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theory</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about a simplified presentation of electromagnetism, incorporating special relativity. For a more general article on the relationship between special relativity and electromagnetism, see <a href="/wiki/Classical_electromagnetism_and_special_relativity" title="Classical electromagnetism and special relativity">Classical electromagnetism and special relativity</a>. 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a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">Articles about</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Electromagnetism" title="Electromagnetism">Electromagnetism</a></th></tr><tr><td class="sidebar-image"><span typeof="mw:File/Frameless"><a href="/wiki/File:VFPt_Solenoid_correct2.svg" class="mw-file-description" title="Solenoid"><img alt="Solenoid" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/VFPt_Solenoid_correct2.svg/190px-VFPt_Solenoid_correct2.svg.png" decoding="async" width="190" height="78" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/VFPt_Solenoid_correct2.svg/285px-VFPt_Solenoid_correct2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0d/VFPt_Solenoid_correct2.svg/380px-VFPt_Solenoid_correct2.svg.png 2x" data-file-width="490" data-file-height="200" /></a></span></td></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Electricity" title="Electricity">Electricity</a></li> <li><a href="/wiki/Magnetism" title="Magnetism">Magnetism</a></li> <li><a href="/wiki/Optics" title="Optics">Optics</a></li> <li><a href="/wiki/History_of_electromagnetic_theory" title="History of electromagnetic theory">History</a></li> <li><a href="/wiki/Computational_electromagnetics" title="Computational electromagnetics">Computational</a></li> <li><a href="/wiki/List_of_textbooks_in_electromagnetism" title="List of textbooks in electromagnetism">Textbooks</a></li> <li><a href="/wiki/List_of_electrical_phenomena" title="List of electrical phenomena">Phenomena</a></li></ul></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Electrostatics" title="Electrostatics">Electrostatics</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Charge_density" title="Charge density">Charge density</a></li> <li><a href="/wiki/Electrical_conductor" title="Electrical conductor">Conductor</a></li> <li><a href="/wiki/Coulomb%27s_law" title="Coulomb's law">Coulomb law</a></li> <li><a href="/wiki/Electret" title="Electret">Electret</a></li> <li><a href="/wiki/Electric_charge" title="Electric charge">Electric charge</a></li> <li><a href="/wiki/Electric_dipole_moment" title="Electric dipole moment">Electric dipole</a></li> <li><a href="/wiki/Electric_field" title="Electric field">Electric field</a></li> <li><a href="/wiki/Electric_flux" title="Electric flux">Electric flux</a></li> <li><a href="/wiki/Electric_potential" title="Electric potential">Electric potential</a></li> <li><a href="/wiki/Electrostatic_discharge" title="Electrostatic discharge">Electrostatic discharge</a></li> <li><a href="/wiki/Electrostatic_induction" title="Electrostatic induction">Electrostatic induction</a></li> <li><a href="/wiki/Gauss%27s_law" title="Gauss's law">Gauss law</a></li> <li><a href="/wiki/Insulator_(electricity)" title="Insulator (electricity)">Insulator</a></li> <li><a href="/wiki/Permittivity" title="Permittivity">Permittivity</a></li> <li><a href="/wiki/Polarization_density" title="Polarization density">Polarization</a></li> <li><a href="/wiki/Electric_potential_energy" title="Electric potential energy">Potential energy</a></li> <li><a href="/wiki/Static_electricity" title="Static electricity">Static electricity</a></li> <li><a href="/wiki/Triboelectric_effect" title="Triboelectric effect">Triboelectricity</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Magnetostatics" title="Magnetostatics">Magnetostatics</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Amp%C3%A8re%27s_circuital_law" title="Ampère's circuital law">Ampère law</a></li> <li><a href="/wiki/Biot%E2%80%93Savart_law" title="Biot–Savart law">Biot–Savart law</a></li> <li><a href="/wiki/Gauss%27s_law_for_magnetism" title="Gauss's law for magnetism">Gauss magnetic law</a></li> <li><a href="/wiki/Magnetic_moment" title="Magnetic moment">Magnetic dipole</a></li> <li><a href="/wiki/Magnetic_field" title="Magnetic field">Magnetic field</a></li> <li><a href="/wiki/Magnetic_flux" title="Magnetic flux">Magnetic flux</a></li> <li><a href="/wiki/Magnetic_scalar_potential" title="Magnetic scalar potential">Magnetic scalar potential</a></li> <li><a href="/wiki/Magnetic_vector_potential" title="Magnetic vector potential">Magnetic vector potential</a></li> <li><a href="/wiki/Magnetization" title="Magnetization">Magnetization</a></li> <li><a href="/wiki/Permeability_(electromagnetism)" title="Permeability (electromagnetism)">Permeability</a></li> <li><a href="/wiki/Right-hand_rule#Electromagnetism" title="Right-hand rule">Right-hand rule</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Classical_electromagnetism" title="Classical electromagnetism">Electrodynamics</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Bremsstrahlung" title="Bremsstrahlung">Bremsstrahlung</a></li> <li><a href="/wiki/Cyclotron_radiation" title="Cyclotron radiation">Cyclotron radiation</a></li> <li><a href="/wiki/Displacement_current" title="Displacement current">Displacement current</a></li> <li><a href="/wiki/Eddy_current" title="Eddy current">Eddy current</a></li> <li><a href="/wiki/Electromagnetic_field" title="Electromagnetic field">Electromagnetic field</a></li> <li><a href="/wiki/Electromagnetic_induction" title="Electromagnetic induction">Electromagnetic induction</a></li> <li><a href="/wiki/Electromagnetic_pulse" title="Electromagnetic pulse">Electromagnetic pulse</a></li> <li><a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">Electromagnetic radiation</a></li> <li><a href="/wiki/Faraday%27s_law_of_induction" title="Faraday's law of induction">Faraday law</a></li> <li><a href="/wiki/Jefimenko%27s_equations" title="Jefimenko's equations">Jefimenko equations</a></li> <li><a href="/wiki/Larmor_formula" title="Larmor formula">Larmor formula</a></li> <li><a href="/wiki/Lenz%27s_law" title="Lenz's law">Lenz law</a></li> <li><a href="/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential" title="Liénard–Wiechert potential">Liénard–Wiechert potential</a></li> <li><a href="/wiki/London_equations" title="London equations">London equations</a></li> <li><a href="/wiki/Lorentz_force" title="Lorentz force">Lorentz force</a></li> <li><a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell equations</a></li> <li><a href="/wiki/Maxwell_stress_tensor" title="Maxwell stress tensor">Maxwell tensor</a></li> <li><a href="/wiki/Poynting_vector" title="Poynting vector">Poynting vector</a></li> <li><a href="/wiki/Synchrotron_radiation" title="Synchrotron radiation">Synchrotron radiation</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Electrical_network" title="Electrical network">Electrical network</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Alternating_current" title="Alternating current">Alternating current</a></li> <li><a href="/wiki/Capacitance" title="Capacitance">Capacitance</a></li> <li><a href="/wiki/Current_density" title="Current density">Current density</a></li> <li><a href="/wiki/Direct_current" title="Direct current">Direct current</a></li> <li><a href="/wiki/Electric_current" title="Electric current">Electric current</a></li> <li><a href="/wiki/Electric_power" title="Electric power">Electric power</a></li> <li><a href="/wiki/Electrolysis" title="Electrolysis">Electrolysis</a></li> <li><a href="/wiki/Electromotive_force" title="Electromotive force">Electromotive force</a></li> <li><a href="/wiki/Electrical_impedance" title="Electrical impedance">Impedance</a></li> <li><a href="/wiki/Inductance" title="Inductance">Inductance</a></li> <li><a href="/wiki/Joule_heating" title="Joule heating">Joule heating</a></li> <li><a href="/wiki/Kirchhoff%27s_circuit_laws" title="Kirchhoff's circuit laws">Kirchhoff laws</a></li> <li><a href="/wiki/Network_analysis_(electrical_circuits)" title="Network analysis (electrical circuits)">Network analysis</a></li> <li><a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm law</a></li> <li><a href="/wiki/Series_and_parallel_circuits#Parallel_circuits" title="Series and parallel circuits">Parallel circuit</a></li> <li><a href="/wiki/Electrical_resistance_and_conductance" title="Electrical resistance and conductance">Resistance</a></li> <li><a href="/wiki/Resonator#Electromagnetics" title="Resonator">Resonant cavities</a></li> <li><a href="/wiki/Series_and_parallel_circuits#Series_circuits" title="Series and parallel circuits">Series circuit</a></li> <li><a href="/wiki/Voltage" title="Voltage">Voltage</a></li> <li><a href="/wiki/Watt" title="Watt">Watt</a></li> <li><a href="/wiki/Waveguide_(radio_frequency)" title="Waveguide (radio frequency)">Waveguides</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Magnetic_circuit" title="Magnetic circuit">Magnetic circuit</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/AC_motor" title="AC motor">AC motor</a></li> <li><a href="/wiki/DC_motor" title="DC motor">DC motor</a></li> <li><a href="/wiki/Electric_machine" title="Electric machine">Electric machine</a></li> <li><a href="/wiki/Electric_motor" title="Electric motor">Electric motor</a></li> <li><a href="/wiki/Gyrator%E2%80%93capacitor_model" title="Gyrator–capacitor model">Gyrator–capacitor</a></li> <li><a href="/wiki/Induction_motor" title="Induction motor">Induction motor</a></li> <li><a href="/wiki/Linear_motor" title="Linear motor">Linear motor</a></li> <li><a href="/wiki/Magnetomotive_force" title="Magnetomotive force">Magnetomotive force</a></li> <li><a href="/wiki/Permeance" title="Permeance">Permeance</a></li> <li><a href="/wiki/Magnetic_complex_reluctance" title="Magnetic complex reluctance">Reluctance (complex)</a></li> <li><a href="/wiki/Magnetic_reluctance" title="Magnetic reluctance">Reluctance (real)</a></li> <li><a href="/wiki/Rotor_(electric)" title="Rotor (electric)">Rotor</a></li> <li><a href="/wiki/Stator" title="Stator">Stator</a></li> <li><a href="/wiki/Transformer" title="Transformer">Transformer</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Covariant_formulation_of_classical_electromagnetism" title="Covariant formulation of classical electromagnetism">Covariant formulation</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Electromagnetic_tensor" title="Electromagnetic tensor">Electromagnetic tensor</a></li> <li><a href="/wiki/Classical_electromagnetism_and_special_relativity" title="Classical electromagnetism and special relativity">Electromagnetism and special relativity</a></li> <li><a href="/wiki/Four-current" title="Four-current">Four-current</a></li> <li><a href="/wiki/Electromagnetic_four-potential" title="Electromagnetic four-potential">Four-potential</a></li> <li><a href="/wiki/Mathematical_descriptions_of_the_electromagnetic_field" title="Mathematical descriptions of the electromagnetic field">Mathematical descriptions</a></li> <li><a href="/wiki/Maxwell%27s_equations_in_curved_spacetime" title="Maxwell's equations in curved spacetime">Maxwell equations in curved spacetime</a></li> <li><a class="mw-selflink selflink">Relativistic electromagnetism</a></li> <li><a href="/wiki/Electromagnetic_stress%E2%80%93energy_tensor" title="Electromagnetic stress–energy tensor">Stress–energy tensor</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Andr%C3%A9-Marie_Amp%C3%A8re" title="André-Marie Ampère">Ampère</a></li> <li><a href="/wiki/Jean-Baptiste_Biot" title="Jean-Baptiste Biot">Biot</a></li> <li><a href="/wiki/Charles-Augustin_de_Coulomb" title="Charles-Augustin de Coulomb">Coulomb</a></li> <li><a href="/wiki/Humphry_Davy" title="Humphry Davy">Davy</a></li> <li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/Michael_Faraday" title="Michael Faraday">Faraday</a></li> <li><a href="/wiki/Hippolyte_Fizeau" title="Hippolyte Fizeau">Fizeau</a></li> <li><a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss</a></li> <li><a href="/wiki/Oliver_Heaviside" title="Oliver Heaviside">Heaviside</a></li> <li><a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Helmholtz</a></li> <li><a href="/wiki/Joseph_Henry" title="Joseph Henry">Henry</a></li> <li><a href="/wiki/Heinrich_Hertz" title="Heinrich Hertz">Hertz</a></li> <li><a href="/wiki/John_Hopkinson" title="John Hopkinson">Hopkinson</a></li> <li><a href="/wiki/Oleg_D._Jefimenko" title="Oleg D. Jefimenko">Jefimenko</a></li> <li><a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">Joule</a></li> <li><a href="/wiki/Lord_Kelvin" title="Lord Kelvin">Kelvin</a></li> <li><a href="/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff">Kirchhoff</a></li> <li><a href="/wiki/Joseph_Larmor" title="Joseph Larmor">Larmor</a></li> <li><a href="/wiki/Emil_Lenz" title="Emil Lenz">Lenz</a></li> <li><a href="/wiki/Alfred-Marie_Li%C3%A9nard" title="Alfred-Marie Liénard">Liénard</a></li> <li><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li> <li><a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell</a></li> <li><a href="/wiki/Franz_Ernst_Neumann" title="Franz Ernst Neumann">Neumann</a></li> <li><a href="/wiki/Georg_Ohm" title="Georg Ohm">Ohm</a></li> <li><a href="/wiki/Hans_Christian_%C3%98rsted" title="Hans Christian Ørsted">Ørsted</a></li> <li><a href="/wiki/Sim%C3%A9on_Denis_Poisson" title="Siméon Denis Poisson">Poisson</a></li> <li><a href="/wiki/John_Henry_Poynting" title="John Henry Poynting">Poynting</a></li> <li><a href="/wiki/William_Ritchie_(physicist)" title="William Ritchie (physicist)">Ritchie</a></li> <li><a href="/wiki/F%C3%A9lix_Savart" title="Félix Savart">Savart</a></li> <li><a href="/wiki/George_Singer" title="George Singer">Singer</a></li> <li><a href="/wiki/Charles_Proteus_Steinmetz" title="Charles Proteus Steinmetz">Steinmetz</a></li> <li><a href="/wiki/Nikola_Tesla" title="Nikola Tesla">Tesla</a></li> <li><a href="/wiki/J._J._Thomson" title="J. J. Thomson">Thomson</a></li> <li><a href="/wiki/Alessandro_Volta" title="Alessandro Volta">Volta</a></li> <li><a href="/wiki/Wilhelm_Eduard_Weber" title="Wilhelm Eduard Weber">Weber</a></li> <li><a href="/wiki/Emil_Wiechert" title="Emil Wiechert">Wiechert</a></li></ul></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Electromagnetism" title="Template:Electromagnetism"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Electromagnetism" title="Template talk:Electromagnetism"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Electromagnetism" title="Special:EditPage/Template:Electromagnetism"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Relativistic electromagnetism</b> is a physical phenomenon explained in <a href="/wiki/Electromagnetic_field" title="Electromagnetic field">electromagnetic field</a> theory due to <a href="/wiki/Coulomb%27s_law" title="Coulomb's law">Coulomb's law</a> and <a href="/wiki/Lorentz_transformation" title="Lorentz transformation">Lorentz transformations</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Electromechanics">Electromechanics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativistic_electromagnetism&action=edit&section=1" title="Edit section: Electromechanics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>After Maxwell proposed the <a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">differential equation model</a> of the electromagnetic field in 1873, the mechanism of action of fields came into question, for instance in the <a href="/wiki/Master_class#Kelvin_in_Baltimore" title="Master class">Kelvin's master class</a> held at <a href="/wiki/Johns_Hopkins_University" title="Johns Hopkins University">Johns Hopkins University</a> in 1884 and commemorated a century later.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>The requirement that the equations remain consistent when viewed from various moving observers led to <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a>, a geometric theory of 4-space where intermediation is by light and radiation.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Spacetime" title="Spacetime">spacetime</a> geometry provided a context for technical description of electric technology, especially generators, motors, and lighting at first. The <a href="/wiki/Coulomb_force" class="mw-redirect" title="Coulomb force">Coulomb force</a> was generalized to the <a href="/wiki/Lorentz_force" title="Lorentz force">Lorentz force</a>. For example, with this model <a href="/wiki/Transmission_line" title="Transmission line">transmission lines</a> and <a href="/wiki/Power_grid" class="mw-redirect" title="Power grid">power grids</a> were developed and <a href="/wiki/Radio_frequency" title="Radio frequency">radio frequency</a> communication explored. </p><p>An effort to mount a full-fledged electromechanics on a relativistic basis is seen in the work of <a href="/wiki/Leigh_Page" title="Leigh Page">Leigh Page</a>, from the project outline in 1912<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> to his <a href="/wiki/Textbook" title="Textbook">textbook</a> <i>Electrodynamics</i> (1940)<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The interplay (according to the differential equations) of electric and magnetic field as viewed over moving observers is examined. What is <a href="/wiki/Charge_density" title="Charge density">charge density</a> in <a href="/wiki/Electrostatics" title="Electrostatics">electrostatics</a> becomes <i>proper charge density</i><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> and generates a magnetic field for a moving observer. </p><p>A revival of interest in this method for <a href="/wiki/Education_and_training_of_electrical_and_electronics_engineers" title="Education and training of electrical and electronics engineers">education and training of electrical and electronics engineers</a> broke out in the 1960s after <a href="/wiki/Richard_Feynman" title="Richard Feynman">Richard Feynman</a>'s textbook.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Rosser's book <i>Classical Electromagnetism via Relativity</i> was popular,<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> as was <a href="/wiki/Anthony_French" title="Anthony French">Anthony French</a>'s treatment in his textbook<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> which illustrated diagrammatically the proper charge density. One author proclaimed, "Maxwell — Out of Newton, Coulomb, and Einstein".<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>The use of <a href="/wiki/Retarded_potential" title="Retarded potential">retarded potentials</a> to describe electromagnetic fields from source-charges is an expression of relativistic electromagnetism. </p> <div class="mw-heading mw-heading2"><h2 id="Principle">Principle</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativistic_electromagnetism&action=edit&section=2" title="Edit section: Principle"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The question of how an electric field in one <a href="/wiki/Inertial_frame_of_reference" title="Inertial frame of reference">inertial frame of reference</a> looks in different reference frames moving with respect to the first is crucial to understanding fields created by moving sources. In the special case, the sources that create the field are at rest with respect to one of the reference frames. Given the <a href="/wiki/Electric_field" title="Electric field">electric field</a> in the frame where the sources are at rest, one can ask: what is the electric field in some other frame?<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Knowing the electric field at some point (in space and time) in the rest frame of the sources, and knowing the relative <a href="/wiki/Velocity" title="Velocity">velocity</a> of the two frames provided all the information needed to calculate the electric field at the same point in the other frame. In other words, the electric field in the other frame does not depend on the particular distribution of the source <a href="/wiki/Charge_(physics)" title="Charge (physics)">charges</a>, only on the local value of the electric field in the first frame at that point. Thus, the electric field is a <i>complete</i> representation of the influence of the far-away charges. </p><p>Alternatively, introductory treatments of <a href="/wiki/Magnetism" title="Magnetism">magnetism</a> introduce the <a href="/wiki/Biot%E2%80%93Savart_law" title="Biot–Savart law">Biot–Savart law</a>, which describes the magnetic field associated with an <a href="/wiki/Electric_current" title="Electric current">electric current</a>. An observer at rest with respect to a system of static, free charges will see no magnetic field. However, a moving observer looking at the same set of charges does perceive a current, and thus a magnetic field. That is, the magnetic field is simply the electric field, as seen in a moving coordinate system. </p> <div class="mw-heading mw-heading2"><h2 id="Redundancy">Redundancy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativistic_electromagnetism&action=edit&section=3" title="Edit section: Redundancy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The title of this article is redundant since all mathematical theories of electromagnetism are relativistic. Indeed, as Einstein wrote, "The special theory of relativity ... was simply a systematic development of the electrodynamics of Clerk Maxwell and Lorentz".<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Combination of spatial and temporal variables in Maxwell's theory required admission of a four-manifold. Finite light speed and other constant motion lines were described with <a href="/wiki/Analytic_geometry" title="Analytic geometry">analytic geometry</a>. <a href="/wiki/Orthogonality" title="Orthogonality">Orthogonality</a> of electric and magnetic vector fields in space was extended by <a href="/wiki/Hyperbolic_orthogonality" title="Hyperbolic orthogonality">hyperbolic orthogonality</a> for the temporal factor. </p><p>When <a href="/wiki/Ludwik_Silberstein" title="Ludwik Silberstein">Ludwik Silberstein</a> published his textbook <i>The Theory of Relativity</i> (1914)<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> he related the new geometry to electromagnetism. <a href="/wiki/Faraday%27s_law_of_induction" title="Faraday's law of induction">Faraday's law of induction</a> was suggestive to Einstein when he wrote in 1905 about the "reciprocal electrodynamic action of a magnet and a conductor".<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>Nevertheless, the aspiration, reflected in references for this article, is for an analytic geometry of spacetime and charges providing a deductive route to forces and currents in practice. Such a royal route to electromagnetic understanding may be lacking, but a path has been opened with <a href="/wiki/Differential_geometry" title="Differential geometry">differential geometry</a>: The tangent space at an event in spacetime is a four-dimensional vector space, operable by linear transformations. Symmetries observed by electricians find expression in <a href="/wiki/Linear_algebra" title="Linear algebra">linear algebra</a> and differential geometry. Using <a href="/wiki/Exterior_algebra" title="Exterior algebra">exterior algebra</a> to construct a 2-form <i>F</i> from electric and magnetic fields, and the implied dual 2-form ★<i>F</i>, the equations <span class="nowrap">d<i>F</i> = 0</span> and <span class="nowrap">d★<i>F</i> = <i>J</i></span> (current) express Maxwell's theory with a <a href="/wiki/Mathematical_descriptions_of_the_electromagnetic_field#Differential_forms_approach" title="Mathematical descriptions of the electromagnetic field">differential form approach</a>. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativistic_electromagnetism&action=edit&section=4" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Covariant_formulation_of_classical_electromagnetism" title="Covariant formulation of classical electromagnetism">Covariant formulation of classical electromagnetism</a></li> <li><a href="/wiki/Special_relativity" title="Special relativity">Special relativity</a></li> <li><a href="/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential" title="Liénard–Wiechert potential">Liénard–Wiechert potential</a></li> <li><a href="/wiki/Moving_magnet_and_conductor_problem" title="Moving magnet and conductor problem">Moving magnet and conductor problem</a></li> <li><a href="/wiki/Wheeler%E2%80%93Feynman_absorber_theory" title="Wheeler–Feynman absorber theory">Wheeler–Feynman absorber theory</a></li> <li><a href="/wiki/Paradox_of_a_charge_in_a_gravitational_field" class="mw-redirect" title="Paradox of a charge in a gravitational field">Paradox of a charge in a gravitational field</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes_and_references">Notes and references</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativistic_electromagnetism&action=edit&section=5" title="Edit section: Notes and references"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFKargonAchinstein1987" class="citation book cs1">Kargon, Robert; Achinstein, Peter (1987). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/kelvinsbaltimore00lord"><i>Kelvin's Baltimore Lectures and Modern Theoretical Physics: Historical and philosophical perspectives</i></a></span>. <a href="/wiki/MIT_Press" title="MIT Press">MIT Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-262-11117-9" title="Special:BookSources/0-262-11117-9"><bdi>0-262-11117-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Kelvin%27s+Baltimore+Lectures+and+Modern+Theoretical+Physics%3A+Historical+and+philosophical+perspectives&rft.pub=MIT+Press&rft.date=1987&rft.isbn=0-262-11117-9&rft.aulast=Kargon&rft.aufirst=Robert&rft.au=Achinstein%2C+Peter&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fkelvinsbaltimore00lord&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativistic+electromagnetism" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">What led me more or less directly to the special theory of relativity was the conviction that the electromotive force acting on a body in motion in a magnetic field was nothing else but an electric field. <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> (1953) <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShankland1964" class="citation journal cs1">Shankland, R. S. (1964). "Michelson-Morley Experiment". <i><a href="/wiki/American_Journal_of_Physics" title="American Journal of Physics">American Journal of Physics</a></i>. <b>32</b> (1): 16–81. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1964AmJPh..32...16S">1964AmJPh..32...16S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1970063">10.1119/1.1970063</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Michelson-Morley+Experiment&rft.volume=32&rft.issue=1&rft.pages=16-81&rft.date=1964&rft_id=info%3Adoi%2F10.1119%2F1.1970063&rft_id=info%3Abibcode%2F1964AmJPh..32...16S&rft.aulast=Shankland&rft.aufirst=R.+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativistic+electromagnetism" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPage1912" class="citation journal cs1"><a href="/wiki/Leigh_Page" title="Leigh Page">Page, Leigh</a> (1912). <a rel="nofollow" class="external text" href="https://zenodo.org/record/1450178">"Derivation of the Fundamental Relations of Electrodynamics from those of Electrostatics"</a>. <i><a href="/wiki/American_Journal_of_Science" title="American Journal of Science">American Journal of Science</a></i>. <b>34</b> (199): 57–68. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1912AmJS...34...57P">1912AmJS...34...57P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2475%2Fajs.s4-34.199.57">10.2475/ajs.s4-34.199.57</a>. <q>If the principle of relativity had been enunciated before the date of Oersted's discovery, the fundamental relations of electrodynamics could have been predicted on theoretical grounds as a direct consequence of the fundamental laws of electrostatics, extended so as to apply to charges relatively in motion as well as charges relatively at rest.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Science&rft.atitle=Derivation+of+the+Fundamental+Relations+of+Electrodynamics+from+those+of+Electrostatics&rft.volume=34&rft.issue=199&rft.pages=57-68&rft.date=1912&rft_id=info%3Adoi%2F10.2475%2Fajs.s4-34.199.57&rft_id=info%3Abibcode%2F1912AmJS...34...57P&rft.aulast=Page&rft.aufirst=Leigh&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F1450178&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativistic+electromagnetism" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPageAdams1940" class="citation book cs1"><a href="/wiki/Leigh_Page" title="Leigh Page">Page, Leigh</a>; Adams, Norman Ilsley (1940). <i>Electrodynamics</i>. D. Van Nostrand Company.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electrodynamics&rft.pub=D.+Van+Nostrand+Company&rft.date=1940&rft.aulast=Page&rft.aufirst=Leigh&rft.au=Adams%2C+Norman+Ilsley&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativistic+electromagnetism" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMould2001" class="citation book cs1">Mould, Richard A. (2001). <i>Basic Relativity</i>. <a href="/wiki/Springer_Science_%26_Business_Media" class="mw-redirect" title="Springer Science & Business Media">Springer Science & Business Media</a>. § 62, Lorentz force. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0387952101" title="Special:BookSources/0387952101"><bdi>0387952101</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Basic+Relativity&rft.pages=%C2%A7-62%2C+Lorentz+force&rft.pub=Springer+Science+%26+Business+Media&rft.date=2001&rft.isbn=0387952101&rft.aulast=Mould&rft.aufirst=Richard+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativistic+electromagnetism" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLawden2012" class="citation book cs1">Lawden, Derek F. (2012). <i>An Introduction to Tensor Calculus: Relativity and Cosmology</i>. Courier Corporation. p. 74. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0486132143" title="Special:BookSources/978-0486132143"><bdi>978-0486132143</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Introduction+to+Tensor+Calculus%3A+Relativity+and+Cosmology&rft.pages=74&rft.pub=Courier+Corporation&rft.date=2012&rft.isbn=978-0486132143&rft.aulast=Lawden&rft.aufirst=Derek+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativistic+electromagnetism" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVanderlinde2006" class="citation book cs1">Vanderlinde, Jack (2006). <i>Classical Electromagnetic Theory</i>. <a href="/wiki/Springer_Science_%26_Business_Media" class="mw-redirect" title="Springer Science & Business Media">Springer Science & Business Media</a>. § 11.1, The Four-potential and Coulomb's Law, page 314. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1402027001" title="Special:BookSources/1402027001"><bdi>1402027001</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Classical+Electromagnetic+Theory&rft.pages=%C2%A7-11.1%2C+The+Four-potential+and+Coulomb%27s+Law%2C+page+314&rft.pub=Springer+Science+%26+Business+Media&rft.date=2006&rft.isbn=1402027001&rft.aulast=Vanderlinde&rft.aufirst=Jack&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativistic+electromagnetism" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://feynmanlectures.caltech.edu/II_13.html#Ch13-S6">The Feynman Lectures on Physics Vol. II Section 13-6: The relativity of magnetic and electric fields</a></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRosser1968" class="citation book cs1">Rosser, W.G.V. (1968). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/classicalelectro0000ross"><i>Classical Electromagnetism via Relativity</i></a></span>. <a href="/wiki/Plenum_Press" class="mw-redirect" title="Plenum Press">Plenum Press</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Classical+Electromagnetism+via+Relativity&rft.pub=Plenum+Press&rft.date=1968&rft.aulast=Rosser&rft.aufirst=W.G.V.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fclassicalelectro0000ross&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativistic+electromagnetism" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFrench1968" class="citation book cs1"><a href="/wiki/Anthony_French" title="Anthony French">French, Anthony</a> (1968). <i>Special Relativity</i>. <a href="/wiki/W._W._Norton_%26_Company" title="W. W. Norton & Company">W. W. Norton & Company</a>. Chapter 8.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Special+Relativity&rft.pages=Chapter-8&rft.pub=W.+W.+Norton+%26+Company&rft.date=1968&rft.aulast=French&rft.aufirst=Anthony&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativistic+electromagnetism" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTessman1966" class="citation journal cs1">Tessman, Jack R. (1966). "Maxwell - Out of Newton, Coulomb, and Einstein". <i><a href="/wiki/American_Journal_of_Physics" title="American Journal of Physics">American Journal of Physics</a></i>. <b>34</b> (11): 1048–1055. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1966AmJPh..34.1048T">1966AmJPh..34.1048T</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1972453">10.1119/1.1972453</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Maxwell+-+Out+of+Newton%2C+Coulomb%2C+and+Einstein&rft.volume=34&rft.issue=11&rft.pages=1048-1055&rft.date=1966&rft_id=info%3Adoi%2F10.1119%2F1.1972453&rft_id=info%3Abibcode%2F1966AmJPh..34.1048T&rft.aulast=Tessman&rft.aufirst=Jack+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativistic+electromagnetism" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPurcell1985" class="citation book cs1">Purcell, Edward M. (1985) [1965]. <i>Electricity and Magnetism</i>. Berkeley Physics Course. Vol. 2 (2nd ed.). McGraw-Hill.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electricity+and+Magnetism&rft.series=Berkeley+Physics+Course&rft.edition=2nd&rft.pub=McGraw-Hill&rft.date=1985&rft.aulast=Purcell&rft.aufirst=Edward+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativistic+electromagnetism" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text">A. Einstein (1934)(Alan Harris translator) <a rel="nofollow" class="external text" href="https://archive.org/details/in.ernet.dli.2015.502402/page/n69">Essays in Science, page 57</a> via Internet Archive</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">L. Silberstein (1914) <a rel="nofollow" class="external text" href="https://archive.org/details/theoryofrelativi00silbrich/page/n7">The Theory of Relativity</a> via Internet Archive</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">A. Einstein (1905) <a href="https://en.wikisource.org/wiki/On_the_Electrodynamics_of_Moving_Bodies_(1920_edition)" class="extiw" title="s:On the Electrodynamics of Moving Bodies (1920 edition)">s:On the Electrodynamics of Moving Bodies (1920 edition)</a></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativistic_electromagnetism&action=edit&section=6" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCorsonLorrain1970" class="citation book cs1">Corson, Dale; Lorrain, Paul (1970). <i>Electromagnetic Fields and Waves</i>. San Francisco, CA: <a href="/wiki/W.H._Freeman" class="mw-redirect" title="W.H. Freeman">W.H. Freeman</a>. Chapter 6.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electromagnetic+Fields+and+Waves&rft.place=San+Francisco%2C+CA&rft.pages=Chapter-6&rft.pub=W.H.+Freeman&rft.date=1970&rft.aulast=Corson&rft.aufirst=Dale&rft.au=Lorrain%2C+Paul&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativistic+electromagnetism" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEasther" class="citation web cs1">Easther, Richard. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150303005731/http://cosmology.auckland.ac.nz/relativistic-em-visualizations/">"Visualizations"</a>. Relativistic E&M. Archived from <a rel="nofollow" class="external text" href="https://cosmology.auckland.ac.nz/relativistic-em-visualizations/">the original</a> on 3 March 2015<span class="reference-accessdate">. Retrieved <span class="nowrap">5 August</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Visualizations&rft.series=Relativistic+E%26M&rft.aulast=Easther&rft.aufirst=Richard&rft_id=http%3A%2F%2Fcosmology.auckland.ac.nz%2Frelativistic-em-visualizations%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativistic+electromagnetism" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJefferies2000" class="citation web cs1">Jefferies, David (2000). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150314063228/http://www.eryptick.net/dj/electrom.htm">"Electromagnetism, Relativity, and Maxwell"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.eryptick.net/dj/electrom.htm">the original</a> on 2015-03-14<span class="reference-accessdate">. Retrieved <span class="nowrap">2010-02-11</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Electromagnetism%2C+Relativity%2C+and+Maxwell&rft.date=2000&rft.aulast=Jefferies&rft.aufirst=David&rft_id=http%3A%2F%2Fwww.eryptick.net%2Fdj%2Felectrom.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativistic+electromagnetism" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchroeder1999" class="citation web cs1">Schroeder, Daniel V. (1999). <a rel="nofollow" class="external text" href="http://physics.weber.edu/schroeder/MRR/mrr.html">"Magnetism, Radiation, and Relativity"</a>. Purcell Simplified.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Magnetism%2C+Radiation%2C+and+Relativity&rft.series=Purcell+Simplified&rft.date=1999&rft.aulast=Schroeder&rft.aufirst=Daniel+V.&rft_id=http%3A%2F%2Fphysics.weber.edu%2Fschroeder%2FMRR%2Fmrr.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativistic+electromagnetism" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFde_Vries2008" class="citation web cs1">de Vries, Hans (2008). <a rel="nofollow" class="external text" href="http://chip-architect.com/physics/Magnetism_from_ElectroStatics_and_SR.pdf">"Magnetism as a relativistic side effect of electrostatics"</a> <span class="cs1-format">(PDF)</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Magnetism+as+a+relativistic+side+effect+of+electrostatics&rft.date=2008&rft.aulast=de+Vries&rft.aufirst=Hans&rft_id=http%3A%2F%2Fchip-architect.com%2Fphysics%2FMagnetism_from_ElectroStatics_and_SR.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativistic+electromagnetism" class="Z3988"></span></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output 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rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Relativity" title="Template:Relativity"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Relativity" title="Template talk:Relativity"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Relativity" title="Special:EditPage/Template:Relativity"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Relativity" style="font-size:114%;margin:0 4em"><a href="/wiki/Theory_of_relativity" title="Theory of relativity">Relativity</a></div></th></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Special_relativity" title="Special relativity">Special<br />relativity</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Background</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Principle_of_relativity" title="Principle of relativity">Principle of relativity</a> (<a href="/wiki/Galilean_invariance" title="Galilean invariance">Galilean relativity</a></li> <li><a href="/wiki/Galilean_transformation" title="Galilean transformation">Galilean transformation</a>)</li> <li><a href="/wiki/Special_relativity" title="Special relativity">Special relativity</a></li> <li><a href="/wiki/Doubly_special_relativity" title="Doubly special relativity">Doubly special relativity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Fundamental<br />concepts</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Frame_of_reference" title="Frame of reference">Frame of reference</a></li> <li><a href="/wiki/Speed_of_light" title="Speed of light">Speed of light</a></li> <li><a href="/wiki/Hyperbolic_orthogonality" title="Hyperbolic orthogonality">Hyperbolic orthogonality</a></li> <li><a href="/wiki/Rapidity" title="Rapidity">Rapidity</a></li> <li><a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a></li> <li><a href="/wiki/Proper_length" title="Proper length">Proper length</a></li> <li><a href="/wiki/Proper_time" title="Proper time">Proper time</a></li> <li><a href="/wiki/Proper_acceleration" title="Proper acceleration">Proper acceleration</a></li> <li><a href="/wiki/Mass_in_special_relativity" title="Mass in special relativity">Relativistic mass</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Formulation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Lorentz_transformation" title="Lorentz transformation">Lorentz transformation</a></li> <li><a href="/wiki/List_of_textbooks_on_relativity" title="List of textbooks on relativity">Textbooks</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Phenomena</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Time_dilation" title="Time dilation">Time dilation</a></li> <li><a href="/wiki/Mass%E2%80%93energy_equivalence" title="Mass–energy equivalence">Mass–energy equivalence (E=mc<sup>2</sup>)</a></li> <li><a href="/wiki/Length_contraction" title="Length contraction">Length contraction</a></li> <li><a href="/wiki/Relativity_of_simultaneity" title="Relativity of simultaneity">Relativity of simultaneity</a></li> <li><a href="/wiki/Relativistic_Doppler_effect" title="Relativistic Doppler effect">Relativistic Doppler effect</a></li> <li><a href="/wiki/Thomas_precession" title="Thomas precession">Thomas precession</a></li> <li><a href="/wiki/Ladder_paradox" title="Ladder paradox">Ladder paradox</a></li> <li><a href="/wiki/Twin_paradox" title="Twin paradox">Twin paradox</a></li> <li><a href="/wiki/Terrell_rotation" title="Terrell rotation">Terrell rotation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;"><a href="/wiki/Spacetime" title="Spacetime">Spacetime</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Light_cone" title="Light cone">Light cone</a></li> <li><a href="/wiki/World_line" title="World line">World line</a></li> <li><a href="/wiki/Minkowski_diagram" class="mw-redirect" title="Minkowski diagram">Minkowski diagram</a></li> <li><a href="/wiki/Biquaternion" title="Biquaternion">Biquaternions</a></li> <li><a href="/wiki/Minkowski_space" title="Minkowski space">Minkowski space</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/General_relativity" title="General relativity">General<br />relativity</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Background</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Introduction_to_general_relativity" title="Introduction to general relativity">Introduction</a></li> <li><a href="/wiki/Mathematics_of_general_relativity" title="Mathematics of general relativity">Mathematical formulation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Fundamental<br />concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Equivalence_principle" title="Equivalence principle">Equivalence principle</a></li> <li><a href="/wiki/Riemannian_geometry" title="Riemannian geometry">Riemannian geometry</a></li> <li><a href="/wiki/Penrose_diagram" title="Penrose diagram">Penrose diagram</a></li> <li><a href="/wiki/Geodesics_in_general_relativity" title="Geodesics in general relativity">Geodesics</a></li> <li><a href="/wiki/Mach%27s_principle" title="Mach's principle">Mach's principle</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Formulation</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/ADM_formalism" title="ADM formalism">ADM formalism</a></li> <li><a href="/wiki/BSSN_formalism" title="BSSN formalism">BSSN formalism</a></li> <li><a href="/wiki/Einstein_field_equations" title="Einstein field equations">Einstein field equations</a></li> <li><a href="/wiki/Linearized_gravity" title="Linearized gravity">Linearized gravity</a></li> <li><a href="/wiki/Parameterized_post-Newtonian_formalism" title="Parameterized post-Newtonian formalism">Post-Newtonian formalism</a></li> <li><a href="/wiki/Raychaudhuri_equation" title="Raychaudhuri equation">Raychaudhuri equation</a></li> <li><a href="/wiki/Hamilton%E2%80%93Jacobi%E2%80%93Einstein_equation" title="Hamilton–Jacobi–Einstein equation">Hamilton–Jacobi–Einstein equation</a></li> <li><a href="/wiki/Ernst_equation" title="Ernst equation">Ernst equation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Phenomena</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Black_hole" title="Black hole">Black hole</a></li> <li><a href="/wiki/Event_horizon" title="Event horizon">Event horizon</a></li> <li><a href="/wiki/Gravitational_singularity" title="Gravitational singularity">Singularity</a></li> <li><a href="/wiki/Two-body_problem_in_general_relativity" title="Two-body problem in general relativity">Two-body problem</a></li></ul> <ul><li><a href="/wiki/Gravitational_wave" title="Gravitational wave">Gravitational waves</a>: <a href="/wiki/Gravitational-wave_astronomy" title="Gravitational-wave astronomy">astronomy</a></li> <li><a href="/wiki/Gravitational-wave_observatory" title="Gravitational-wave observatory">detectors</a> (<a href="/wiki/LIGO" title="LIGO">LIGO</a> and <a href="/wiki/LIGO_Scientific_Collaboration" title="LIGO Scientific Collaboration">collaboration</a></li> <li><a href="/wiki/Virgo_interferometer" title="Virgo interferometer">Virgo</a></li> <li><a href="/wiki/LISA_Pathfinder" title="LISA Pathfinder">LISA Pathfinder</a></li> <li><a href="/wiki/GEO600" title="GEO600">GEO</a>)</li> <li><a href="/wiki/Hulse%E2%80%93Taylor_binary" class="mw-redirect" title="Hulse–Taylor binary">Hulse–Taylor binary</a></li></ul> <ul><li><a href="/wiki/Tests_of_general_relativity" title="Tests of general relativity">Other tests</a>: <a href="/wiki/Apsidal_precession" title="Apsidal precession">precession</a> of Mercury</li> <li><a href="/wiki/Gravitational_lens" title="Gravitational lens">lensing</a> (together with <a href="/wiki/Einstein_cross" class="mw-redirect" title="Einstein cross">Einstein cross</a> and <a href="/wiki/Einstein_rings" class="mw-redirect" title="Einstein rings">Einstein rings</a>)</li> <li><a href="/wiki/Gravitational_redshift" title="Gravitational redshift">redshift</a></li> <li><a href="/wiki/Shapiro_time_delay" title="Shapiro time delay">Shapiro delay</a></li> <li><a href="/wiki/Frame-dragging" title="Frame-dragging">frame-dragging</a> / <a href="/wiki/Geodetic_effect" title="Geodetic effect">geodetic effect</a> (<a href="/wiki/Lense%E2%80%93Thirring_precession" title="Lense–Thirring precession">Lense–Thirring precession</a>)</li> <li><a href="/wiki/Pulsar_timing_array" title="Pulsar timing array">pulsar timing arrays</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Advanced<br />theories</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Brans%E2%80%93Dicke_theory" title="Brans–Dicke theory">Brans–Dicke theory</a></li> <li><a href="/wiki/Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein</a></li> <li><a href="/wiki/Quantum_gravity" title="Quantum gravity">Quantum gravity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;"><a href="/wiki/Exact_solutions_in_general_relativity" title="Exact solutions in general relativity">Solutions</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li>Cosmological: <a href="/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" title="Friedmann–Lemaître–Robertson–Walker metric">Friedmann–Lemaître–Robertson–Walker</a> (<a href="/wiki/Friedmann_equations" title="Friedmann equations">Friedmann equations</a>)</li> <li><a href="/wiki/Lema%C3%AEtre%E2%80%93Tolman_metric" title="Lemaître–Tolman metric">Lemaître–Tolman</a></li> <li><a href="/wiki/Kasner_metric" title="Kasner metric">Kasner</a></li> <li><a href="/wiki/BKL_singularity" title="BKL singularity">BKL singularity</a></li> <li><a href="/wiki/G%C3%B6del_metric" title="Gödel metric">Gödel</a></li> <li><a href="/wiki/Milne_model" title="Milne model">Milne</a></li></ul> <ul><li>Spherical: <a href="/wiki/Schwarzschild_metric" title="Schwarzschild metric">Schwarzschild</a> (<a href="/wiki/Interior_Schwarzschild_metric" title="Interior Schwarzschild metric">interior</a></li> <li><a href="/wiki/Tolman%E2%80%93Oppenheimer%E2%80%93Volkoff_equation" title="Tolman–Oppenheimer–Volkoff equation">Tolman–Oppenheimer–Volkoff equation</a>)</li> <li><a href="/wiki/Reissner%E2%80%93Nordstr%C3%B6m_metric" title="Reissner–Nordström metric">Reissner–Nordström</a></li></ul> <ul><li>Axisymmetric: <a href="/wiki/Kerr_metric" title="Kerr metric">Kerr</a> (<a href="/wiki/Kerr%E2%80%93Newman_metric" title="Kerr–Newman metric">Kerr–Newman</a>)</li> <li><a href="/wiki/Weyl%E2%88%92Lewis%E2%88%92Papapetrou_coordinates" class="mw-redirect" title="Weyl−Lewis−Papapetrou coordinates">Weyl−Lewis−Papapetrou</a></li> <li><a href="/wiki/Taub%E2%80%93NUT_space" title="Taub–NUT space">Taub–NUT</a></li> <li><a href="/wiki/Van_Stockum_dust" title="Van Stockum dust">van Stockum dust</a></li> <li><a href="/wiki/Relativistic_disk" title="Relativistic disk">discs</a></li></ul> <ul><li>Others: <a href="/wiki/Pp-wave_spacetime" title="Pp-wave spacetime">pp-wave</a></li> <li><a href="/wiki/Ozsv%C3%A1th%E2%80%93Sch%C3%BCcking_metric" title="Ozsváth–Schücking metric">Ozsváth–Schücking</a></li> <li><a href="/wiki/Alcubierre_drive" title="Alcubierre drive">Alcubierre</a></li></ul> <ul><li>In computational physics: <a href="/wiki/Numerical_relativity" title="Numerical relativity">Numerical relativity</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Scientists</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré</a></li> <li><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li> <li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/David_Hilbert" title="David Hilbert">Hilbert</a></li> <li><a href="/wiki/Karl_Schwarzschild" title="Karl Schwarzschild">Schwarzschild</a></li> <li><a href="/wiki/Willem_de_Sitter" title="Willem de Sitter">de Sitter</a></li> <li><a href="/wiki/Hermann_Weyl" title="Hermann Weyl">Weyl</a></li> <li><a href="/wiki/Arthur_Eddington" title="Arthur Eddington">Eddington</a></li> <li><a href="/wiki/Alexander_Friedmann" title="Alexander Friedmann">Friedmann</a></li> <li><a href="/wiki/Georges_Lema%C3%AEtre" title="Georges Lemaître">Lemaître</a></li> <li><a href="/wiki/Edward_Arthur_Milne" title="Edward Arthur Milne">Milne</a></li> <li><a href="/wiki/Howard_P._Robertson" title="Howard P. Robertson">Robertson</a></li> <li><a href="/wiki/Subrahmanyan_Chandrasekhar" title="Subrahmanyan Chandrasekhar">Chandrasekhar</a></li> <li><a href="/wiki/Fritz_Zwicky" title="Fritz Zwicky">Zwicky</a></li> <li><a href="/wiki/John_Archibald_Wheeler" title="John Archibald Wheeler">Wheeler</a></li> <li><a href="/wiki/Yvonne_Choquet-Bruhat" title="Yvonne Choquet-Bruhat">Choquet-Bruhat</a></li> <li><a href="/wiki/Roy_Kerr" title="Roy Kerr">Kerr</a></li> <li><a href="/wiki/Yakov_Zeldovich" title="Yakov Zeldovich">Zel'dovich</a></li> <li><a href="/wiki/Igor_Dmitriyevich_Novikov" title="Igor Dmitriyevich Novikov">Novikov</a></li> <li><a href="/wiki/J%C3%BCrgen_Ehlers" title="Jürgen Ehlers">Ehlers</a></li> <li><a href="/wiki/Robert_Geroch" title="Robert Geroch">Geroch</a></li> <li><a href="/wiki/Roger_Penrose" title="Roger Penrose">Penrose</a></li> <li><a href="/wiki/Stephen_Hawking" title="Stephen Hawking">Hawking</a></li> <li><a href="/wiki/Joseph_Hooton_Taylor_Jr." title="Joseph Hooton Taylor Jr.">Taylor</a></li> <li><a href="/wiki/Russell_Alan_Hulse" title="Russell Alan Hulse">Hulse</a></li> <li><a href="/wiki/Hermann_Bondi" title="Hermann Bondi">Bondi</a></li> <li><a href="/wiki/Charles_W._Misner" title="Charles W. Misner">Misner</a></li> <li><a href="/wiki/Shing-Tung_Yau" title="Shing-Tung Yau">Yau</a></li> <li><a href="/wiki/Kip_Thorne" title="Kip Thorne">Thorne</a></li> <li><a href="/wiki/Rainer_Weiss" title="Rainer Weiss">Weiss</a></li> <li><a href="/wiki/List_of_contributors_to_general_relativity" title="List of contributors to general relativity"><i>others</i></a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="text-align:center;"><div><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Theory_of_relativity" title="Category:Theory of relativity">Category</a></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Major_branches_of_physics" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Branches_of_physics" title="Template:Branches of physics"><abbr title="View this 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physics">Engineering</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Approaches</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Experimental_physics" title="Experimental physics">Experimental</a></li> <li><a href="/wiki/Theoretical_physics" title="Theoretical physics">Theoretical</a> <ul><li><a href="/wiki/Computational_physics" title="Computational physics">Computational</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Classical_physics" title="Classical physics">Classical</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a> <ul><li><a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of 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