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class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Newtonian gravitation</span> </div> </a> <button aria-controls="toc-Newtonian_gravitation-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Newtonian gravitation subsection</span> </button> <ul id="toc-Newtonian_gravitation-sublist" class="vector-toc-list"> <li id="toc-Newtonian_mechanics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Newtonian_mechanics"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Newtonian mechanics</span> </div> </a> <ul id="toc-Newtonian_mechanics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Beginning_of_aether_theories" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Beginning_of_aether_theories"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Beginning of aether theories</span> </div> </a> <ul id="toc-Beginning_of_aether_theories-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Eulerian_fluid_dynamics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Eulerian_fluid_dynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Eulerian fluid dynamics</span> </div> </a> <ul id="toc-Eulerian_fluid_dynamics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Potential_theory" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Potential_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Potential theory</span> </div> </a> <ul id="toc-Potential_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Forces_of_electricity_and_magnetism" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Forces_of_electricity_and_magnetism"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Forces of electricity and magnetism</span> </div> </a> <button aria-controls="toc-Forces_of_electricity_and_magnetism-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Forces of electricity and magnetism subsection</span> </button> <ul id="toc-Forces_of_electricity_and_magnetism-sublist" class="vector-toc-list"> <li id="toc-Luminiferous_aether" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Luminiferous_aether"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Luminiferous aether</span> </div> </a> <ul id="toc-Luminiferous_aether-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Introduction_of_fields" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Introduction_of_fields"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Introduction of fields</span> </div> </a> <button aria-controls="toc-Introduction_of_fields-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Introduction of fields subsection</span> </button> <ul id="toc-Introduction_of_fields-sublist" class="vector-toc-list"> <li id="toc-Faraday's_lines_of_force" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Faraday's_lines_of_force"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Faraday's lines of force</span> </div> </a> <ul id="toc-Faraday's_lines_of_force-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kelvin's_definition" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kelvin's_definition"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Kelvin's definition</span> </div> </a> <ul id="toc-Kelvin's_definition-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Maxwell's_electromagnetic_field" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Maxwell's_electromagnetic_field"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Maxwell's electromagnetic field</span> </div> </a> <ul id="toc-Maxwell's_electromagnetic_field-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Relativistic_field_theory" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Relativistic_field_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Relativistic field theory</span> </div> </a> <button aria-controls="toc-Relativistic_field_theory-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Relativistic field theory subsection</span> </button> <ul id="toc-Relativistic_field_theory-sublist" class="vector-toc-list"> <li id="toc-Special_relativity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Special_relativity"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Special relativity</span> </div> </a> <ul id="toc-Special_relativity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Space-time_as_a_field" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Space-time_as_a_field"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Space-time as a field</span> </div> </a> <ul id="toc-Space-time_as_a_field-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Unification_attempts" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Unification_attempts"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Unification attempts</span> </div> </a> <ul id="toc-Unification_attempts-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantum_fields" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Quantum_fields"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Quantum fields</span> </div> </a> <ul id="toc-Quantum_fields-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span 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data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><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 classical field theory. For quantum theory, see <a href="/wiki/History_of_quantum_field_theory" title="History of quantum field theory">history of quantum field theory</a>. For for the non-field theory, see <a href="/wiki/History_of_classical_mechanics" title="History of classical mechanics">History of classical mechanics</a>.</div><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Magnet0873.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Magnet0873.png/220px-Magnet0873.png" decoding="async" width="220" height="148" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Magnet0873.png/330px-Magnet0873.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/57/Magnet0873.png/440px-Magnet0873.png 2x" data-file-width="444" data-file-height="298" /></a><figcaption>Iron filings used to show the magnetic field lines of a bar magnet.</figcaption></figure> <p>In the <a href="/wiki/History_of_physics" title="History of physics">history of physics</a>, the concept of <a href="/wiki/Field_(physics)" title="Field (physics)">fields</a> had its origins in the 18th century in a mathematical formulation of <a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation">Newton's law of universal gravitation</a>, but it was seen as deficient as it implied <a href="/wiki/Action_at_a_distance" title="Action at a distance">action at a distance</a>. In 1852, <a href="/wiki/Michael_Faraday" title="Michael Faraday">Michael Faraday</a> treated the <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a> as a physical object, reasoning about <a href="/wiki/Line_of_force" title="Line of force">lines of force</a>. <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Clerk Maxwell</a> used Faraday's conceptualisation to help formulate his unification of electricity and magnetism in his field theory of <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a>. </p><p>With <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>'s <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a> and the <a href="/wiki/Michelson%E2%80%93Morley_experiment" title="Michelson–Morley experiment">Michelson–Morley experiment</a>, it became clear that <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic waves</a> could travel in <a href="/wiki/Vacuum" title="Vacuum">vacuum</a> without the need of a medium or <a href="/wiki/Luminiferous_aether" title="Luminiferous aether">luminiferous aether</a>. Einstein also developed <a href="/wiki/General_relativity" title="General relativity">general relativity</a>, in which <a href="/wiki/Spacetime" title="Spacetime">spacetime</a> was treated as a field and its curvature was the origin of the gravitational interactions, putting an end to action at a distance. </p><p>In <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a>, fields become the fundamental objects of study, and particles are excitations of these fields. To differentiale from quantum field theory, previously developed field theories were called <a href="/wiki/Classical_field_theory" title="Classical field theory">classical field theories</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Early_mechanical_explanations_of_forces">Early mechanical explanations of forces</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=1" title="Edit section: Early mechanical explanations of forces"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Magnetism">Magnetism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=2" title="Edit section: Magnetism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Descartes_magnetic_field.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Descartes_magnetic_field.jpg/220px-Descartes_magnetic_field.jpg" decoding="async" width="220" height="187" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Descartes_magnetic_field.jpg/330px-Descartes_magnetic_field.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Descartes_magnetic_field.jpg/440px-Descartes_magnetic_field.jpg 2x" data-file-width="1372" data-file-height="1165" /></a><figcaption><a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">René Descartes</a> drawing of a magnetic effluvia from 1644. It shows the magnetic effluvia of the Earth <i>(D)</i> attracting several round lodestones <i>(I, K, L, M, N)</i> and illustrates his theory of magnetism.</figcaption></figure><p>The first record of explanations of how magnets works comes from <a href="/wiki/Ancient_Greece" title="Ancient Greece">ancient Greece</a>.<sup id="cite_ref-:3_1-0" class="reference"><a href="#cite_note-:3-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Thinkers like <a href="/wiki/Thales_of_Miletus" title="Thales of Miletus">Thales of Miletus</a>, <a href="/wiki/Aristotle" title="Aristotle">Aristotle</a> and <a href="/wiki/Diogenes_Laertius" title="Diogenes Laertius">Diogenes Laertius</a> considered that magnets were animated and should have a <a href="/wiki/Soul" title="Soul">soul</a> in order to move.<sup id="cite_ref-:3_1-1" class="reference"><a href="#cite_note-:3-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Empedocles" title="Empedocles">Empedocles</a> tried to provide a mechanical explanation of why magnets could influence each other by introducing the concept of "effluences" emanated by magnets.<sup id="cite_ref-:3_1-2" class="reference"><a href="#cite_note-:3-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> According to book <i>Quaestiones</i> by <a href="/wiki/Alexander_of_Aphrodisias" title="Alexander of Aphrodisias">Alexander of Aphrodisias</a> from about 200 AD, this was Empedocles view:<sup id="cite_ref-:3_1-3" class="reference"><a href="#cite_note-:3-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style></p><blockquote class="templatequote"><p>On the reason why the lodestone attracts iron. Empedocles says that the iron is attracted to the stone by the effluences which issue from both, and because the pores of the stone are commensurate with the effluences from the iron. The effluences from the stone stir and disperse the air lying upon and obstructing the pores of the iron and when this is removed the iron is drawn on by a concerted outflow. As the effluences from the iron travel towards the pores of the stone, because they are commensurate with them and fit into them the iron itself follows and moves together with them.</p></blockquote> <p><a href="/wiki/Democritus" title="Democritus">Democritus</a> had a similar view as Empedocles but added that the effluences created a void. Metals and rocks could also contain void in order to be less or more attracted to magnets.<sup id="cite_ref-:3_1-4" class="reference"><a href="#cite_note-:3-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>This idea survived up to the <a href="/wiki/Scientific_Revolution" title="Scientific Revolution">Scientific Revolution</a>. In 1664, <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">René Descartes</a> produced his theory of magnetism, in which the flow of effluences or effluvia rarified the air, creating differences in air pressure. According to Descartes, these effluvia circulated inside and around the magnet in closed loops.<sup id="cite_ref-:1_2-0" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Gravitation">Gravitation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=3" title="Edit section: Gravitation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Mechanical_explanations_of_gravitation" title="Mechanical explanations of gravitation">Mechanical explanations of gravitation</a></div> <p>In ancient times, Greek thinkers like <a href="/wiki/Posidonius" title="Posidonius">Posidonius</a> (1 BC) noticed a relation between the tides and the position of the <a href="/wiki/Moon" title="Moon">Moon</a> in the sky. He considered that light from the Moon had an influence on the tides.<sup id="cite_ref-:5_3-0" class="reference"><a href="#cite_note-:5-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>In the 9th century, <a href="/wiki/Abu_Ma%27shar_al-Balkhi" title="Abu Ma'shar al-Balkhi">Abu Ma'shar al-Balkhi</a> (Latinized as Albumasar) wrote his book on <i>The Great Introduction to the Science of Astrology</i> (<i>Kitāb al-madkhal al-kabīr</i>) recorded the correlation between the tides and the Moon, noticing that there were two tides in a day.<sup id="cite_ref-:4_4-0" class="reference"><a href="#cite_note-:4-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> As there is no moonlight when the Moon is the opposite side of Earth, he proposed that the Moon had some intrinsic virtue that attracted the water. The Sun would have some of that virtue but less than the moon.<sup id="cite_ref-:5_3-1" class="reference"><a href="#cite_note-:5-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> This book was translated to Latin and was a reference for European medieval scholars.<sup id="cite_ref-:4_4-1" class="reference"><a href="#cite_note-:4-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> One writer that rejected this astrological reading was <a href="/wiki/Robert_Grosseteste" title="Robert Grosseteste">Robert Grosseteste</a> who wrote <i>On the Ebb and Flow of the Sea</i> (<a href="/wiki/Latin_language" class="mw-redirect" title="Latin language">Latin</a>: <i lang="la">Questio de fluxu et refluxu maris</i>), written around 1227, in which he insisted that light from the Moon rarefied the air producing the tides.<sup id="cite_ref-:4_4-2" class="reference"><a href="#cite_note-:4-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> He explained the tides when the Moon is below the horizon as reflections from the celestial sphere.<sup id="cite_ref-:5_3-2" class="reference"><a href="#cite_note-:5-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Two theories coexisted, the idea of light influencing the tides and Albumasar' virtue. <a href="/wiki/Roger_Bacon" title="Roger Bacon">Roger Bacon</a> supported the idea of Grosseteste, <a href="/wiki/Albertus_Magnus" title="Albertus Magnus">Albertus Magnus</a> supported a mix of both, and others like <a href="/wiki/Jean_Buridan" title="Jean Buridan">Jean Buridan</a> hesitated between the two.<sup id="cite_ref-:5_3-3" class="reference"><a href="#cite_note-:5-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>In 17th century, <a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Johannes Kepler</a> who came up with the <a href="/wiki/Kepler%27s_laws_of_planetary_motion" title="Kepler's laws of planetary motion">Kepler's laws of planetary motion</a>, proposed the idea that the Sun emitted some sort of invisible "species" that traveled instantaneously and acted more strongly depending on the distance, size and density of the planet. Kepler considered that if the Sun rotated, it would create a whirlpool of species that drags all planets to orbit around it.<sup id="cite_ref-:4_4-3" class="reference"><a href="#cite_note-:4-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The idea of the rotation of the Sun was confirmed by <a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo Galilei</a>, but the frequency did not match Kepler's calculations.<sup id="cite_ref-:4_4-4" class="reference"><a href="#cite_note-:4-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> To explain the tides, Kepler considered that the species would behave similar to magnetic forces.<sup id="cite_ref-:4_4-5" class="reference"><a href="#cite_note-:4-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Descartes rejected Kepler's theory<sup id="cite_ref-:4_4-6" class="reference"><a href="#cite_note-:4-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> and also constructed also a mechanical explanation of gravitation based on the ideas vortices, considering space continuous.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Newtonian_gravitation">Newtonian gravitation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=4" title="Edit section: Newtonian gravitation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Newtonian_gravity_field_(physics).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Newtonian_gravity_field_%28physics%29.svg/220px-Newtonian_gravity_field_%28physics%29.svg.png" decoding="async" width="220" height="234" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Newtonian_gravity_field_%28physics%29.svg/330px-Newtonian_gravity_field_%28physics%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Newtonian_gravity_field_%28physics%29.svg/440px-Newtonian_gravity_field_%28physics%29.svg.png 2x" data-file-width="217" data-file-height="231" /></a><figcaption>In <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a>'s <a href="/wiki/Classical_gravitation" class="mw-redirect" title="Classical gravitation">classical gravitation</a>, <a href="/wiki/Mass" title="Mass">mass</a> is the source of an attractive <a href="/wiki/Gravitational_field" title="Gravitational field">gravitational field</a>.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Newtonian_mechanics">Newtonian mechanics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=5" title="Edit section: Newtonian mechanics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Before Newton, only a few mechanical explanations of gravity existed. </p><p>In 1687, <a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a>'s <i><a href="/wiki/Philosophi%C3%A6_Naturalis_Principia_Mathematica" title="Philosophiæ Naturalis Principia Mathematica">Principia</a></i> in 1687 provided a framework with which to investigate the motion and forces. He introduced mathematical definition of gravitational force with his <a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation">law of universal gravitation</a>, in which the gravitational force between two bodies is directed along the line separating the bodies and its magnitude is proportional to the product of their masses, divided by the square of their distance apart.<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> </p><p>While Newton explanation of gravity was very successful in astronomy, it did not explain how it could act at a distance and instantaneously. Newton, considered <a href="/wiki/Action_at_a_distance" title="Action at a distance">action at a distance</a> to be: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it.<sup id="cite_ref-sep-qm-action-distance_7-0" class="reference"><a href="#cite_note-sep-qm-action-distance-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup></p><div class="templatequotecite">— <cite>Isaac Newton, Letters to Bentley, 1692/3</cite></div></blockquote> <p><a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a> complained that Newtonian mechanics violated the <a href="/wiki/Metaphysics" title="Metaphysics">metaphysics</a> of continuity according to <i><a href="/wiki/Natura_non_facit_saltus" title="Natura non facit saltus">natura non facit saltus</a></i>, in which every cause and effect should be connected to one another.<sup id="cite_ref-:1_2-1" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Roger_Joseph_Boscovich" title="Roger Joseph Boscovich">Roger Joseph Boscovich</a> rejected Leibniz take considering that bodies would have discontinuous changes in density at the boundaries and that if came into contact their velocities would change discontinuously.<sup id="cite_ref-:1_2-2" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>British <a href="/wiki/Empiricism" title="Empiricism">empiricist</a> like <a href="/wiki/John_Locke" title="John Locke">John Locke</a>, <a href="/wiki/George_Locke" title="George Locke">George Locke</a> and <a href="/wiki/David_Hume" title="David Hume">David Hume</a> regarded <a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newton's second law of motion</a> as sufficient, as it establishes a causal relation between force and acceleration.<sup id="cite_ref-:1_2-3" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Beginning_of_aether_theories">Beginning of aether theories</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=6" title="Edit section: Beginning of aether theories"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Aether_theories" title="Aether theories">Aether theories</a></div> <p>To solve the issue of action at a distance, aether theories were developed. The aether was considered as a yet undetected medium and responsible agent for conducting the force. In a letter to <a href="/wiki/Robert_Boyle" title="Robert Boyle">Robert Boyle</a> in 1679 Newton proposed an "aethereal substance" to explain gravity.<sup id="cite_ref-:4_4-7" class="reference"><a href="#cite_note-:4-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Later in his work <i><a href="/wiki/Opticks" title="Opticks">Opticks</a></i> of 1717 he considered the aether to be made of impenetrable corpuscules.<sup id="cite_ref-:4_4-8" class="reference"><a href="#cite_note-:4-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:0_8-0" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Newtonian aether was very dilute and elastic.<sup id="cite_ref-:0_8-1" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Immanuel_Kant" title="Immanuel Kant">Immanuel Kant</a> considered Newton's aether inconsistent as requiring additional forces between corpuscles.<sup id="cite_ref-:0_8-2" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Leibniz on the other hand considered a continuous medium.<sup id="cite_ref-:0_8-3" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Eulerian_fluid_dynamics">Eulerian fluid dynamics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=7" title="Edit section: Eulerian fluid dynamics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Stokes_sphere.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Stokes_sphere.svg/220px-Stokes_sphere.svg.png" decoding="async" width="220" height="317" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Stokes_sphere.svg/330px-Stokes_sphere.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Stokes_sphere.svg/440px-Stokes_sphere.svg.png 2x" data-file-width="403" data-file-height="580" /></a><figcaption>Velocity field around a ball in a fluid. The arrows indicate the velocity of the fluid.</figcaption></figure> <p>An important development of field theories appeared with <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a> who expanded Newtonian mechanics in his work <i><a href="/wiki/Mechanica" title="Mechanica">Mechanica</a></i> of 1736. Euler work expanded on how to deal with rotations of rigid bodies, elasticity and fluid mechanics. To describe fluids he considered a <a href="/wiki/Flow_velocity" title="Flow velocity">flow velocity</a> function (today called velocity field) defined at every point in space.<sup id="cite_ref-:4_4-9" class="reference"><a href="#cite_note-:4-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> However this function was for a long time considered significantly different from that of the forces of gravitation as it was only defined inside a medium and thus was considered a real quantity.<sup id="cite_ref-:4_4-10" class="reference"><a href="#cite_note-:4-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Modern science historian <a href="/wiki/Mary_Hesse" title="Mary Hesse">Mary Hesse</a> attributed the origin of field theory to Euler flow velocity field.<sup id="cite_ref-:4_4-11" class="reference"><a href="#cite_note-:4-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Euler also introduced between 1755 and 1759 the <a href="/wiki/Lagrangian_and_Eulerian_specification_of_the_flow_field" title="Lagrangian and Eulerian specification of the flow field">Lagrangian and Eulerian specifications</a> for the flow<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> that would be important to detach motion of particles from field properties.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (October 2024)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="Potential_theory">Potential theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=8" title="Edit section: Potential theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange">Joseph-Louis Lagrange</a> is often cited for introducing the concept of a <a href="/wiki/Scalar_potential" title="Scalar potential">potential</a> in 1777, and independently by <a href="/wiki/Adrien-Marie_Legendre" title="Adrien-Marie Legendre">Adrien-Marie Legendre</a> (1784–1794) and <a href="/wiki/Pierre-Simon_Laplace" title="Pierre-Simon Laplace">Pierre-Simon Laplace</a> (1782–1799).<sup id="cite_ref-:6_10-0" class="reference"><a href="#cite_note-:6-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><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> Lagrange notice that he could introduce a <a href="/wiki/Gravitational_potential" title="Gravitational potential">gravitational potential</a> to derive the gravitational force.<sup id="cite_ref-:6_10-1" class="reference"><a href="#cite_note-:6-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> This function was called a potential function by mathematician <a href="/wiki/George_Green_(mathematician)" title="George Green (mathematician)">George Green</a> 1828 and by <a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Carl Friedrich Gauss</a> in 1840 just as "potential".<sup id="cite_ref-:6_10-2" class="reference"><a href="#cite_note-:6-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Forces_of_electricity_and_magnetism">Forces of electricity and magnetism</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=9" title="Edit section: Forces of electricity and magnetism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Charles-Augustin_de_Coulomb" title="Charles-Augustin de Coulomb">Charles-Augustin de Coulomb</a> showed in 1785 that the repulsive <a href="/wiki/Force" title="Force">force</a> between two electrically charged spheres obeys the same (up to a sign) force law as Newton's law of universal gravitation. In 1823, <a href="/wiki/Sim%C3%A9on_Denis_Poisson" title="Siméon Denis Poisson">Siméon Denis Poisson</a> introduced the <a href="/wiki/Poisson%27s_equation" title="Poisson's equation">Poisson's equation</a>, explaining the electric forces in terms of an <a href="/wiki/Electric_potential" title="Electric potential">electric potential</a>.<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> The same year <a href="/wiki/Andr%C3%A9-Marie_Amp%C3%A8re" title="André-Marie Ampère">André-Marie Ampère</a> showed that the force between infinitesimal lengths of current-carrying wires similarly obeys an <a href="/wiki/Inverse-square_law" title="Inverse-square law">inverse-square law</a> such that the force is directed along the line of separation between the wire elements.<sup id="cite_ref-:0_8-4" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> These law suffered from the same problem of action-at-a-distance. </p> <div class="mw-heading mw-heading3"><h3 id="Luminiferous_aether">Luminiferous aether</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=10" title="Edit section: Luminiferous aether"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1800, <a href="/wiki/Thomas_Young_(scientist)" title="Thomas Young (scientist)">Thomas Young</a> proved the wave nature of light using the <a href="/wiki/Double-slit_experiment" title="Double-slit experiment">double-slit experiment</a>. This discovery led him in 1802 to consider the existence of <a href="/wiki/Luminiferous_aether" title="Luminiferous aether">luminiferous aether</a> in which light traveled.<sup id="cite_ref-:0_8-5" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Augustin-Jean_Fresnel" title="Augustin-Jean Fresnel">Augustin-Jean Fresnel</a> considered it to be an elastic medium.<sup id="cite_ref-:0_8-6" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> The motion of this aether were described mathematically by scientist like <a href="/wiki/Claude-Louis_Navier" title="Claude-Louis Navier">Claude-Louis Navier</a> (in 1821) and <a href="/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy">Augustin-Louis Cauchy</a> (in 1828) as discrete medium.<sup id="cite_ref-:0_8-7" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> About 1840, <a href="/wiki/Sir_George_Stokes,_1st_Baronet" title="Sir George Stokes, 1st Baronet">George Stokes</a> and <a href="/wiki/Lord_Kelvin" title="Lord Kelvin">Lord Kelvin</a> extended the formalism to describe a continuous aether using the idea of a potential theory. This development was important as it allowed to describe any deformable medium in terms of continuous functions.<sup id="cite_ref-:0_8-8" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Introduction_of_fields">Introduction of fields</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=11" title="Edit section: Introduction of fields"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/History_of_electromagnetic_theory" title="History of electromagnetic theory">History of electromagnetic theory</a></div> <div class="mw-heading mw-heading3"><h3 id="Faraday's_lines_of_force"><span id="Faraday.27s_lines_of_force"></span>Faraday's lines of force</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=12" title="Edit section: Faraday's lines of force"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Line_of_force" title="Line of force">Line of force</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:VFPt_Dipole_field.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/VFPt_Dipole_field.svg/220px-VFPt_Dipole_field.svg.png" decoding="async" width="220" height="189" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/VFPt_Dipole_field.svg/330px-VFPt_Dipole_field.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/70/VFPt_Dipole_field.svg/440px-VFPt_Dipole_field.svg.png 2x" data-file-width="700" data-file-height="600" /></a><figcaption>Magnetic field lines of a magnetic dipole.</figcaption></figure> <p><a href="/wiki/Michael_Faraday" title="Michael Faraday">Michael Faraday</a> developed the concept of <a href="/wiki/Line_of_force" title="Line of force">lines of force</a> to describe electric and magnetic phenomena.<sup id="cite_ref-:7_13-0" class="reference"><a href="#cite_note-:7-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> In 1831, he writes<sup id="cite_ref-:7_13-1" class="reference"><a href="#cite_note-:7-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>By magnetic curves, I mean the lines of magnetic forces, however modified by the juxtaposition of poles, which would be depicted by iron filings; or those to ·which a very small magnetic needle would form a tangent."</p></blockquote> <p>He provided a definition in 1845,<sup id="cite_ref-:7_13-2" class="reference"><a href="#cite_note-:7-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>But before I proceed to them, I will define the meaning I connect with certain terms which I shall have occasion to use: thus, by <i>line of magnetic force</i>, or <i>magnetic line of force</i>, or <i>magnetic curve</i>, I mean that exercise of magnetic force which is exerted in the lines usually called magnetic curves, and which equally exist as passing from or to magnetic poles, or forming concentric circles round an electric current. By <i>line of electric force</i>, I mean the force exerted in the lines joining two bodies, acting on each other according to the principles of static electric induction, which may also be either in curved or straight lines.</p></blockquote> <p>In his work, he also coined the term "<a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a>" in this sense in 1845, which he later used frequently.<sup id="cite_ref-:7_13-3" class="reference"><a href="#cite_note-:7-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> He provided a clear definition in 1850, stating<sup id="cite_ref-:7_13-4" class="reference"><a href="#cite_note-:7-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>I will now endeavour to consider what the influence is which paramagnetic and diamagnetic bodies, viewed as conductors, exert upon the lines of force in a magnetic field. <i>Any portion of space traversed by lines of magnetic power, may be taken as such a field</i>, and there is probably no space without them. The condition of the field may vary in intensity of power. from place to place, either along the lines or across them; but it will be better to assume for the present consideration a field of equal force throughout, and I have formerly described how this may, for a certain limited space, be produced.</p></blockquote> <p>Faraday did not conceive of this field as a mere mathematical construct for calculating the forces between particles—having only rudimentary mathematical training, he had no use for abstracting reality to make quantitative predictions.<sup id="cite_ref-:0_8-9" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Instead he conjectured that there was force filling the space where <a href="/wiki/Electromagnetic_field" title="Electromagnetic field">electromagnetic fields</a> were generated and reasoned qualitatively about these forces with lines of force:<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> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>Important to the definition of these lines is that they represent a determinate and unchanging amount of force. Though, therefore, their forms, as they exist between two or more centers or sources of power, may vary greatly, and also the space through which they may be traced, yet the sum of power contained in any one section of a given portion of the lines is exactly equal to the sum of power in any other section of the same lines, however altered in form or however convergent or divergent they may be at the second place.</p></blockquote> <p>However Faraday never used the term "<a href="/wiki/Electric_field" title="Electric field">electric field</a>" explicitly.<sup id="cite_ref-:7_13-5" class="reference"><a href="#cite_note-:7-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Nevertheless Faraday's insights into the behavior of magnetic fields would prove invaluable for the development of <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a> and field theory. </p> <div class="mw-heading mw-heading3"><h3 id="Kelvin's_definition"><span id="Kelvin.27s_definition"></span>Kelvin's definition</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=13" title="Edit section: Kelvin's definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div><p> In 1845, Lord Kelvin formalized the mathematical similarities between the fields of electromagnetic phenomena and <a href="/wiki/Joseph_Fourier" title="Joseph Fourier">Joseph Fourier</a> work on heat; and in 1947 between electric conduction and elasticity.<sup id="cite_ref-:1_2-4" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> These similarities led Lord Kelvin to propose a formal definition of magnetic field<sup id="cite_ref-:1_2-5" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> in 1851:<sup id="cite_ref-:4_4-12" class="reference"><a href="#cite_note-:4-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"></p><blockquote class="templatequote"><p>Any space at every point of which there is a finite magnetic force is called ‘a field of magnetic force’ or (magnetic being understood) simply ‘a field of force,’ or sometimes ‘a magnetic field’.</p><div class="templatequotecite">— <cite>Lord Kelvin, On the theory of magnetic induction in crystalline and non-crystalline substances, <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></cite></div></blockquote><p>Kelvin also introduced the concept of a <a href="/wiki/Magnetic_vector_potential" title="Magnetic vector potential">magnetic vector potential</a>.<sup id="cite_ref-:8_16-0" class="reference"><a href="#cite_note-:8-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><div class="mw-heading mw-heading3"><h3 id="Maxwell's_electromagnetic_field"><span id="Maxwell.27s_electromagnetic_field"></span>Maxwell's electromagnetic field</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=14" title="Edit section: Maxwell's electromagnetic field"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Electromagnetic_wave_EN.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Electromagnetic_wave_EN.svg/300px-Electromagnetic_wave_EN.svg.png" decoding="async" width="300" height="159" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Electromagnetic_wave_EN.svg/450px-Electromagnetic_wave_EN.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Electromagnetic_wave_EN.svg/600px-Electromagnetic_wave_EN.svg.png 2x" data-file-width="599" data-file-height="317" /></a><figcaption>Electric and magnetic fields of an electromagnetic wave along an axis. In vacuum these two fields are orthogonal and propagate at the speed of light as predicted by Maxwell.</figcaption></figure> <p>In 1864, <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Clerk Maxwell</a> published "<a href="/wiki/A_Dynamical_Theory_of_the_Electromagnetic_Field" title="A Dynamical Theory of the Electromagnetic Field">A Dynamical Theory of the Electromagnetic Field</a>" in which he compiled all known equations of electricity and magnetism. <a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a> led to an <a href="/wiki/Electromagnetic_wave_equation" title="Electromagnetic wave equation">electromagnetic wave equation</a> with waves that propagated in vacuum at the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a>. He describes his research as </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>(3) The theory I propose may therefore be called a theory of the <i>Electromagnetic Field</i>, because it has to do with the space in the neighbourhood of the electric and magnetic bodies, and it may be called a <i>Dynamical Theory</i>, because it assumes that in that space there is matter in motion, by which the observed electromagnetic phenomena are produced</p></blockquote> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p> (4) The electromagnetic field is that part of space which contains and surrounds bodies in electric or magnetic conditions</p></blockquote> <p>In <i><a href="/wiki/A_Treatise_on_Electricity_and_Magnetism" title="A Treatise on Electricity and Magnetism">A Treatise on Electricity and Magnetism</a></i> of 1873, he writes "the electric field is the portion of space in the neighbourhood of electrified bodies, considered with reference to electric phenomena." And for magnetic fields </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>lt appears therefore that in the space surrounding a wire transmitting an electric current a magnet is acted on by forces dependent on the position of the wire and on the strength of the current. The space in which these forces act may therefore be considered as a magnetic field, and we may study it in the same way as we have already studied the field in the neighbourhood of ordinary magnets, by tracing the course of the lines of magnetic force, and measuring the intensity of the force at every point.</p></blockquote> <p>Maxwell had to settle for the idea of a <a href="/wiki/Luminiferous_aether" title="Luminiferous aether">luminiferous aether</a>. He wrote<sup id="cite_ref-:8_16-1" class="reference"><a href="#cite_note-:8-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>We have therefore some reason to believe, from the phenomena of light and heat, that there is an aethereal medium filling space and permeating bodies, capable of being set in motion and of transmitting that motion from one part to another, and of communicating that motion to gross matter so as to heat it and affect it in various ways.</p></blockquote> <p>Maxwell was conflicted on the idea on the nature of the fields, he considered the aether to a mechanical medium in order to carry energy.<sup id="cite_ref-:1_2-6" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> In 1868 <a href="/wiki/Carl_Neumann" title="Carl Neumann">Carl Neumann</a> discussed the idea of the electromagnetic field being an independent energy field.<sup id="cite_ref-:1_2-7" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>In 1887, <a href="/wiki/Heinrich_Hertz" title="Heinrich Hertz">Heinrich Hertz</a> published his experimental evidence of the existence of electromagnetic waves.<sup id="cite_ref-:1_2-8" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Relativistic_field_theory">Relativistic field theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=15" title="Edit section: Relativistic field theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Special_relativity">Special relativity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=16" title="Edit section: Special relativity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/History_of_special_relativity" title="History of special relativity">History of special relativity</a></div> <p>The 1887 <a href="/wiki/Michelson%E2%80%93Morley_experiment" title="Michelson–Morley experiment">Michelson–Morley experiment</a> attempted to prove that electromagnetic radiation were oscillations of a <a href="/wiki/Luminiferous_aether" title="Luminiferous aether">luminiferous aether</a>, however the result was negative, indicating that radiation could travel in vacuum. To explain this phenomenon, <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> developed his theory of <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a> (1905) which resolved the conflicts between classical mechanics and electromagnetism. Einstein introduced the <a href="/wiki/Lorentz_transformation" title="Lorentz transformation">Lorentz transformation</a> for electromagnetic fields between reference frames. </p> <div class="mw-heading mw-heading3"><h3 id="Space-time_as_a_field">Space-time as a field</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=17" title="Edit section: Space-time as a field"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/History_of_general_relativity" title="History of general relativity">History of general relativity</a></div> <p>Einstein developed the <a href="/wiki/Einstein_field_equations" title="Einstein field equations">Einstein field equations</a> of <a href="/wiki/General_relativity" title="General relativity">general relativity</a> in 1915, consistent with special relativity and that could explain gravitation in terms of a field theory of <a href="/wiki/Spacetime" title="Spacetime">spacetime</a>. This removed the need of a gravitational aether. </p><p>In 1918, <a href="/wiki/Emmy_Noether" title="Emmy Noether">Emmy Noether</a> publishes the her theorem on the relations between symmetries and conservation laws.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Noether%27s_theorem" title="Noether's theorem">Noether's theorem</a> was adapted to general relativity as well as to non-relativistic field theories.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Unification_attempts">Unification attempts</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=18" title="Edit section: Unification attempts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Classical_unified_field_theories" title="Classical unified field theories">Classical unified field theories</a></div> <p>Attempts to create a unified field theory based on classical physics are classical unified field theories. During the years between the two <a href="/wiki/World_war" title="World war">World Wars</a>, the idea of unification of gravity with electromagnetism was actively pursued by several mathematicians and physicists like Einstein, <a href="/wiki/Theodor_Kaluza" title="Theodor Kaluza">Theodor Kaluza</a>,<sup id="cite_ref-kal_19-0" class="reference"><a href="#cite_note-kal-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Hermann_Weyl" title="Hermann Weyl">Hermann Weyl</a>,<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Arthur_Eddington" title="Arthur Eddington">Arthur Eddington</a>,<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Gustav_Mie" title="Gustav Mie">Gustav Mie</a><sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> and Ernst Reichenbacher.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p>Early attempts to create such theory were based on incorporation of electromagnetic fields into the geometry of general relativity. In 1918, the case for the first geometrization of the electromagnetic field was proposed in 1918 by Weyl.<sup id="cite_ref-Tilman_24-0" class="reference"><a href="#cite_note-Tilman-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> In this work Weyl coins the term <a href="/wiki/Gauge_theory" title="Gauge theory">gauge theory</a>.<sup id="cite_ref-Brading_25-0" class="reference"><a href="#cite_note-Brading-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> Weyl, in an attempt to generalize the geometrical ideas of general relativity to include electromagnetism, conjectured that <i>Eichinvarianz</i> or invariance under the change of <a href="/wiki/Scale_(measurement)" class="mw-redirect" title="Scale (measurement)">scale</a> (or "gauge") might also be a local symmetry of general relativity. </p><p>In 1919, the idea of a five-dimensional approach was suggested by Kaluza.<sup id="cite_ref-Tilman_24-1" class="reference"><a href="#cite_note-Tilman-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> From that, a theory called <a href="/wiki/Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein theory</a> was developed. It attempts to unify gravitation and electromagnetism, in a five-dimensional space-time. There are several ways of extending the representational framework for a unified field theory which have been considered by Einstein and other researchers. These extensions in general are based in two options.<sup id="cite_ref-Tilman_24-2" class="reference"><a href="#cite_note-Tilman-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> The first option is based in relaxing the conditions imposed on the original formulation, and the second is based in introducing other mathematical objects into the theory.<sup id="cite_ref-Tilman_24-3" class="reference"><a href="#cite_note-Tilman-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> An example of the first option is relaxing the restrictions to four-dimensional space-time by considering higher-dimensional representations.<sup id="cite_ref-Tilman_24-4" class="reference"><a href="#cite_note-Tilman-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> That is used in Kaluza–Klein theory. For the second, the most prominent example arises from the concept of the <a href="/wiki/Affine_connection" title="Affine connection">affine connection</a> that was introduced into general relativity mainly through the work of <a href="/wiki/Tullio_Levi-Civita" title="Tullio Levi-Civita">Tullio Levi-Civita</a> and Weyl.<sup id="cite_ref-Tilman_24-5" class="reference"><a href="#cite_note-Tilman-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p><p>Further development of <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a> changed the focus of searching for unified field theory from classical to quantum description. Because of that, many theoretical physicists gave up looking for a classical unified field theory.<sup id="cite_ref-Tilman_24-6" class="reference"><a href="#cite_note-Tilman-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> Quantum field theory would include unification of two other <a href="/wiki/Fundamental_interaction" title="Fundamental interaction">fundamental interactions</a> of nature, the <a href="/wiki/Strong_nuclear_force" class="mw-redirect" title="Strong nuclear force">strong</a> and <a href="/wiki/Weak_nuclear_force" class="mw-redirect" title="Weak nuclear force">weak nuclear force</a> which act on the subatomic level.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Quantum_fields">Quantum fields</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=19" title="Edit section: Quantum fields"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/History_of_quantum_field_theory" title="History of quantum field theory">History of quantum field theory</a></div> <p>Fields become the fundamental object of study in quantum field theory. Mathematically, quantum fields are formalized as operator-valued distributions.<sup id="cite_ref-:2_28-0" class="reference"><a href="#cite_note-:2-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> Although there is no direct method of measuring the fields themselves, the framework asserts that all particles are "excitations" of these fields. For example: whereas Maxwell's theory of <a href="/wiki/Classical_electromagnetism" title="Classical electromagnetism">classical electromagnetism</a> describes light as a self-propagating wave in the electromagnetic field, in <a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">quantum electrodynamics</a> light is the massless <a href="/wiki/Gauge_boson" title="Gauge boson">gauge boson</a> particle called the <a href="/wiki/Photon" title="Photon">photon</a>. Furthermore, the number of particles in an isolated system need not be conserved; an example of a process for which this is the case is <a href="/wiki/Bremsstrahlung" title="Bremsstrahlung">bremsstrahlung</a>. More detailed understanding of the framework is obtained by studying the <a href="/wiki/Lagrangian_(field_theory)" title="Lagrangian (field theory)">Lagrangian density</a> of a field theory which encodes the information of its allowed particle interactions.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </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=History_of_classical_field_theory&action=edit&section=20" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/History_of_classical_mechanics" title="History of classical mechanics">History of classical mechanics</a></li> <li><a href="/wiki/Corpuscularianism" title="Corpuscularianism">Corpuscularianism</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=History_of_classical_field_theory&action=edit&section=21" title="Edit section: 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-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-:3-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-:3_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:3_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:3_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:3_1-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-:3_1-4"><sup><i><b>e</b></i></sup></a></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="CITEREFGuimarães2005" class="citation book cs1">Guimarães, Alberto Passos (2005). "A Stone with a Soul". <a rel="nofollow" class="external text" href="https://books.google.com/books?id=tdDaAAAAMAAJ&q=From+Lodestone+to+Supermagnets"><i>From Lodestone to Supermagnets: Understanding Magnetic Phenomena</i></a>. Wiley-VCH. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-527-40557-2" title="Special:BookSources/978-3-527-40557-2"><bdi>978-3-527-40557-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=A+Stone+with+a+Soul&rft.btitle=From+Lodestone+to+Supermagnets%3A+Understanding+Magnetic+Phenomena&rft.pub=Wiley-VCH&rft.date=2005&rft.isbn=978-3-527-40557-2&rft.aulast=Guimar%C3%A3es&rft.aufirst=Alberto+Passos&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DtdDaAAAAMAAJ%26q%3DFrom%2BLodestone%2Bto%2BSupermagnets&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+classical+field+theory" class="Z3988"></span></span> </li> <li id="cite_note-:1-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:1_2-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:1_2-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-:1_2-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-:1_2-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-:1_2-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-:1_2-7"><sup><i><b>h</b></i></sup></a> <a href="#cite_ref-:1_2-8"><sup><i><b>i</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCao2019" class="citation book cs1">Cao, Tian Yu (2019-10-03). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=vaCsDwAAQBAJ&q=Conceptual+developments+of+20th+century+field+theories"><i>Conceptual Development of 20th Century Field Theories</i></a>. 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(2006-08-03). "The History and Present Status of Quantum Field Theory in Curved Spacetime". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/0608018">gr-qc/0608018</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=The+History+and+Present+Status+of+Quantum+Field+Theory+in+Curved+Spacetime&rft.date=2006-08-03&rft_id=info%3Aarxiv%2Fgr-qc%2F0608018&rft.aulast=Wald&rft.aufirst=Robert+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+classical+field+theory" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFV.1995" class="citation book cs1">V., Schroeder, Daniel (1995). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/introductiontoqu0000pesk"><i>An introduction to quantum field theory</i></a></span>. Addison-Wesley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780201503975" title="Special:BookSources/9780201503975"><bdi>9780201503975</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/20393204">20393204</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+quantum+field+theory&rft.pub=Addison-Wesley&rft.date=1995&rft_id=info%3Aoclcnum%2F20393204&rft.isbn=9780201503975&rft.aulast=V.&rft.aufirst=Schroeder%2C+Daniel&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fintroductiontoqu0000pesk&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHistory+of+classical+field+theory" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite 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id="History_of_physics_(timeline)" style="font-size:114%;margin:0 4em"><a href="/wiki/History_of_physics" title="History of physics">History of physics</a> (<a href="/wiki/Timeline_of_fundamental_physics_discoveries" title="Timeline of fundamental physics discoveries">timeline</a>)</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Classical_physics" title="Classical physics">Classical physics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/History_of_astronomy" title="History of astronomy">Astronomy</a> <ul><li><a href="/wiki/Timeline_of_astronomy" title="Timeline of astronomy">timeline</a></li></ul></li> <li><a href="/wiki/History_of_electromagnetic_theory" title="History of electromagnetic theory">Electromagnetism</a> <ul><li><a href="/wiki/Timeline_of_electromagnetism_and_classical_optics" title="Timeline of electromagnetism and classical optics">timeline</a></li> <li><a href="/wiki/History_of_electrical_engineering" title="History of electrical engineering">Electrical engineering</a></li> <li><a href="/wiki/History_of_Maxwell%27s_equations" title="History of Maxwell's equations">Maxwell's equations</a></li></ul></li> <li><a href="/wiki/History_of_fluid_mechanics" title="History of fluid mechanics">Fluid mechanics</a> <ul><li><a href="/wiki/Timeline_of_fluid_and_continuum_mechanics" title="Timeline of fluid and continuum mechanics">timeline</a></li> <li><a href="/wiki/History_of_aerodynamics" title="History of aerodynamics">Aerodynamics</a></li></ul></li> <li><a class="mw-selflink selflink">Field theory</a></li> <li><a href="/wiki/History_of_gravitational_theory" title="History of gravitational theory">Gravitational theory</a> <ul><li><a href="/wiki/Timeline_of_gravitational_physics_and_relativity" title="Timeline of gravitational physics and relativity">timeline</a></li></ul></li> <li><a href="/wiki/History_of_materials_science" title="History of materials science">Material science</a> <ul><li><a href="/wiki/Timeline_of_materials_technology" title="Timeline of materials technology">timeline</a></li> <li><a href="/wiki/History_of_metamaterials" title="History of metamaterials">Metamaterials</a></li></ul></li> <li><a href="/wiki/History_of_classical_mechanics" title="History of classical mechanics">Mechanics</a> <ul><li><a href="/wiki/Timeline_of_classical_mechanics" title="Timeline of classical mechanics">timeline</a></li> <li><a href="/wiki/History_of_variational_principles_in_physics" title="History of variational principles in physics">Variational principles</a></li></ul></li> <li><a href="/wiki/History_of_optics" title="History of optics">Optics</a> <ul><li><a href="/wiki/History_of_spectroscopy" title="History of spectroscopy">Spectroscopy</a></li></ul></li> <li><a href="/wiki/History_of_thermodynamics" title="History of thermodynamics">Thermodynamics</a> <ul><li><a href="/wiki/Timeline_of_thermodynamics" title="Timeline of thermodynamics">timeline</a></li> <li><a href="/wiki/History_of_energy" title="History of energy">Energy</a></li> <li><a href="/wiki/History_of_entropy" title="History of entropy">Entropy</a></li> <li><a href="/wiki/History_of_perpetual_motion_machines" title="History of perpetual motion machines">Perpetual motion</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Modern_physics" title="Modern physics">Modern physics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Computational physics <ul><li><a href="/wiki/Timeline_of_computational_physics" title="Timeline of computational physics">timeline</a></li></ul></li> <li>Condensed matter <ul><li><a href="/wiki/Timeline_of_condensed_matter_physics" title="Timeline of condensed matter physics">timeline</a></li> <li><a href="/wiki/History_of_superconductivity" title="History of superconductivity">Superconductivity</a></li></ul></li> <li>Cosmology <ul><li><a href="/wiki/Timeline_of_cosmological_theories" title="Timeline of cosmological theories">timeline</a></li> <li><a href="/wiki/History_of_the_Big_Bang_theory" title="History of the Big Bang theory">Big Bang theory</a></li></ul></li> <li><a href="/wiki/History_of_general_relativity" title="History of general relativity">General relativity</a> <ul><li><a href="/wiki/Tests_of_general_relativity" title="Tests of general relativity">tests</a></li></ul></li> <li><a href="/wiki/History_of_geophysics" title="History of geophysics">Geophysics</a></li> <li>Nuclear physics <ul><li><a href="/wiki/Discovery_of_nuclear_fission" title="Discovery of nuclear fission">Fission</a></li> <li><a href="/wiki/History_of_nuclear_fusion" title="History of nuclear fusion">Fusion</a></li> <li><a href="/wiki/History_of_nuclear_power" title="History of nuclear power">Power</a></li> <li><a href="/wiki/History_of_nuclear_weapons" title="History of nuclear weapons">Weapons</a></li></ul></li> <li><a href="/wiki/History_of_quantum_mechanics" title="History of quantum mechanics">Quantum mechanics</a> <ul><li><a href="/wiki/Timeline_of_quantum_mechanics" title="Timeline of quantum mechanics">timeline</a></li> <li><a href="/wiki/History_of_atomic_theory" title="History of atomic theory">Atoms</a></li> <li><a href="/wiki/History_of_molecular_theory" title="History of molecular theory">Molecules</a></li> <li><a href="/wiki/History_of_quantum_field_theory" title="History of quantum field theory">Quantum field theory</a></li></ul></li> <li><a href="/wiki/History_of_subatomic_physics" title="History of subatomic physics">Subatomic physics</a> <ul><li><a href="/wiki/Timeline_of_atomic_and_subatomic_physics" title="Timeline of atomic and subatomic physics">timeline</a></li></ul></li> <li><a href="/wiki/History_of_special_relativity" title="History of special relativity">Special relativity</a> <ul><li><a href="/wiki/Timeline_of_special_relativity_and_the_speed_of_light" title="Timeline of special relativity and the speed of light">timeline</a></li> <li><a href="/wiki/History_of_Lorentz_transformations" title="History of Lorentz transformations">Lorentz transformations</a></li> <li><a href="/wiki/Tests_of_special_relativity" title="Tests of special relativity">tests</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Recent developments</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Quantum information <ul><li><a href="/wiki/Timeline_of_quantum_computing_and_communication" title="Timeline of quantum computing and communication">timeline</a></li></ul></li> <li><a href="/wiki/History_of_loop_quantum_gravity" title="History of loop quantum gravity">Loop quantum gravity</a></li> <li><a href="/wiki/History_of_nanotechnology" title="History of nanotechnology">Nanotechnology</a></li> <li><a href="/wiki/History_of_string_theory" title="History of string theory">String theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">On specific discoveries</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Discovery_of_cosmic_microwave_background_radiation" title="Discovery of cosmic microwave background radiation">Cosmic microwave background</a></li> <li><a href="/wiki/Discovery_of_graphene" title="Discovery of graphene">Graphene</a></li> <li><a href="/wiki/First_observation_of_gravitational_waves" title="First observation of gravitational waves">Gravitational waves</a></li> <li>Subatomic particles <ul><li><a href="/wiki/Timeline_of_particle_discoveries" title="Timeline of particle discoveries">timeline</a></li> <li><a href="/wiki/Search_for_the_Higgs_boson" title="Search for the Higgs boson">Higgs boson</a></li> <li><a href="/wiki/Discovery_of_the_neutron" title="Discovery of the neutron">Neutron</a></li></ul></li> <li><a href="/wiki/R%C3%B8mer%27s_determination_of_the_speed_of_light" title="Rømer's determination of the speed of light">Speed of light</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By periods</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Copernican_Revolution" title="Copernican Revolution">Copernican Revolution</a></li> <li><a href="/wiki/Golden_age_of_physics" title="Golden age of physics">Golden age of physics</a></li> <li><a href="/wiki/Golden_age_of_cosmology" title="Golden age of cosmology">Golden age of cosmology</a></li> <li><a href="/wiki/Physics_in_the_medieval_Islamic_world" title="Physics in the medieval Islamic world">Medieval Islamic world</a> <ul><li><a href="/wiki/Astronomy_in_the_medieval_Islamic_world" title="Astronomy in the medieval Islamic world">Astronomy</a></li></ul></li> <li><a href="/wiki/Noisy_intermediate-scale_quantum_era" title="Noisy intermediate-scale quantum era">Noisy intermediate-scale quantum era</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By groups</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Harvard_Computers" title="Harvard Computers">Harvard Computers</a></li> <li><a href="/wiki/The_Martians_(scientists)" title="The Martians (scientists)">The Martians</a></li> <li><a href="/wiki/Oxford_Calculators" title="Oxford Calculators">Oxford Calculators</a></li> <li><a href="/wiki/Via_Panisperna_boys" title="Via Panisperna boys">Via Panisperna boys</a></li> <li><a href="/wiki/Women_in_physics" title="Women in physics">Women in physics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Scientific disputes</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bohr%E2%80%93Einstein_debates" title="Bohr–Einstein debates">Bohr–Einstein</a></li> <li><a href="/wiki/Chandrasekhar%E2%80%93Eddington_dispute" title="Chandrasekhar–Eddington dispute">Chandrasekhar–Eddington</a></li> <li><a href="/wiki/Galileo_affair" title="Galileo affair">Galileo affair</a></li> <li><a href="/wiki/Leibniz%E2%80%93Newton_calculus_controversy" title="Leibniz–Newton calculus controversy">Leibniz–Newton</a></li> <li><a href="/wiki/Mechanical_equivalent_of_heat" title="Mechanical equivalent of heat">Joule–von Mayer</a></li> <li><a href="/wiki/Great_Debate_(astronomy)" title="Great Debate (astronomy)">Shapley–Curtis</a></li> <li>Relativity priority <ul><li><a href="/wiki/Relativity_priority_dispute" title="Relativity priority 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