin paradox. Einstein's principle of velocity reciprocity (EPVR) reads We postulate that the relation between the coordinates of the two systems is linear. Then the inverse transformation is also linear and the complete non-preference of the one or the other system demands that the transformation shall be identical with the original one, except for a change of v to \u2212v With less careful interpretation, the EPVR is seemingly violated in some models. There is, of course, no true paradox present. Let it be u the velocity in which the lab reference frame moves respect an object called A and let it be v the velocity in which another object called B is moving, measured from the lab reference frame. If u and v are not aligned the relative velocities of these two bodies will not be opposite, that is since there is a rotation between them The velocity that A will measure on B will be: The Lorentz factor for the velocities that either A sees on B or B sees on A: The angle of rotation can be calculated in two ways: Or: And the axis of rotation is:"@en . @prefix gold: . dbr:Wigner_rotation gold:hypernym dbr:Composition . @prefix prov: . dbr:Wigner_rotation prov:wasDerivedFrom . @prefix xsd: . dbr:Wigner_rotation dbo:wikiPageLength "42760"^^xsd:nonNegativeInteger . @prefix wikipedia-en: . dbr:Wigner_rotation foaf:isPrimaryTopicOf wikipedia-en:Wigner_rotation .