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class="vector-toc-numb">2</span> <span>Variations of the experiment</span> </div> </a> <button aria-controls="toc-Variations_of_the_experiment-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 Variations of the experiment subsection</span> </button> <ul id="toc-Variations_of_the_experiment-sublist" class="vector-toc-list"> <li id="toc-Interference_from_individual_particles" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Interference_from_individual_particles"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Interference from individual particles</span> </div> </a> <ul id="toc-Interference_from_individual_particles-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mach-Zehnder_interferometer" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mach-Zehnder_interferometer"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Mach-Zehnder interferometer</span> </div> </a> <ul id="toc-Mach-Zehnder_interferometer-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-"Which-way"_experiments_and_the_principle_of_complementarity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#"Which-way"_experiments_and_the_principle_of_complementarity"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>"Which-way" experiments and the principle of complementarity</span> </div> </a> <ul id="toc-"Which-way"_experiments_and_the_principle_of_complementarity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Delayed_choice_and_quantum_eraser_variations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Delayed_choice_and_quantum_eraser_variations"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Delayed choice and quantum eraser variations</span> </div> </a> <ul id="toc-Delayed_choice_and_quantum_eraser_variations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Weak_measurement" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Weak_measurement"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Weak measurement</span> </div> </a> <ul id="toc-Weak_measurement-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_variations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_variations"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Other variations</span> </div> </a> <ul id="toc-Other_variations-sublist" class="vector-toc-list"> <li id="toc-Hydrodynamic_pilot_wave_analogs" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Hydrodynamic_pilot_wave_analogs"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6.1</span> <span>Hydrodynamic pilot wave analogs</span> </div> </a> <ul id="toc-Hydrodynamic_pilot_wave_analogs-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Double-slit_experiment_on_time" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Double-slit_experiment_on_time"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6.2</span> <span>Double-slit experiment on time</span> </div> </a> <ul id="toc-Double-slit_experiment_on_time-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Classical_wave-optics_formulation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Classical_wave-optics_formulation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Classical wave-optics formulation</span> </div> </a> <ul id="toc-Classical_wave-optics_formulation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Path-integral_formulation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Path-integral_formulation"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Path-integral formulation</span> </div> </a> <ul id="toc-Path-integral_formulation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Interpretations_of_the_experiment" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Interpretations_of_the_experiment"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Interpretations of the experiment</span> </div> </a> <button aria-controls="toc-Interpretations_of_the_experiment-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 Interpretations of the experiment subsection</span> </button> <ul id="toc-Interpretations_of_the_experiment-sublist" class="vector-toc-list"> <li id="toc-Standard_quantum_physics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Standard_quantum_physics"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Standard quantum physics</span> </div> </a> <ul id="toc-Standard_quantum_physics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Complementarity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Complementarity"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Complementarity</span> </div> </a> <ul id="toc-Complementarity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Copenhagen_interpretation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Copenhagen_interpretation"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Copenhagen interpretation</span> </div> </a> <ul id="toc-Copenhagen_interpretation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relational_interpretation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Relational_interpretation"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Relational interpretation</span> </div> </a> <ul id="toc-Relational_interpretation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Many-worlds_interpretation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Many-worlds_interpretation"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5</span> <span>Many-worlds interpretation</span> </div> </a> <ul id="toc-Many-worlds_interpretation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-De_Broglie–Bohm_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#De_Broglie–Bohm_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.6</span> <span>De Broglie–Bohm theory</span> </div> </a> <ul id="toc-De_Broglie–Bohm_theory-sublist" class="vector-toc-list"> </ul> </li> </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 class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <button aria-controls="toc-References-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 References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>External links</span> </div> </a> <button aria-controls="toc-External_links-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 External links subsection</span> </button> <ul id="toc-External_links-sublist" class="vector-toc-list"> <li id="toc-Interactive_animations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Interactive_animations"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Interactive animations</span> </div> </a> <ul id="toc-Interactive_animations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Single_particle_experiments" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Single_particle_experiments"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2</span> <span>Single particle experiments</span> </div> </a> <ul id="toc-Single_particle_experiments-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hydrodynamic_analog" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hydrodynamic_analog"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.3</span> <span>Hydrodynamic analog</span> </div> </a> <ul id="toc-Hydrodynamic_analog-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Computer_simulations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Computer_simulations"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.4</span> <span>Computer simulations</span> </div> </a> <ul id="toc-Computer_simulations-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Double-slit experiment</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 40 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-40" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">40 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Doppelspaltexperiment" title="Doppelspaltexperiment – Alemannic" lang="gsw" hreflang="gsw" data-title="Doppelspaltexperiment" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%AC%D8%B1%D8%A8%D8%A9_%D8%A7%D9%84%D8%B4%D9%82_%D8%A7%D9%84%D9%85%D8%B2%D8%AF%D9%88%D8%AC" title="تجربة الشق المزدوج – Arabic" lang="ar" hreflang="ar" data-title="تجربة الشق المزدوج" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A6%E0%A7%8D%E0%A6%AC%E0%A6%BF-%E0%A6%9A%E0%A6%BF%E0%A6%A1%E0%A6%BC_%E0%A6%AA%E0%A6%B0%E0%A7%80%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A6%A3" title="দ্বি-চিড় পরীক্ষণ – Bangla" lang="bn" hreflang="bn" data-title="দ্বি-চিড় পরীক্ষণ" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Experiment_de_la_doble_escletxa" title="Experiment de la doble escletxa – Catalan" lang="ca" hreflang="ca" data-title="Experiment de la doble escletxa" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Dvou-dvou%C5%A1t%C4%9Brbinov%C3%BD_experiment" title="Dvou-dvouštěrbinový experiment – Czech" lang="cs" hreflang="cs" data-title="Dvou-dvouštěrbinový experiment" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Dobbeltspalte-eksperiment" title="Dobbeltspalte-eksperiment – Danish" lang="da" hreflang="da" data-title="Dobbeltspalte-eksperiment" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Doppelspaltexperiment" title="Doppelspaltexperiment – German" lang="de" hreflang="de" data-title="Doppelspaltexperiment" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et badge-Q70894304 mw-list-item" title=""><a href="https://et.wikipedia.org/wiki/Kahe_pilu_katse" title="Kahe pilu katse – Estonian" lang="et" hreflang="et" data-title="Kahe pilu katse" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CE%B5%CE%AF%CF%81%CE%B1%CE%BC%CE%B1_%CF%84%CF%89%CE%BD_%CE%B4%CF%8D%CE%BF_%CF%83%CF%87%CE%B9%CF%83%CE%BC%CF%8E%CE%BD" title="Πείραμα των δύο σχισμών – Greek" lang="el" hreflang="el" data-title="Πείραμα των δύο σχισμών" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Experimento_de_la_doble_rendija" title="Experimento de la doble rendija – Spanish" lang="es" hreflang="es" data-title="Experimento de la doble rendija" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Zirrikitu_bikoitzaren_saiakuntza" title="Zirrikitu bikoitzaren saiakuntza – Basque" lang="eu" hreflang="eu" data-title="Zirrikitu bikoitzaren saiakuntza" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A2%D8%B2%D9%85%D8%A7%DB%8C%D8%B4_%D8%AF%D9%88_%D8%B4%DA%A9%D8%A7%D9%81" title="آزمایش دو شکاف – Persian" lang="fa" hreflang="fa" data-title="آزمایش دو شکاف" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr badge-Q70894304 mw-list-item" title=""><a href="https://fr.wikipedia.org/wiki/Exp%C3%A9rience_de_la_double_fente" title="Expérience de la double fente – French" lang="fr" hreflang="fr" data-title="Expérience de la double fente" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Experimento_da_dobre_fenda" title="Experimento da dobre fenda – Galician" lang="gl" hreflang="gl" data-title="Experimento da dobre fenda" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9D%B4%EC%A4%91%EC%8A%AC%EB%A6%BF_%EC%8B%A4%ED%97%98" title="이중슬릿 실험 – Korean" lang="ko" hreflang="ko" data-title="이중슬릿 실험" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BF%D6%80%D5%AF%D5%B6%D5%A1%D5%AF%D5%AB_%D5%B3%D5%A5%D5%B2%D6%84%D5%B8%D5%BE_%D6%83%D5%B8%D6%80%D5%B1" title="Կրկնակի ճեղքով փորձ – Armenian" lang="hy" hreflang="hy" data-title="Կրկնակի ճեղքով փորձ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%A6%E0%A5%8B_%E0%A4%9D%E0%A4%BF%E0%A4%B0%E0%A5%80_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AF%E0%A5%8B%E0%A4%97" title="दो झिरी प्रयोग – Hindi" lang="hi" hreflang="hi" data-title="दो झिरी प्रयोग" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Percobaan_celah_ganda" title="Percobaan celah ganda – Indonesian" lang="id" hreflang="id" data-title="Percobaan celah ganda" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Esperimento_della_doppia_fenditura" title="Esperimento della doppia fenditura – Italian" lang="it" hreflang="it" data-title="Esperimento della doppia fenditura" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A0%D7%99%D7%A1%D7%95%D7%99_%D7%A9%D7%A0%D7%99_%D7%94%D7%A1%D7%93%D7%A7%D7%99%D7%9D" title="ניסוי שני הסדקים – Hebrew" lang="he" hreflang="he" data-title="ניסוי שני הסדקים" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9D%E1%83%A0%E1%83%AD%E1%83%A0%E1%83%98%E1%83%9A%E1%83%9D%E1%83%95%E1%83%90%E1%83%9C%E1%83%98_%E1%83%94%E1%83%A5%E1%83%A1%E1%83%9E%E1%83%94%E1%83%A0%E1%83%98%E1%83%9B%E1%83%94%E1%83%9C%E1%83%A2%E1%83%98" title="ორჭრილოვანი ექსპერიმენტი – Georgian" lang="ka" hreflang="ka" data-title="ორჭრილოვანი ექსპერიმენტი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Dvigubo_ply%C5%A1io_eksperimentas" title="Dvigubo plyšio eksperimentas – Lithuanian" lang="lt" hreflang="lt" data-title="Dvigubo plyšio eksperimentas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/K%C3%A9tr%C3%A9s-k%C3%ADs%C3%A9rlet" title="Kétrés-kísérlet – Hungarian" lang="hu" hreflang="hu" data-title="Kétrés-kísérlet" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a 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.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">"Slit experiment" redirects here. For other uses, see <a href="/wiki/Slit_experiment_(disambiguation)" class="mw-disambig" title="Slit experiment (disambiguation)">Slit experiment (disambiguation)</a>.</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1237032888/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:255px;max-width:255px"><div class="trow"><div class="tsingle" style="width:253px;max-width:253px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Double-slit.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Double-slit.svg/251px-Double-slit.svg.png" decoding="async" width="251" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Double-slit.svg/377px-Double-slit.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Double-slit.svg/502px-Double-slit.svg.png 2x" data-file-width="512" data-file-height="245" /></a></span></div><div class="thumbcaption">Photons or matter (like electrons) produce an interference pattern when two slits are used</div></div></div><div class="trow"><div class="tsingle" style="width:253px;max-width:253px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Young%27s_slits.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/Young%27s_slits.jpg/251px-Young%27s_slits.jpg" decoding="async" width="251" height="69" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/Young%27s_slits.jpg/377px-Young%27s_slits.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/39/Young%27s_slits.jpg/502px-Young%27s_slits.jpg 2x" data-file-width="4267" data-file-height="1179" /></a></span></div><div class="thumbcaption">Light from a green laser passing through two slits 0.4 mm wide and 0.1 mm apart</div></div></div></div></div> <p>In <a href="/wiki/Modern_physics" title="Modern physics">modern physics</a>, the <b>double-slit experiment</b> demonstrates that light and matter can exhibit behavior of both classical <a href="/wiki/Particle" title="Particle">particles</a> and classical <a href="/wiki/Wave" title="Wave">waves</a>. This type of experiment was first performed by <a href="/wiki/Thomas_Young_(scientist)" title="Thomas Young (scientist)">Thomas Young</a> in 1801, as a demonstration of the wave behavior of visible light.<sup id="cite_ref-The_Bakerian_lecture_1-0" class="reference"><a href="#cite_note-The_Bakerian_lecture-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> In 1927, <a href="/wiki/Davisson%E2%80%93Germer_experiment" title="Davisson–Germer experiment">Davisson and Germer</a> and, independently, <a href="/wiki/George_Paget_Thomson" title="George Paget Thomson">George Paget Thomson</a> and his research student Alexander Reid<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> demonstrated that electrons show the same behavior, which was later extended to atoms and molecules.<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><sup id="cite_ref-medium.com_4-0" class="reference"><a href="#cite_note-medium.com-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Eibenberger_2013_pp._14696–14700_5-0" class="reference"><a href="#cite_note-Eibenberger_2013_pp._14696–14700-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Thomas Young's experiment with light was part of <a href="/wiki/Classical_physics" title="Classical physics">classical physics</a> long before the development of quantum mechanics and the concept of <a href="/wiki/Wave%E2%80%93particle_duality" title="Wave–particle duality">wave–particle duality</a>. He believed it demonstrated that the <a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Christiaan Huygens'</a> <a href="/wiki/Wave_theory_of_light" class="mw-redirect" title="Wave theory of light">wave theory of light</a> was correct, and his experiment is sometimes referred to as <a href="/wiki/Young%27s_interference_experiment" title="Young's interference experiment">Young's experiment</a><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> or Young's slits.<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> </p><p> The experiment belongs to a general class of "double path" experiments, in which a wave is split into two separate waves (the wave is typically made of many photons and better referred to as a wave front, not to be confused with the wave properties of the individual photon) that later combine into a single wave. Changes in the path-lengths of both waves result in a <a href="/wiki/Phase_shift" class="mw-redirect" title="Phase shift">phase shift</a>, creating an <a href="/wiki/Interference_pattern" class="mw-redirect" title="Interference pattern">interference pattern</a>. Another version is the <a href="/wiki/Mach%E2%80%93Zehnder_interferometer" title="Mach–Zehnder interferometer">Mach–Zehnder interferometer</a>, which splits the beam with a <a href="/wiki/Beam_splitter" title="Beam splitter">beam splitter</a>.<style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist 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rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"></p><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist nowraplinks" style="width:19.0em;"><tbody><tr><td class="sidebar-pretitle">Part of a series of articles about</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></th></tr><tr><td class="sidebar-image"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi mathvariant="normal">Ψ</mi> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi mathvariant="normal">Ψ</mi> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1799e4a910c7d26396922a20ef5ceec25ca1871c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:16.882ex; height:5.509ex;" alt="{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }"></span><div class="sidebar-caption" style="font-size:90%;padding-top:0.4em;font-style:italic;"><a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a></div></td></tr><tr><td class="sidebar-above hlist nowrap" style="display:block;margin-bottom:0.4em;"> <ul><li><a href="/wiki/Introduction_to_quantum_mechanics" title="Introduction to quantum mechanics">Introduction</a></li> <li><a href="/wiki/Glossary_of_elementary_quantum_mechanics" title="Glossary of elementary quantum mechanics">Glossary</a></li> <li><a href="/wiki/History_of_quantum_mechanics" title="History of quantum mechanics">History</a></li></ul></td></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Background</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"> <ul><li><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a></li> <li><a href="/wiki/Old_quantum_theory" title="Old quantum theory">Old quantum theory</a></li> <li><a href="/wiki/Bra%E2%80%93ket_notation" title="Bra–ket notation">Bra–ket notation</a></li></ul> <div class="hlist"> <ul><li><a href="/wiki/Hamiltonian_(quantum_mechanics)" title="Hamiltonian (quantum mechanics)">Hamiltonian</a></li> <li><a href="/wiki/Wave_interference" title="Wave interference">Interference</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Fundamentals</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li><a href="/wiki/Complementarity_(physics)" title="Complementarity (physics)">Complementarity</a></li> <li><a href="/wiki/Quantum_decoherence" title="Quantum decoherence">Decoherence</a></li> <li><a href="/wiki/Quantum_entanglement" title="Quantum entanglement">Entanglement</a></li> <li><a href="/wiki/Energy_level" title="Energy level">Energy level</a></li> <li><a href="/wiki/Measurement_in_quantum_mechanics" title="Measurement in quantum mechanics">Measurement</a></li> <li><a href="/wiki/Quantum_nonlocality" title="Quantum nonlocality">Nonlocality</a></li> <li><a href="/wiki/Quantum_number" title="Quantum number">Quantum number</a></li> <li><a href="/wiki/Quantum_state" title="Quantum state">State</a></li> <li><a href="/wiki/Quantum_superposition" title="Quantum superposition">Superposition</a></li> <li><a href="/wiki/Symmetry_in_quantum_mechanics" title="Symmetry in quantum mechanics">Symmetry</a></li> <li><a href="/wiki/Quantum_tunnelling" title="Quantum tunnelling">Tunnelling</a></li> <li><a href="/wiki/Uncertainty_principle" title="Uncertainty principle">Uncertainty</a></li> <li><a href="/wiki/Wave_function" title="Wave function">Wave function</a> <ul><li><a href="/wiki/Wave_function_collapse" title="Wave function collapse">Collapse</a></li></ul></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Experiments</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li><a href="/wiki/Bell_test" title="Bell test">Bell's inequality</a></li> <li><a href="/wiki/CHSH_inequality" title="CHSH inequality">CHSH inequality</a></li> <li><a href="/wiki/Davisson%E2%80%93Germer_experiment" title="Davisson–Germer experiment">Davisson–Germer</a></li> <li><a class="mw-selflink selflink">Double-slit</a></li> <li><a href="/wiki/Elitzur%E2%80%93Vaidman_bomb_tester" title="Elitzur–Vaidman bomb tester">Elitzur–Vaidman</a></li> <li><a href="/wiki/Franck%E2%80%93Hertz_experiment" title="Franck–Hertz experiment">Franck–Hertz</a></li> <li><a href="/wiki/Leggett_inequality" title="Leggett inequality">Leggett inequality</a></li> <li><a href="/wiki/Leggett%E2%80%93Garg_inequality" title="Leggett–Garg inequality">Leggett–Garg inequality</a></li> <li><a href="/wiki/Mach%E2%80%93Zehnder_interferometer" title="Mach–Zehnder interferometer">Mach–Zehnder</a></li> <li><a href="/wiki/Popper%27s_experiment" title="Popper's experiment">Popper</a></li></ul> </div> <ul><li><a href="/wiki/Quantum_eraser_experiment" title="Quantum eraser experiment">Quantum eraser</a> <ul><li><a href="/wiki/Delayed-choice_quantum_eraser" title="Delayed-choice quantum eraser">Delayed-choice</a></li></ul></li></ul> <div class="hlist"> <ul><li><a href="/wiki/Schr%C3%B6dinger%27s_cat" title="Schrödinger's cat">Schrödinger's cat</a></li> <li><a href="/wiki/Stern%E2%80%93Gerlach_experiment" title="Stern–Gerlach experiment">Stern–Gerlach</a></li> <li><a href="/wiki/Wheeler%27s_delayed-choice_experiment" title="Wheeler's delayed-choice experiment">Wheeler's delayed-choice</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Formulations</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"> <ul><li><a href="/wiki/Mathematical_formulation_of_quantum_mechanics" title="Mathematical formulation of quantum mechanics">Overview</a></li></ul> <div class="hlist"> <ul><li><a href="/wiki/Heisenberg_picture" title="Heisenberg picture">Heisenberg</a></li> <li><a href="/wiki/Interaction_picture" title="Interaction picture">Interaction</a></li> <li><a href="/wiki/Matrix_mechanics" title="Matrix mechanics">Matrix</a></li> <li><a href="/wiki/Phase-space_formulation" title="Phase-space formulation">Phase-space</a></li> <li><a href="/wiki/Schr%C3%B6dinger_picture" title="Schrödinger picture">Schrödinger</a></li> <li><a href="/wiki/Path_integral_formulation" title="Path integral formulation">Sum-over-histories (path integral)</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Equations</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li><a href="/wiki/Dirac_equation" title="Dirac equation">Dirac</a></li> <li><a href="/wiki/Klein%E2%80%93Gordon_equation" title="Klein–Gordon equation">Klein–Gordon</a></li> <li><a href="/wiki/Pauli_equation" title="Pauli equation">Pauli</a></li> <li><a href="/wiki/Rydberg_formula" title="Rydberg formula">Rydberg</a></li> <li><a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)"><a href="/wiki/Interpretations_of_quantum_mechanics" title="Interpretations of quantum mechanics">Interpretations</a></div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li><a href="/wiki/Quantum_Bayesianism" title="Quantum Bayesianism">Bayesian</a></li> <li><a href="/wiki/Consistent_histories" title="Consistent histories">Consistent histories</a></li> <li><a href="/wiki/Copenhagen_interpretation" title="Copenhagen interpretation">Copenhagen</a></li> <li><a href="/wiki/De_Broglie%E2%80%93Bohm_theory" title="De Broglie–Bohm theory">de Broglie–Bohm</a></li> <li><a href="/wiki/Ensemble_interpretation" title="Ensemble interpretation">Ensemble</a></li> <li><a href="/wiki/Hidden-variable_theory" title="Hidden-variable theory">Hidden-variable</a> <ul><li><a href="/wiki/Local_hidden-variable_theory" title="Local hidden-variable theory">Local</a> <ul><li><a href="/wiki/Superdeterminism" title="Superdeterminism">Superdeterminism</a></li></ul></li></ul></li> <li><a href="/wiki/Many-worlds_interpretation" title="Many-worlds interpretation">Many-worlds</a></li> <li><a href="/wiki/Objective-collapse_theory" title="Objective-collapse theory">Objective-collapse</a></li> <li><a href="/wiki/Quantum_logic" title="Quantum logic">Quantum logic</a></li> <li><a href="/wiki/Relational_quantum_mechanics" title="Relational quantum mechanics">Relational</a></li> <li><a href="/wiki/Transactional_interpretation" title="Transactional interpretation">Transactional</a></li> <li><a href="/wiki/Von_Neumann%E2%80%93Wigner_interpretation" title="Von Neumann–Wigner interpretation">Von Neumann–Wigner</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Advanced topics</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"> <ul><li><a href="/wiki/Relativistic_quantum_mechanics" title="Relativistic quantum mechanics">Relativistic quantum mechanics</a></li> <li><a href="/wiki/Quantum_field_theory" title="Quantum field theory">Quantum field theory</a></li> <li><a href="/wiki/Quantum_information_science" title="Quantum information science">Quantum information science</a></li> <li><a href="/wiki/Quantum_computing" title="Quantum computing">Quantum computing</a></li> <li><a href="/wiki/Quantum_chaos" title="Quantum chaos">Quantum chaos</a></li> <li><a href="/wiki/Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox" title="Einstein–Podolsky–Rosen paradox">EPR paradox</a></li> <li><a href="/wiki/Density_matrix" title="Density matrix">Density matrix</a></li> <li><a href="/wiki/Scattering_theory" class="mw-redirect" title="Scattering theory">Scattering theory</a></li> <li><a href="/wiki/Quantum_statistical_mechanics" title="Quantum statistical mechanics">Quantum statistical mechanics</a></li> <li><a href="/wiki/Quantum_machine_learning" title="Quantum machine learning">Quantum machine learning</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li><a href="/wiki/Yakir_Aharonov" title="Yakir Aharonov">Aharonov</a></li> <li><a href="/wiki/John_Stewart_Bell" title="John Stewart Bell">Bell</a></li> <li><a href="/wiki/Hans_Bethe" title="Hans Bethe">Bethe</a></li> <li><a href="/wiki/Patrick_Blackett" title="Patrick Blackett">Blackett</a></li> <li><a href="/wiki/Felix_Bloch" title="Felix Bloch">Bloch</a></li> <li><a href="/wiki/David_Bohm" title="David Bohm">Bohm</a></li> <li><a href="/wiki/Niels_Bohr" title="Niels Bohr">Bohr</a></li> <li><a href="/wiki/Max_Born" title="Max Born">Born</a></li> <li><a href="/wiki/Satyendra_Nath_Bose" title="Satyendra Nath Bose">Bose</a></li> <li><a href="/wiki/Louis_de_Broglie" title="Louis de Broglie">de Broglie</a></li> <li><a href="/wiki/Arthur_Compton" title="Arthur Compton">Compton</a></li> <li><a href="/wiki/Paul_Dirac" title="Paul Dirac">Dirac</a></li> <li><a href="/wiki/Clinton_Davisson" title="Clinton Davisson">Davisson</a></li> <li><a href="/wiki/Peter_Debye" title="Peter Debye">Debye</a></li> <li><a href="/wiki/Paul_Ehrenfest" title="Paul Ehrenfest">Ehrenfest</a></li> <li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/Hugh_Everett_III" title="Hugh Everett III">Everett</a></li> <li><a href="/wiki/Vladimir_Fock" title="Vladimir Fock">Fock</a></li> <li><a href="/wiki/Enrico_Fermi" title="Enrico Fermi">Fermi</a></li> <li><a href="/wiki/Richard_Feynman" title="Richard Feynman">Feynman</a></li> <li><a href="/wiki/Roy_J._Glauber" title="Roy J. Glauber">Glauber</a></li> <li><a href="/wiki/Martin_Gutzwiller" title="Martin Gutzwiller">Gutzwiller</a></li> <li><a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Heisenberg</a></li> <li><a href="/wiki/David_Hilbert" title="David Hilbert">Hilbert</a></li> <li><a href="/wiki/Pascual_Jordan" title="Pascual Jordan">Jordan</a></li> <li><a href="/wiki/Hans_Kramers" title="Hans Kramers">Kramers</a></li> <li><a href="/wiki/Willis_Lamb" title="Willis Lamb">Lamb</a></li> <li><a href="/wiki/Lev_Landau" title="Lev Landau">Landau</a></li> <li><a href="/wiki/Max_von_Laue" title="Max von Laue">Laue</a></li> <li><a href="/wiki/Henry_Moseley" title="Henry Moseley">Moseley</a></li> <li><a href="/wiki/Robert_Andrews_Millikan" title="Robert Andrews Millikan">Millikan</a></li> <li><a href="/wiki/Heike_Kamerlingh_Onnes" title="Heike Kamerlingh Onnes">Onnes</a></li> <li><a href="/wiki/Wolfgang_Pauli" title="Wolfgang Pauli">Pauli</a></li> <li><a href="/wiki/Max_Planck" title="Max Planck">Planck</a></li> <li><a href="/wiki/Isidor_Isaac_Rabi" title="Isidor Isaac Rabi">Rabi</a></li> <li><a href="/wiki/C._V._Raman" title="C. V. Raman">Raman</a></li> <li><a href="/wiki/Johannes_Rydberg" title="Johannes Rydberg">Rydberg</a></li> <li><a href="/wiki/Erwin_Schr%C3%B6dinger" title="Erwin Schrödinger">Schrödinger</a></li> <li><a href="/wiki/Michelle_Simmons" title="Michelle Simmons">Simmons</a></li> <li><a href="/wiki/Arnold_Sommerfeld" title="Arnold Sommerfeld">Sommerfeld</a></li> <li><a href="/wiki/John_von_Neumann" title="John von Neumann">von Neumann</a></li> <li><a href="/wiki/Hermann_Weyl" title="Hermann Weyl">Weyl</a></li> <li><a href="/wiki/Wilhelm_Wien" title="Wilhelm Wien">Wien</a></li> <li><a href="/wiki/Eugene_Wigner" title="Eugene Wigner">Wigner</a></li> <li><a href="/wiki/Pieter_Zeeman" title="Pieter Zeeman">Zeeman</a></li> <li><a href="/wiki/Anton_Zeilinger" title="Anton Zeilinger">Zeilinger</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-navbar" style="border-top:1px solid #aaa;padding-top:0.1em;"><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:Quantum_mechanics" title="Template:Quantum mechanics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Quantum_mechanics" title="Template talk:Quantum mechanics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Quantum_mechanics" title="Special:EditPage/Template:Quantum mechanics"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>In the basic version of this experiment, a <a href="/wiki/Coherence_(physics)" title="Coherence (physics)">coherent light source</a>, such as a <a href="/wiki/Laser" title="Laser">laser</a> beam, illuminates a plate pierced by two parallel slits, and the light passing through the slits is observed on a screen behind the plate.<sup id="cite_ref-Lederman_8-0" class="reference"><a href="#cite_note-Lederman-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Feynman_9-0" class="reference"><a href="#cite_note-Feynman-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> The wave nature of light causes the light waves passing through the two slits to <a href="/wiki/Interference_(wave_propagation)" class="mw-redirect" title="Interference (wave propagation)">interfere</a>, producing bright and dark bands on the screen – a result that would not be expected if light consisted of classical particles.<sup id="cite_ref-Lederman_8-1" class="reference"><a href="#cite_note-Lederman-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><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> However, the light is always found to be absorbed at the screen at discrete points, as individual particles (not waves); the interference pattern appears via the varying density of these particle hits on the screen.<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> Furthermore, versions of the experiment that include detectors at the slits find that each detected <a href="/wiki/Photon" title="Photon">photon</a> passes through one slit (as would a classical particle), and not through both slits (as would a wave).<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><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><sup id="cite_ref-Müller-Kirsten_14-0" class="reference"><a href="#cite_note-Müller-Kirsten-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Plotnitsky_15-0" class="reference"><a href="#cite_note-Plotnitsky-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Rae_16-0" class="reference"><a href="#cite_note-Rae-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> However, <a href="#Which_way">such experiments</a> demonstrate that particles do not form the interference pattern if one detects which slit they pass through. These results demonstrate the principle of <a href="/wiki/Wave%E2%80%93particle_duality" title="Wave–particle duality">wave–particle duality</a>.<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><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><p>Other atomic-scale entities, such as <a href="/wiki/Electrons" class="mw-redirect" title="Electrons">electrons</a>, are found to exhibit the same behavior when fired towards a double slit.<sup id="cite_ref-Feynman_9-1" class="reference"><a href="#cite_note-Feynman-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Additionally, the detection of individual discrete impacts is observed to be inherently probabilistic, which is inexplicable using <a href="/wiki/Classical_mechanics" title="Classical mechanics">classical mechanics</a>.<sup id="cite_ref-Feynman_9-2" class="reference"><a href="#cite_note-Feynman-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>The experiment can be done with entities much larger than electrons and photons, although it becomes more difficult as size increases. The largest entities for which the double-slit experiment has been performed were <a href="/wiki/Molecule" title="Molecule">molecules</a> that each comprised 2000 atoms (whose total mass was 25,000 <a href="/wiki/Atomic_mass_units" class="mw-redirect" title="Atomic mass units">atomic mass units</a>).<sup id="cite_ref-Yaakov_Y._Fein_1242–1245_19-0" class="reference"><a href="#cite_note-Yaakov_Y._Fein_1242–1245-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>The double-slit experiment (and its variations) has become a classic for its clarity in expressing the central puzzles of quantum mechanics. <a href="/wiki/Richard_Feynman" title="Richard Feynman">Richard Feynman</a> called it "a phenomenon which is impossible […] to explain in any <a href="/wiki/Classical_mechanics" title="Classical mechanics">classical way</a>, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery [of quantum mechanics]."<sup id="cite_ref-Feynman_9-3" class="reference"><a href="#cite_note-Feynman-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=1" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Single_slit_and_double_slit2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Single_slit_and_double_slit2.jpg/350px-Single_slit_and_double_slit2.jpg" decoding="async" width="350" height="264" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Single_slit_and_double_slit2.jpg/525px-Single_slit_and_double_slit2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/c/c2/Single_slit_and_double_slit2.jpg 2x" data-file-width="560" data-file-height="422" /></a><figcaption>Same double-slit assembly (0.7 mm between slits); in top image, one slit is closed. In the single-slit image, a <a href="/wiki/Diffraction_pattern" class="mw-redirect" title="Diffraction pattern">diffraction pattern</a> (the faint spots on either side of the main band) forms due to the nonzero width of the slit. This diffraction pattern is also seen in the double-slit image, but with many smaller interference fringes.</figcaption></figure> <p>If light consisted strictly of ordinary or <a href="/wiki/Classical_mechanics" title="Classical mechanics">classical</a> particles, and these particles were fired in a straight line through a slit and allowed to strike a screen on the other side, we would expect to see a pattern corresponding to the size and shape of the slit. However, when this "single-slit experiment" is actually performed, the pattern on the screen is a <a href="/wiki/Diffraction_pattern" class="mw-redirect" title="Diffraction pattern">diffraction pattern</a> in which the light is spread out. The smaller the slit, the greater the angle of spread. The top portion of the image shows the central portion of the pattern formed when a red laser illuminates a slit and, if one looks carefully, two faint side bands. More bands can be seen with a more highly refined apparatus. <a href="/wiki/Diffraction" title="Diffraction">Diffraction</a> explains the pattern as being the result of the interference of light waves from the slit. </p><p>If one illuminates two parallel slits, the light from the two slits again interferes. Here the interference is a more pronounced pattern with a series of alternating light and dark bands. The width of the bands is a property of the frequency of the illuminating light.<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> (See the bottom photograph to the right.) </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Young_diffraction.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/Young_diffraction.svg/220px-Young_diffraction.svg.png" decoding="async" width="220" height="110" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/Young_diffraction.svg/330px-Young_diffraction.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/61/Young_diffraction.svg/440px-Young_diffraction.svg.png 2x" data-file-width="695" data-file-height="348" /></a><figcaption>Young's drawing of diffraction</figcaption></figure> <p>When <a href="/wiki/Thomas_Young_(scientist)" title="Thomas Young (scientist)">Thomas Young</a> (1773–1829) first demonstrated this phenomenon, it indicated that light consists of waves, as the distribution of brightness can be explained by the alternately additive and subtractive interference of <a href="/wiki/Wavefront" title="Wavefront">wavefronts</a>.<sup id="cite_ref-Feynman_9-4" class="reference"><a href="#cite_note-Feynman-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Young's experiment, performed in the early 1800s, played a crucial role in the understanding of the wave theory of light, vanquishing the <a href="/wiki/Corpuscular_theory_of_light" title="Corpuscular theory of light">corpuscular theory of light</a> proposed by <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a>, which had been the accepted model of light propagation in the 17th and 18th centuries. </p><p>However, the later discovery of the <a href="/wiki/Photoelectric_effect" title="Photoelectric effect">photoelectric effect</a> demonstrated that under different circumstances, light can behave as if it is composed of discrete particles. These seemingly contradictory discoveries made it necessary to go beyond classical physics and take into account the <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum</a> nature of light. </p><p>Feynman was fond of saying that all of quantum mechanics can be gleaned from carefully thinking through the implications of this single experiment.<sup id="cite_ref-Greene_1999_21-0" class="reference"><a href="#cite_note-Greene_1999-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> He also proposed (as a thought experiment) that if detectors were placed before each slit, the interference pattern would disappear.<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> </p><p>The <a href="/wiki/Englert%E2%80%93Greenberger_duality_relation" class="mw-redirect" title="Englert–Greenberger duality relation">Englert–Greenberger duality relation</a> provides a detailed treatment of the mathematics of double-slit interference in the context of quantum mechanics. </p><p>A low-intensity double-slit experiment was first performed by <a href="/wiki/Geoffrey_Ingram_Taylor" class="mw-redirect" title="Geoffrey Ingram Taylor">G. I. Taylor</a> in 1909,<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> by reducing the level of incident light until photon emission/absorption events were mostly non-overlapping. <span class="anchor" id="Claus_Jönsson"></span> A slit interference experiment was not performed with anything other than light until 1961, when <a href="/wiki/Claus_J%C3%B6nsson" title="Claus Jönsson">Claus Jönsson</a> of the <a href="/wiki/University_of_T%C3%BCbingen" title="University of Tübingen">University of Tübingen</a> performed it with coherent electron beams and multiple slits.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> In 1974, the Italian physicists Pier Giorgio Merli, Gian Franco Missiroli, and <a href="/wiki/Giulio_Pozzi" title="Giulio Pozzi">Giulio Pozzi</a> performed a related experiment using single electrons from a coherent source and a biprism beam splitter, showing the statistical nature of the buildup of the interference pattern, as predicted by quantum theory.<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> In 2002, the single-electron version of the experiment was voted "the most beautiful experiment" by readers of <i><a href="/wiki/Physics_World" title="Physics World">Physics World</a>.</i><sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> Since that time a number of related experiments have been published, with a little controversy.<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><p>In 2012, Stefano Frabboni and co-workers sent single electrons onto nanofabricated slits (about 100 nm wide) and, by detecting the transmitted electrons with a single-electron detector, they could show the build-up of a double-slit interference pattern.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> Many related experiments involving the coherent interference have been performed; they are the basis of modern electron diffraction, microscopy and high resolution imaging.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p><p>In 2018, single particle interference was demonstrated for antimatter in the <a rel="nofollow" class="external text" href="https://www.positron.fisi.polimi.it/">Positron Laboratory</a> (L-NESS, <a href="/wiki/Politecnico_di_Milano" class="mw-redirect" title="Politecnico di Milano">Politecnico di Milano</a>) of Rafael Ferragut in <a href="/wiki/Como" title="Como">Como</a> (<a href="/wiki/Italy" title="Italy">Italy</a>), by a group led by Marco Giammarchi.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Variations_of_the_experiment">Variations of the experiment</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=2" title="Edit section: Variations of the experiment"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Interference_from_individual_particles">Interference from individual particles</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=3" title="Edit section: Interference from individual particles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An important version of this experiment involves single particle detection. Illuminating the double-slit with a low intensity results in single particles being detected as white dots on the screen. Remarkably, however, an interference pattern emerges when these particles are allowed to build up one by one (see the image below). </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237032888/mw-parser-output/.tmulti"><div class="thumb tmulti tnone center"><div class="thumbinner multiimageinner" style="width:312px;max-width:312px"><div class="trow"><div class="tsingle" style="width:310px;max-width:310px"><div class="thumbimage" style="border:none;;height:47px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Roger_Bach_et_al_2013_New_J._Phys._15_033018_Figure_3_cropped_to_top_frame.jpg" class="mw-file-description"><img alt="Electron diffraction pattern" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Roger_Bach_et_al_2013_New_J._Phys._15_033018_Figure_3_cropped_to_top_frame.jpg/308px-Roger_Bach_et_al_2013_New_J._Phys._15_033018_Figure_3_cropped_to_top_frame.jpg" decoding="async" width="308" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/8/88/Roger_Bach_et_al_2013_New_J._Phys._15_033018_Figure_3_cropped_to_top_frame.jpg 1.5x" data-file-width="324" data-file-height="50" /></a></span></div></div></div><div class="trow"><div class="tsingle" style="width:310px;max-width:310px"><div class="thumbimage" style="border:none;;height:138px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Electron_buildup_movie_from_%22Controlled_double-slit_electron_diffraction%22_Roger_Bach_et_al_2013_New_J._Phys._15_033018.gif" class="mw-file-description"><img alt="Dots slowly filling an interference pattern." src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Electron_buildup_movie_from_%22Controlled_double-slit_electron_diffraction%22_Roger_Bach_et_al_2013_New_J._Phys._15_033018.gif/308px-Electron_buildup_movie_from_%22Controlled_double-slit_electron_diffraction%22_Roger_Bach_et_al_2013_New_J._Phys._15_033018.gif" decoding="async" width="308" height="139" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Electron_buildup_movie_from_%22Controlled_double-slit_electron_diffraction%22_Roger_Bach_et_al_2013_New_J._Phys._15_033018.gif/462px-Electron_buildup_movie_from_%22Controlled_double-slit_electron_diffraction%22_Roger_Bach_et_al_2013_New_J._Phys._15_033018.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Electron_buildup_movie_from_%22Controlled_double-slit_electron_diffraction%22_Roger_Bach_et_al_2013_New_J._Phys._15_033018.gif/616px-Electron_buildup_movie_from_%22Controlled_double-slit_electron_diffraction%22_Roger_Bach_et_al_2013_New_J._Phys._15_033018.gif 2x" data-file-width="800" data-file-height="360" /></a></span></div><div class="thumbcaption">Experimental electron double slit diffraction pattern.<sup id="cite_ref-Bach_Pope_Liou_Batelaan_2013_p=033018_34-0" class="reference"><a href="#cite_note-Bach_Pope_Liou_Batelaan_2013_p=033018-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> Across the middle of the image at the top, the intensity alternates from high to low, showing interference in the signal from the two slits. Bottom: movie of the pattern being built up dot-by-dot. <b>Click on the thumbnail to enlarge the movie.</b></div></div></div></div></div> <p>This demonstrates the <a href="/wiki/Wave%E2%80%93particle_duality" title="Wave–particle duality">wave–particle duality</a>, which states that all matter exhibits both wave and particle properties: The particle is measured as a single pulse at a single position, while the modulus squared of the wave describes the <a href="/wiki/Probability_amplitude" title="Probability amplitude">probability</a> of detecting the particle at a specific place on the screen giving a statistical interference pattern.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> This phenomenon has been shown to occur with photons,<sup id="cite_ref-Ananthaswamy_36-0" class="reference"><a href="#cite_note-Ananthaswamy-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> electrons,<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> atoms, and even some molecules: with <a href="/wiki/Buckminsterfullerene" title="Buckminsterfullerene">buckminsterfullerene</a> (<span class="chemf nowrap">C<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">60</sub></span></span></span>) in 2001,<sup id="cite_ref-buckyballs_38-0" class="reference"><a href="#cite_note-buckyballs-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> with 2 molecules of 430 atoms (<span class="chemf nowrap">C<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">60</sub></span></span>(C<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">12</sub></span></span>F<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">25</sub></span></span>)<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">10</sub></span></span></span> and <span class="chemf nowrap">C<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">168</sub></span></span>H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">94</sub></span></span>F<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">152</sub></span></span>O<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">8</sub></span></span>N<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span>S<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span></span>) in 2011,<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> and with molecules of up to 2000 atoms in 2019.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> In addition to interference patterns built up from single particles, up to 4 <a href="/wiki/Quantum_entanglement" title="Quantum entanglement">entangled</a> photons can also show interference patterns.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> </p><p><span class="anchor" id="Which_way"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Mach-Zehnder_interferometer">Mach-Zehnder interferometer</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=4" title="Edit section: Mach-Zehnder interferometer"><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/Mach%E2%80%93Zehnder_interferometer" title="Mach–Zehnder interferometer">Mach–Zehnder interferometer</a></div> <p>The Mach–Zehnder interferometer can be seen as a simplified version of the double-slit experiment.<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> Instead of propagating through free space after the two slits, and hitting any position in an extended screen, in the interferometer the photons can only propagate via two paths, and hit two discrete photodetectors. This makes it possible to describe it via simple linear algebra in dimension 2, rather than differential equations. </p><p>A photon emitted by the laser hits the first beam splitter and is then in a superposition between the two possible paths. In the second beam splitter these paths interfere, causing the photon to hit the photodetector on the right with probability one, and the photodetector on the bottom with probability zero.<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> Blocking one of the paths, or equivalently detecting the presence of a photon on a path eliminates interference between the paths: both photodetectors will be hit with probability 1/2. This indicates that after the first beam splitter the photon does not take one path or another, but rather exists in a quantum superposition of the two paths.<sup id="cite_ref-vedral_47-0" class="reference"><a href="#cite_note-vedral-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id=""Which-way"_experiments_and_the_principle_of_complementarity"><span id=".22Which-way.22_experiments_and_the_principle_of_complementarity"></span>"Which-way" experiments and the principle of complementarity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=5" title="Edit section: "Which-way" experiments and the principle of complementarity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A well-known <a href="/wiki/Thought_experiment" title="Thought experiment">thought experiment</a> predicts that if particle detectors are positioned at the slits, showing through which slit a photon goes, the interference pattern will disappear.<sup id="cite_ref-Feynman_9-5" class="reference"><a href="#cite_note-Feynman-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> This which-way experiment illustrates the <a href="/wiki/Complementarity_(physics)" title="Complementarity (physics)">complementarity</a> principle that photons can behave as either particles or waves, but cannot be observed as both at the same time.<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> Despite the importance of this thought experiment in the history of quantum mechanics (for example, see the discussion on <a href="/wiki/Bohr%E2%80%93Einstein_debates#Post-revolution:_First_stage" title="Bohr–Einstein debates">Einstein's version of this experiment</a>), technically feasible realizations of this experiment were not proposed until the 1970s.<sup id="cite_ref-Bartell1980_51-0" class="reference"><a href="#cite_note-Bartell1980-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> (Naive implementations of the textbook thought experiment are not possible because photons cannot be detected without absorbing the photon.) Currently, multiple experiments have been performed illustrating various aspects of complementarity.<sup id="cite_ref-Zeilinger1999_52-0" class="reference"><a href="#cite_note-Zeilinger1999-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> </p><p>An experiment performed in 1987<sup id="cite_ref-Mittelstaedt_53-0" class="reference"><a href="#cite_note-Mittelstaedt-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> produced results that demonstrated that partial information could be obtained regarding which path a particle had taken without destroying the interference altogether. This "wave-particle trade-off" takes the form of an <a href="/wiki/Wave%E2%80%93particle_duality_relation" title="Wave–particle duality relation">inequality</a> relating the visibility of the interference pattern and the distinguishability of the which-way paths.<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Delayed_choice_and_quantum_eraser_variations">Delayed choice and quantum eraser variations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=6" title="Edit section: Delayed choice and quantum eraser variations"><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/Delayed-choice_quantum_eraser" title="Delayed-choice quantum eraser">Delayed-choice quantum eraser</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Wheeler_telescopes_set-up.svg" class="mw-file-description"><img alt="Wheeler's Delayed Choice Experiment" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Wheeler_telescopes_set-up.svg/220px-Wheeler_telescopes_set-up.svg.png" decoding="async" width="220" height="189" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Wheeler_telescopes_set-up.svg/330px-Wheeler_telescopes_set-up.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/42/Wheeler_telescopes_set-up.svg/440px-Wheeler_telescopes_set-up.svg.png 2x" data-file-width="442" data-file-height="379" /></a><figcaption>A diagram of Wheeler's delayed choice experiment, showing the principle of determining the path of the photon after it passes through the slit</figcaption></figure> <p><a href="/wiki/Wheeler%27s_delayed-choice_experiment" title="Wheeler's delayed-choice experiment">Wheeler's delayed-choice experiments</a> demonstrate that extracting "which path" information after a particle passes through the slits can seem to retroactively alter its previous behavior at the slits. </p><p><a href="/wiki/Quantum_eraser" class="mw-redirect" title="Quantum eraser">Quantum eraser</a> experiments demonstrate that wave behavior can be restored by erasing or otherwise making permanently unavailable the "which path" information. </p><p>A simple do-it-at-home illustration of the quantum eraser phenomenon was given in an article in <i>Scientific American</i>.<sup id="cite_ref-Hillmer2007_56-0" class="reference"><a href="#cite_note-Hillmer2007-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> If one sets polarizers before each slit with their axes orthogonal to each other, the interference pattern will be eliminated. The polarizers can be considered as introducing which-path information to each beam. Introducing a third polarizer in front of the detector with an axis of 45° relative to the other polarizers "erases" this information, allowing the interference pattern to reappear. This can also be accounted for by considering the light to be a classical wave,<sup id="cite_ref-Hillmer2007_56-1" class="reference"><a href="#cite_note-Hillmer2007-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 91">: 91 </span></sup> and also when using circular polarizers and single photons.<sup id="cite_ref-Chiao1995_57-0" class="reference"><a href="#cite_note-Chiao1995-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 6">: 6 </span></sup> Implementations of the polarizers using <a href="/wiki/Quantum_entanglement" title="Quantum entanglement">entangled</a> photon pairs have no classical explanation.<sup id="cite_ref-Chiao1995_57-1" class="reference"><a href="#cite_note-Chiao1995-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Weak_measurement">Weak measurement</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=7" title="Edit section: Weak measurement"><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/Weak_measurement" title="Weak measurement">Weak measurement</a></div> <p>In a highly publicized experiment in 2012, researchers claimed to have identified the path each particle had taken without any adverse effects at all on the interference pattern generated by the particles.<sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> In order to do this, they used a setup such that particles coming to the screen were not from a point-like source, but from a source with two intensity maxima. However, commentators such as Svensson<sup id="cite_ref-Svensson2013_59-0" class="reference"><a href="#cite_note-Svensson2013-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> have pointed out that there is in fact no conflict between the <a href="/wiki/Weak_measurement" title="Weak measurement">weak measurements</a> performed in this variant of the double-slit experiment and the <a href="/wiki/Heisenberg_uncertainty_principle" class="mw-redirect" title="Heisenberg uncertainty principle">Heisenberg uncertainty principle</a>. Weak measurement followed by post-selection did not allow simultaneous position and momentum measurements for each individual particle, but rather allowed measurement of the average trajectory of the particles that arrived at different positions. In other words, the experimenters were creating a statistical map of the full trajectory landscape.<sup id="cite_ref-Svensson2013_59-1" class="reference"><a href="#cite_note-Svensson2013-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Other_variations">Other variations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=8" title="Edit section: Other variations"><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:Double-slit_wall_sm.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c1/Double-slit_wall_sm.jpg" decoding="async" width="187" height="178" class="mw-file-element" data-file-width="187" data-file-height="178" /></a><figcaption>A laboratory double-slit assembly; distance between top posts is approximately 2.5 cm (one inch).</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Plasmonic_Young%27s_double_slits_interference.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Plasmonic_Young%27s_double_slits_interference.png/220px-Plasmonic_Young%27s_double_slits_interference.png" decoding="async" width="220" height="97" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Plasmonic_Young%27s_double_slits_interference.png/330px-Plasmonic_Young%27s_double_slits_interference.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Plasmonic_Young%27s_double_slits_interference.png/440px-Plasmonic_Young%27s_double_slits_interference.png 2x" data-file-width="930" data-file-height="411" /></a><figcaption>Near-field intensity distribution patterns for plasmonic slits with equal widths (A) and non-equal widths (B).</figcaption></figure> <p>In 1967, Pfleegor and Mandel demonstrated two-source interference using two separate lasers as light sources.<sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> </p><p>It was shown experimentally in 1972 that in a double-slit system where only one slit was open at any time, interference was nonetheless observed provided the path difference was such that the detected photon could have come from either slit.<sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-63" class="reference"><a href="#cite_note-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> The experimental conditions were such that the photon density in the system was much less than 1. </p><p>In 1991, Carnal and Mlynek performed the classic Young's double slit experiment with <a href="/wiki/Metastability" title="Metastability">metastable</a> helium atoms passing through micrometer-scale slits in gold foil.<sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-65" class="reference"><a href="#cite_note-65"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> </p><p>In 1999, a quantum interference experiment (using a diffraction grating, rather than two slits) was successfully performed with buckyball molecules (each of which comprises 60 carbon atoms).<sup id="cite_ref-buckyballs_38-1" class="reference"><a href="#cite_note-buckyballs-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-66" class="reference"><a href="#cite_note-66"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup> A buckyball is large enough (diameter about 0.7 <a href="/wiki/Nanometre" title="Nanometre">nm</a>, nearly half a million times larger than a proton) to be seen in an <a href="/wiki/Electron_microscope" title="Electron microscope">electron microscope</a>. </p><p>In 2002, an electron field emission source was used to demonstrate the double-slit experiment. In this experiment, a coherent electron wave was emitted from two closely located emission sites on the needle apex, which acted as double slits, splitting the wave into two coherent electron waves in a vacuum. The interference pattern between the two electron waves could then be observed.<sup id="cite_ref-67" class="reference"><a href="#cite_note-67"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup> In 2017, researchers performed the double-slit experiment using light-induced field electron emitters. With this technique, emission sites can be optically selected on a scale of ten nanometers. By selectively deactivating (closing) one of the two emissions (slits), researchers were able to show that the interference pattern disappeared.<sup id="cite_ref-68" class="reference"><a href="#cite_note-68"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup> </p><p>In 2005, E. R. Eliel presented an experimental and theoretical study of the optical transmission of a thin metal screen perforated by two subwavelength slits, separated by many optical wavelengths. The total intensity of the far-field double-slit pattern is shown to be reduced or enhanced as a function of the wavelength of the incident light beam.<sup id="cite_ref-69" class="reference"><a href="#cite_note-69"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup> </p><p>In 2012, researchers at the <a href="/wiki/University_of_Nebraska%E2%80%93Lincoln" title="University of Nebraska–Lincoln">University of Nebraska–Lincoln</a> performed the double-slit experiment with electrons as described by <a href="/wiki/Richard_Feynman" title="Richard Feynman">Richard Feynman</a>, using new instruments that allowed control of the transmission of the two slits and the monitoring of single-electron detection events. Electrons were fired by an electron gun and passed through one or two slits of 62 nm wide × 4 μm tall.<sup id="cite_ref-70" class="reference"><a href="#cite_note-70"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup> </p><p>In 2013, a quantum interference experiment (using diffraction gratings, rather than two slits) was successfully performed with molecules that each comprised 810 atoms (whose total mass was over 10,000 <a href="/wiki/Atomic_mass_units" class="mw-redirect" title="Atomic mass units">atomic mass units</a>).<sup id="cite_ref-medium.com_4-1" class="reference"><a href="#cite_note-medium.com-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Eibenberger_2013_pp._14696–14700_5-1" class="reference"><a href="#cite_note-Eibenberger_2013_pp._14696–14700-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> The record was raised to 2000 atoms (25,000 amu) in 2019.<sup id="cite_ref-Yaakov_Y._Fein_1242–1245_19-1" class="reference"><a href="#cite_note-Yaakov_Y._Fein_1242–1245-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Hydrodynamic_pilot_wave_analogs">Hydrodynamic pilot wave analogs</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=9" title="Edit section: Hydrodynamic pilot wave analogs"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Hydrodynamic_quantum_analogs" title="Hydrodynamic quantum analogs">Hydrodynamic analogs</a> have been developed that can recreate various aspects of quantum mechanical systems, including single-particle interference through a double-slit.<sup id="cite_ref-Bush2015_71-0" class="reference"><a href="#cite_note-Bush2015-71"><span class="cite-bracket">[</span>71<span class="cite-bracket">]</span></a></sup> A silicone oil droplet, bouncing along the surface of a liquid, self-propels via resonant interactions with its own wave field. The droplet gently sloshes the liquid with every bounce. At the same time, ripples from past bounces affect its course. The droplet's interaction with its own ripples, which form what is known as a <a href="/wiki/Pilot_wave" class="mw-redirect" title="Pilot wave">pilot wave</a>, causes it to exhibit behaviors previously thought to be peculiar to elementary particles – including behaviors customarily taken as evidence that elementary particles are spread through space like waves, without any specific location, until they are measured.<sup id="cite_ref-Bush2010_72-0" class="reference"><a href="#cite_note-Bush2010-72"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-73" class="reference"><a href="#cite_note-73"><span class="cite-bracket">[</span>73<span class="cite-bracket">]</span></a></sup> </p><p>Behaviors mimicked via this hydrodynamic pilot-wave system include quantum single particle diffraction,<sup id="cite_ref-CouderFort2012_74-0" class="reference"><a href="#cite_note-CouderFort2012-74"><span class="cite-bracket">[</span>74<span class="cite-bracket">]</span></a></sup> tunneling, quantized orbits, orbital level splitting, spin, and multimodal statistics. It is also possible to infer uncertainty relations and exclusion principles. Videos are available illustrating various features of this system. <a href="#External_links">(See the External links.)</a> </p><p>However, more complicated systems that involve two or more particles in superposition are not amenable to such a simple, classically intuitive explanation.<sup id="cite_ref-Baggott,_Jim_2011_pp._76_75-0" class="reference"><a href="#cite_note-Baggott,_Jim_2011_pp._76-75"><span class="cite-bracket">[</span>75<span class="cite-bracket">]</span></a></sup> Accordingly, no hydrodynamic analog of entanglement has been developed.<sup id="cite_ref-Bush2015_71-1" class="reference"><a href="#cite_note-Bush2015-71"><span class="cite-bracket">[</span>71<span class="cite-bracket">]</span></a></sup> Nevertheless, optical analogs are possible.<sup id="cite_ref-76" class="reference"><a href="#cite_note-76"><span class="cite-bracket">[</span>76<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Double-slit_experiment_on_time">Double-slit experiment on time</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=10" title="Edit section: Double-slit experiment on time"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 2023, an experiment was reported recreating an interference pattern in time by shining a <a href="/wiki/Pump_laser" class="mw-redirect" title="Pump laser">pump laser</a> pulse at a screen coated in <a href="/wiki/Indium_tin_oxide" title="Indium tin oxide">indium tin oxide (ITO)</a> which would alter the properties of the electrons within the material due to the <a href="/wiki/Kerr_effect" title="Kerr effect">Kerr effect</a>, changing it from transparent to reflective for around 200 femtoseconds long where a subsequent probe laser beam hitting the ITO screen would then see this temporary change in optical properties as a slit in time and two of them as a double slit with a phase difference adding up destructively or constructively on each frequency component resulting in an interference pattern.<sup id="cite_ref-:0_77-0" class="reference"><a href="#cite_note-:0-77"><span class="cite-bracket">[</span>77<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-78" class="reference"><a href="#cite_note-78"><span class="cite-bracket">[</span>78<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_79-0" class="reference"><a href="#cite_note-:1-79"><span class="cite-bracket">[</span>79<span class="cite-bracket">]</span></a></sup> Similar results have been obtained classically on water waves.<sup id="cite_ref-:0_77-1" class="reference"><a href="#cite_note-:0-77"><span class="cite-bracket">[</span>77<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_79-1" class="reference"><a href="#cite_note-:1-79"><span class="cite-bracket">[</span>79<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Classical_wave-optics_formulation">Classical wave-optics formulation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=11" title="Edit section: Classical wave-optics formulation"><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:Doubleslit3Dspectrum.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Doubleslit3Dspectrum.gif/220px-Doubleslit3Dspectrum.gif" decoding="async" width="220" height="225" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/3/33/Doubleslit3Dspectrum.gif 1.5x" data-file-width="293" data-file-height="300" /></a><figcaption>Two-slit diffraction pattern with an incident plane wave</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Double_slit_interference.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Double_slit_interference.png/220px-Double_slit_interference.png" decoding="async" width="220" height="236" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Double_slit_interference.png/330px-Double_slit_interference.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Double_slit_interference.png/440px-Double_slit_interference.png 2x" data-file-width="1406" data-file-height="1510" /></a><figcaption>Photo of the double-slit interference of sunlight.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Doubleslit.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Doubleslit.svg/200px-Doubleslit.svg.png" decoding="async" width="200" height="182" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Doubleslit.svg/300px-Doubleslit.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Doubleslit.svg/400px-Doubleslit.svg.png 2x" data-file-width="514" data-file-height="467" /></a><figcaption>Two slits are illuminated by a plane wave, showing the path difference.</figcaption></figure> <p>Much of the behaviour of light can be modelled using classical wave theory. The <a href="/wiki/Huygens%E2%80%93Fresnel_principle" title="Huygens–Fresnel principle">Huygens–Fresnel principle</a> is one such model; it states that each point on a wavefront generates a secondary wavelet, and that the disturbance at any subsequent point can be found by <a href="/wiki/Superposition_principle" title="Superposition principle">summing</a> the contributions of the individual wavelets at that point. This summation needs to take into account the <a href="/wiki/Phase_(waves)" title="Phase (waves)">phase</a> as well as the <a href="/wiki/Amplitude" title="Amplitude">amplitude</a> of the individual wavelets. Only the <a href="/wiki/Intensity_(physics)" title="Intensity (physics)">intensity</a> of a light field can be measured—this is proportional to the square of the amplitude. </p><p>In the double-slit experiment, the two slits are illuminated by the quasi-monochromatic light of a single laser. If the width of the slits is small enough (much less than the wavelength of the laser light), the slits diffract the light into cylindrical waves. These two cylindrical wavefronts are superimposed, and the amplitude, and therefore the intensity, at any point in the combined wavefronts depends on both the magnitude and the phase of the two wavefronts. The difference in phase between the two waves is determined by the difference in the distance travelled by the two waves. </p><p>If the viewing distance is large compared with the separation of the slits (the <a href="/wiki/Far_field" class="mw-redirect" title="Far field">far field</a>), the phase difference can be found using the geometry shown in the figure below right. The path difference between two waves travelling at an angle <span class="texhtml">θ</span> is given by: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d\sin \theta \approx d\theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> <mo>≈</mo> <mi>d</mi> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d\sin \theta \approx d\theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30ba078c07833be521d4d3594755598c8ed78334" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.341ex; height:2.176ex;" alt="{\displaystyle d\sin \theta \approx d\theta }"></span></dd></dl> <p>Where d is the distance between the two slits. When the two waves are in phase, i.e. the path difference is equal to an integral number of wavelengths, the summed amplitude, and therefore the summed intensity is maximum, and when they are in anti-phase, i.e. the path difference is equal to half a wavelength, one and a half wavelengths, etc., then the two waves cancel and the summed intensity is zero. This effect is known as <a href="/wiki/Interference_(optics)" class="mw-redirect" title="Interference (optics)">interference</a>. The interference fringe maxima occur at angles </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~d\theta _{n}=n\lambda ,~n=0,1,2,\ldots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>d</mi> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mi>n</mi> <mi>λ</mi> <mo>,</mo> <mtext> </mtext> <mi>n</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ~d\theta _{n}=n\lambda ,~n=0,1,2,\ldots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/974c817b5a1a5fa973410b4fb888cfe0d7b69760" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:25.374ex; height:2.509ex;" alt="{\displaystyle ~d\theta _{n}=n\lambda ,~n=0,1,2,\ldots }"></span></dd></dl> <p>where λ is the <a href="/wiki/Wavelength" title="Wavelength">wavelength</a> of the light. The angular spacing of the fringes, <span class="texhtml">θ<sub><i>f</i></sub></span>, is given by </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta _{f}\approx \lambda /d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo>≈</mo> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta _{f}\approx \lambda /d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9872d99313d6b0c9b9cfe4ea71cc4f3053a83e13" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.059ex; height:3.009ex;" alt="{\displaystyle \theta _{f}\approx \lambda /d}"></span></dd></dl> <p>The spacing of the fringes at a distance <span class="texhtml"><i>z</i></span> from the slits is given by </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~w=z\theta _{f}=z\lambda /d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>w</mi> <mo>=</mo> <mi>z</mi> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mi>z</mi> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ~w=z\theta _{f}=z\lambda /d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9165c4f8985e6ba6cbacccf50b194d3756119cd0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:16.578ex; height:3.009ex;" alt="{\displaystyle ~w=z\theta _{f}=z\lambda /d}"></span></dd></dl> <p>For example, if two slits are separated by 0.5 mm (<span class="texhtml"><i>d</i></span>), and are illuminated with a 0.6 μm wavelength laser (<span class="texhtml">λ</span>), then at a distance of 1 m (<span class="texhtml"><i>z</i></span>), the spacing of the fringes will be 1.2 mm. </p><p>If the width of the slits <span class="texhtml"><i>b</i></span> is appreciable compared to the wavelength, the <a href="/wiki/Fraunhofer_diffraction" title="Fraunhofer diffraction">Fraunhofer diffraction</a> equation is needed to determine the intensity of the diffracted light as follows:<sup id="cite_ref-80" class="reference"><a href="#cite_note-80"><span class="cite-bracket">[</span>80<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}I(\theta )&\propto \cos ^{2}\left[{\frac {\pi d\sin \theta }{\lambda }}\right]~\mathrm {sinc} ^{2}\left[{\frac {\pi b\sin \theta }{\lambda }}\right]\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>I</mi> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>∝</mo> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>π</mi> <mi>d</mi> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> </mrow> <mi>λ</mi> </mfrac> </mrow> <mo>]</mo> </mrow> <mtext> </mtext> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>π</mi> <mi>b</mi> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> </mrow> <mi>λ</mi> </mfrac> </mrow> <mo>]</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}I(\theta )&\propto \cos ^{2}\left[{\frac {\pi d\sin \theta }{\lambda }}\right]~\mathrm {sinc} ^{2}\left[{\frac {\pi b\sin \theta }{\lambda }}\right]\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5fb832693cac4bc3093639a4c6ccf7916e76a06a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:38.897ex; height:6.176ex;" alt="{\displaystyle {\begin{aligned}I(\theta )&\propto \cos ^{2}\left[{\frac {\pi d\sin \theta }{\lambda }}\right]~\mathrm {sinc} ^{2}\left[{\frac {\pi b\sin \theta }{\lambda }}\right]\end{aligned}}}"></span></dd></dl> <p>where the <a href="/wiki/Sinc_function" title="Sinc function">sinc function</a> is defined as sinc(<i>x</i>) = sin(<i>x</i>)/<i>x</i> for <i>x</i> ≠ 0, and sinc(0) = 1. </p><p>This is illustrated in the figure above, where the first pattern is the diffraction pattern of a single slit, given by the <span class="texhtml">sinc</span> function in this equation, and the second figure shows the combined intensity of the light diffracted from the two slits, where the <span class="texhtml">cos</span> function represents the fine structure, and the coarser structure represents diffraction by the individual slits as described by the <span class="texhtml">sinc</span> function. </p><p>Similar calculations for the <a href="/wiki/Near_and_far_field" title="Near and far field">near field</a> can be made by applying the <a href="/wiki/Fresnel_diffraction" title="Fresnel diffraction">Fresnel diffraction</a> equation, which implies that as the plane of observation gets closer to the plane in which the slits are located, the diffraction patterns associated with each slit decrease in size, so that the area in which interference occurs is reduced, and may vanish altogether when there is no overlap in the two diffracted patterns.<sup id="cite_ref-81" class="reference"><a href="#cite_note-81"><span class="cite-bracket">[</span>81<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Path-integral_formulation">Path-integral formulation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=12" title="Edit section: Path-integral formulation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Wiener_process_3d.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Wiener_process_3d.png/200px-Wiener_process_3d.png" decoding="async" width="200" height="195" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Wiener_process_3d.png/300px-Wiener_process_3d.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Wiener_process_3d.png/400px-Wiener_process_3d.png 2x" data-file-width="904" data-file-height="883" /></a><figcaption>One of an infinite number of equally likely paths used in the Feynman path integral (see also: <a href="/wiki/Wiener_process" title="Wiener process">Wiener process</a>)</figcaption></figure> <p>The double-slit experiment can illustrate the <a href="/wiki/Path_integral_formulation" title="Path integral formulation">path integral formulation</a> of quantum mechanics provided by Feynman.<sup id="cite_ref-82" class="reference"><a href="#cite_note-82"><span class="cite-bracket">[</span>82<span class="cite-bracket">]</span></a></sup> The path integral formulation replaces the classical notion of a single, unique trajectory for a system, with a sum over all possible trajectories. The trajectories are added together by using <a href="/wiki/Functional_integration" title="Functional integration">functional integration</a>. </p><p>Each path is considered equally likely, and thus contributes the same amount. However, the <a href="/wiki/Phase_(waves)" title="Phase (waves)">phase</a> of this contribution at any given point along the path is determined by the <a href="/wiki/Action_(physics)" title="Action (physics)">action</a> along the path: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\text{path}}(x,y,z,t)=e^{iS(x,y,z,t)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>path</mtext> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>S</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\text{path}}(x,y,z,t)=e^{iS(x,y,z,t)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/837d6046cb81fe91b6fc9d2a2fde65b024253832" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:26.403ex; height:3.509ex;" alt="{\displaystyle A_{\text{path}}(x,y,z,t)=e^{iS(x,y,z,t)}}"></span> </p><p>All these contributions are then added together, and the <a href="/wiki/Magnitude_(mathematics)" title="Magnitude (mathematics)">magnitude</a> of the final result is <a href="/wiki/Square_(algebra)" title="Square (algebra)">squared</a>, to get the probability distribution for the position of a particle: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p(x,y,z,t)\propto \left\vert \int _{\text{all paths}}e^{iS(x,y,z,t)}\right\vert ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>∝</mo> <msup> <mrow> <mo>|</mo> <mrow> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>all paths</mtext> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>S</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mrow> <mo>|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p(x,y,z,t)\propto \left\vert \int _{\text{all paths}}e^{iS(x,y,z,t)}\right\vert ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cfbd48f4128b98517b4317f059ffc709c8402dc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; margin-left: -0.089ex; width:32.911ex; height:7.009ex;" alt="{\displaystyle p(x,y,z,t)\propto \left\vert \int _{\text{all paths}}e^{iS(x,y,z,t)}\right\vert ^{2}}"></span> </p><p>As is always the case when calculating <a href="/wiki/Probability" title="Probability">probability</a>, the results must then be <a href="/wiki/Normalizing_constant" title="Normalizing constant">normalized</a> by imposing: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \iiint _{\text{all space}}p(x,y,z,t)\,dV=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∭</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>all space</mtext> </mrow> </msub> <mi>p</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>V</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \iiint _{\text{all space}}p(x,y,z,t)\,dV=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/91e931663d0d5f30b932f27124a7067a380ea6f8" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:28.624ex; height:6.009ex;" alt="{\displaystyle \iiint _{\text{all space}}p(x,y,z,t)\,dV=1}"></span> </p><p>The probability distribution of the outcome is the normalized square of the norm of the <a href="/wiki/Superposition_principle" title="Superposition principle">superposition</a>, over all paths from the point of origin to the final point, of <a href="/wiki/Wave" title="Wave">waves</a> <a href="/wiki/Wave_propagation" class="mw-redirect" title="Wave propagation">propagating</a> <a href="/wiki/Proportionality_(mathematics)" title="Proportionality (mathematics)">proportionally</a> to the action along each path. The differences in the cumulative action along the different paths (and thus the relative phases of the contributions) produces the <a href="/wiki/Interference_(wave_propagation)" class="mw-redirect" title="Interference (wave propagation)">interference pattern</a> observed by the double-slit experiment. Feynman stressed that his formulation is merely a mathematical description, not an attempt to describe a real process that we can measure. </p> <div class="mw-heading mw-heading2"><h2 id="Interpretations_of_the_experiment">Interpretations of the experiment</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=13" title="Edit section: Interpretations of the experiment"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Like the <a href="/wiki/Schr%C3%B6dinger%27s_cat" title="Schrödinger's cat">Schrödinger's cat</a> <a href="/wiki/Thought_experiment" title="Thought experiment">thought experiment</a>, the double-slit experiment is often used to highlight the differences and similarities between the various <a href="/wiki/Interpretations_of_quantum_mechanics" title="Interpretations of quantum mechanics">interpretations of quantum mechanics</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Standard_quantum_physics">Standard quantum physics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=14" title="Edit section: Standard quantum physics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The standard interpretation of the double slit experiment is that the pattern is a wave phenomenon, representing interference between two probability amplitudes, one for each slit. Low intensity experiments demonstrate that the pattern is filled in one particle detection at a time. Any change to the apparatus designed to detect a particle at a particular slit alters the probability amplitudes and the interference disappears.<sup id="cite_ref-Zeilinger1999_52-1" class="reference"><a href="#cite_note-Zeilinger1999-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: S298">: S298 </span></sup> This interpretation is independent of any conscious observer.<sup id="cite_ref-83" class="reference"><a href="#cite_note-83"><span class="cite-bracket">[</span>83<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap">: <span title="Page / location: S281
Quotation: "The analysis of some interference experiments confronts us with fundamental questions of interpretation and brings out that the quantum state reflects not what we know about the system, but rather what is knowable in principle. This avoids any reference to consciousness in the interpretation of the state."" class="tooltip tooltip-dashed" style="border-bottom: 1px dashed;">S281</span> </sup> </p> <div class="mw-heading mw-heading3"><h3 id="Complementarity">Complementarity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=15" title="Edit section: Complementarity"><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/Complementarity_(physics)" title="Complementarity (physics)">Complementarity (physics)</a></div> <p><a href="/wiki/Niels_Bohr" title="Niels Bohr">Niels Bohr</a> interpreted quantum experiments like the double-slit experiment using the concept of complementarity.<sup id="cite_ref-Faye-Stanford_84-0" class="reference"><a href="#cite_note-Faye-Stanford-84"><span class="cite-bracket">[</span>84<span class="cite-bracket">]</span></a></sup> In Bohr's view quantum systems are not classical, but measurements can only give classical results. Certain pairs of classical properties will never be observed in a quantum system simultaneously: the interference pattern of waves in the double slit experiment will disappear if particles are detected at the slits. Modern quantitative versions of the concept allow for a continuous tradeoff between the visibility of the interference fringes and the probability of particle detection at a slit.<sup id="cite_ref-85" class="reference"><a href="#cite_note-85"><span class="cite-bracket">[</span>85<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-86" class="reference"><a href="#cite_note-86"><span class="cite-bracket">[</span>86<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Copenhagen_interpretation">Copenhagen interpretation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=16" title="Edit section: Copenhagen interpretation"><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/Copenhagen_interpretation" title="Copenhagen interpretation">Copenhagen interpretation</a></div> <p>The <a href="/wiki/Copenhagen_interpretation" title="Copenhagen interpretation">Copenhagen interpretation</a> is a collection of views about the meaning of <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>, stemming from the work of <a href="/wiki/Niels_Bohr" title="Niels Bohr">Niels Bohr</a>, <a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Werner Heisenberg</a>, <a href="/wiki/Max_Born" title="Max Born">Max Born</a>, and others. The term "Copenhagen interpretation" was apparently coined by Heisenberg during the 1950s to refer to ideas developed in the 1925–1927 period, glossing over his disagreements with Bohr.<sup id="cite_ref-Faye-Stanford_84-1" class="reference"><a href="#cite_note-Faye-Stanford-84"><span class="cite-bracket">[</span>84<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-camilleri2015_87-0" class="reference"><a href="#cite_note-camilleri2015-87"><span class="cite-bracket">[</span>87<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-88" class="reference"><a href="#cite_note-88"><span class="cite-bracket">[</span>88<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Mermin_2017_89-0" class="reference"><a href="#cite_note-Mermin_2017-89"><span class="cite-bracket">[</span>89<span class="cite-bracket">]</span></a></sup> Consequently, there is no definitive historical statement of what the interpretation entails. Features common across versions of the Copenhagen interpretation include the idea that quantum mechanics is intrinsically <a href="/wiki/Indeterminism" title="Indeterminism">indeterministic</a>, with probabilities calculated using the <a href="/wiki/Born_rule" title="Born rule">Born rule</a>, and some form of <a href="/wiki/Complementarity_(physics)" title="Complementarity (physics)">complementarity</a> principle.<sup id="cite_ref-omnes1999_90-0" class="reference"><a href="#cite_note-omnes1999-90"><span class="cite-bracket">[</span>90<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 41–54">: 41–54 </span></sup> Moreover, the act of "observing" or "measuring" an object is irreversible, and no truth can be attributed to an object, <a href="/wiki/Counterfactual_definiteness" title="Counterfactual definiteness">except according to the results of its measurement</a>. In the Copenhagen interpretation, complementarity means a particular experiment can demonstrate particle behavior (passing through a definite slit) or wave behavior (interference), but not both at the same time.<sup id="cite_ref-omnes1999_90-1" class="reference"><a href="#cite_note-omnes1999-90"><span class="cite-bracket">[</span>90<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap">: <span title="Page / location: 49
Quotation: "We may speak of an electron by using the language of waves when it crosses two slits in an interfering device, and we speak of the same electron as a particle when it is detected, but we cannot use the two modes of speaking at the same time."" class="tooltip tooltip-dashed" style="border-bottom: 1px dashed;">49</span> </sup><sup id="cite_ref-91" class="reference"><a href="#cite_note-91"><span class="cite-bracket">[</span>91<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-peres_92-0" class="reference"><a href="#cite_note-peres-92"><span class="cite-bracket">[</span>92<span class="cite-bracket">]</span></a></sup> In a Copenhagen-type view, the question of which slit a particle travels through has no meaning when there is no detector.<sup id="cite_ref-omnes_93-0" class="reference"><a href="#cite_note-omnes-93"><span class="cite-bracket">[</span>93<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-94" class="reference"><a href="#cite_note-94"><span class="cite-bracket">[</span>94<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Relational_interpretation">Relational interpretation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=17" title="Edit section: Relational interpretation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>According to the <a href="/wiki/Relational_quantum_mechanics" title="Relational quantum mechanics">relational interpretation of quantum mechanics</a>, first proposed by <a href="/wiki/Carlo_Rovelli" title="Carlo Rovelli">Carlo Rovelli</a>,<sup id="cite_ref-95" class="reference"><a href="#cite_note-95"><span class="cite-bracket">[</span>95<span class="cite-bracket">]</span></a></sup> observations such as those in the double-slit experiment result specifically from the interaction between the <a href="/wiki/Observer_(quantum_physics)" title="Observer (quantum physics)">observer</a> (measuring device) and the object being observed (physically interacted with), not any absolute property possessed by the object. In the case of an electron, if it is initially "observed" at a particular slit, then the observer–particle (photon–electron) interaction includes information about the electron's position. This partially constrains the particle's eventual location at the screen. If it is "observed" (measured with a photon) not at a particular slit but rather at the screen, then there is no "which path" information as part of the interaction, so the electron's "observed" position on the screen is determined strictly by its probability function. This makes the resulting pattern on the screen the same as if each individual electron had passed through both slits.<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. (September 2023)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Many-worlds_interpretation">Many-worlds interpretation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=18" title="Edit section: Many-worlds interpretation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As with Copenhagen, there are multiple variants of the <a href="/wiki/Many-worlds_interpretation" title="Many-worlds interpretation">many-worlds interpretation</a>. The unifying theme is that physical reality is identified with a wavefunction, and this wavefunction always evolves unitarily, i.e., following the Schrödinger equation with no collapses.<sup id="cite_ref-96" class="reference"><a href="#cite_note-96"><span class="cite-bracket">[</span>96<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-vaidman_stanfordencyclopedia_97-0" class="reference"><a href="#cite_note-vaidman_stanfordencyclopedia-97"><span class="cite-bracket">[</span>97<span class="cite-bracket">]</span></a></sup> Consequently, there are many parallel universes, which only interact with each other through interference. <a href="/wiki/David_Deutsch" title="David Deutsch">David Deutsch</a> argues that the way to understand the double-slit experiment is that in each universe the particle travels through a specific slit, but its motion is affected by interference with particles in other universes, and this interference creates the observable fringes.<sup id="cite_ref-98" class="reference"><a href="#cite_note-98"><span class="cite-bracket">[</span>98<span class="cite-bracket">]</span></a></sup> David Wallace, another advocate of the many-worlds interpretation, writes that in the familiar setup of the double-slit experiment the two paths are not sufficiently separated for a description in terms of parallel universes to make sense.<sup id="cite_ref-99" class="reference"><a href="#cite_note-99"><span class="cite-bracket">[</span>99<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="De_Broglie–Bohm_theory"><span id="De_Broglie.E2.80.93Bohm_theory"></span>De Broglie–Bohm theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=19" title="Edit section: De Broglie–Bohm theory"><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/De_Broglie%E2%80%93Bohm_theory" title="De Broglie–Bohm theory">de Broglie–Bohm theory</a></div> <p>An alternative to the standard understanding of quantum mechanics, the <a href="/wiki/De_Broglie%E2%80%93Bohm_theory" title="De Broglie–Bohm theory">De Broglie–Bohm theory</a> states that particles also have precise locations at all times, and that their velocities are defined by the wave-function. So while a single particle will travel through one particular slit in the double-slit experiment, the so-called "pilot wave" that influences it will travel through both. The two slit de Broglie-Bohm trajectories were first calculated by Chris Dewdney while working with Chris Philippidis and Basil Hiley at Birkbeck College (London).<sup id="cite_ref-100" class="reference"><a href="#cite_note-100"><span class="cite-bracket">[</span>100<span class="cite-bracket">]</span></a></sup> The de Broglie-Bohm theory produces the same statistical results as standard quantum mechanics, but dispenses with many of its conceptual difficulties by adding complexity through an <i>ad hoc</i> quantum potential to guide the particles.<sup id="cite_ref-101" class="reference"><a href="#cite_note-101"><span class="cite-bracket">[</span>101<span class="cite-bracket">]</span></a></sup> </p><p>While the model is in many ways similar to <a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a>, it is known to fail for relativistic cases<sup id="cite_ref-102" class="reference"><a href="#cite_note-102"><span class="cite-bracket">[</span>102<span class="cite-bracket">]</span></a></sup> and does not account for features such as particle creation or annihilation in <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a>. Many authors such as nobel laureates <a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Werner Heisenberg</a>,<sup id="cite_ref-103" class="reference"><a href="#cite_note-103"><span class="cite-bracket">[</span>103<span class="cite-bracket">]</span></a></sup> Sir <a href="/wiki/Anthony_James_Leggett" title="Anthony James Leggett">Anthony James Leggett</a><sup id="cite_ref-104" class="reference"><a href="#cite_note-104"><span class="cite-bracket">[</span>104<span class="cite-bracket">]</span></a></sup> and Sir <a href="/wiki/Roger_Penrose" title="Roger Penrose">Roger Penrose</a><sup id="cite_ref-105" class="reference"><a href="#cite_note-105"><span class="cite-bracket">[</span>105<span class="cite-bracket">]</span></a></sup> have criticized it for not adding anything new. </p><p>More complex variants of this type of approach have appeared, for instance the <i>three wave hypothesis</i><sup id="cite_ref-106" class="reference"><a href="#cite_note-106"><span class="cite-bracket">[</span>106<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-107" class="reference"><a href="#cite_note-107"><span class="cite-bracket">[</span>107<span class="cite-bracket">]</span></a></sup> of <a href="/wiki/Ryszard_Horodecki" title="Ryszard Horodecki">Ryszard Horodecki</a> as well as other complicated combinations of de Broglie and Compton waves.<sup id="cite_ref-108" class="reference"><a href="#cite_note-108"><span class="cite-bracket">[</span>108<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-109" class="reference"><a href="#cite_note-109"><span class="cite-bracket">[</span>109<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-110" class="reference"><a href="#cite_note-110"><span class="cite-bracket">[</span>110<span class="cite-bracket">]</span></a></sup> To date there is no evidence that these are useful. </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237032888/mw-parser-output/.tmulti"><div class="thumb tmulti tnone center"><div class="thumbinner multiimageinner" style="width:892px;max-width:892px"><div class="trow"><div class="theader">Bohmian trajectories</div></div><div class="trow"><div class="tsingle" style="width:242px;max-width:242px"><div class="thumbimage" style="height:217px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Doppelspalt.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Doppelspalt.svg/240px-Doppelspalt.svg.png" decoding="async" width="240" height="217" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Doppelspalt.svg/360px-Doppelspalt.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/02/Doppelspalt.svg/480px-Doppelspalt.svg.png 2x" data-file-width="249" data-file-height="225" /></a></span></div><div class="thumbcaption">Trajectories of particles in De Broglie–Bohm theory in the double-slit experiment.</div></div><div class="tsingle" style="width:318px;max-width:318px"><div class="thumbimage" style="height:217px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:100_trajectories_guided_by_the_wave_function.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/100_trajectories_guided_by_the_wave_function.png/316px-100_trajectories_guided_by_the_wave_function.png" decoding="async" width="316" height="217" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/100_trajectories_guided_by_the_wave_function.png/474px-100_trajectories_guided_by_the_wave_function.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/69/100_trajectories_guided_by_the_wave_function.png/632px-100_trajectories_guided_by_the_wave_function.png 2x" data-file-width="2000" data-file-height="1375" /></a></span></div><div class="thumbcaption">100 trajectories guided by the wave function. In De Broglie-Bohm's theory, a particle is represented, at any time, by a wave function <i>and</i> a position (center of mass). This is a kind of augmented reality compared to the standard interpretation.</div></div><div class="tsingle" style="width:326px;max-width:326px"><div class="thumbimage" style="height:217px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Interference_electrons_double-slit_at_10cm.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Interference_electrons_double-slit_at_10cm.png/324px-Interference_electrons_double-slit_at_10cm.png" decoding="async" width="324" height="217" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Interference_electrons_double-slit_at_10cm.png/486px-Interference_electrons_double-slit_at_10cm.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/69/Interference_electrons_double-slit_at_10cm.png/648px-Interference_electrons_double-slit_at_10cm.png 2x" data-file-width="1512" data-file-height="1012" /></a></span></div><div class="thumbcaption">Numerical simulation of the double-slit experiment with electrons. Figure on the left: evolution (from left to right) of the intensity of the electron beam at the exit of the slits (left) up to the detection screen located 10 cm after the slits (right). The higher the intensity, the more the color is light blue – Figure in the center: impacts of the electrons observed on the screen – Figure on the right: intensity of the electrons in the <a href="/wiki/Fraunhofer_diffraction" title="Fraunhofer diffraction">far field</a> approximation (on the screen). Numerical data from Claus Jönsson's experiment (1961). Photons, atoms and molecules follow a similar evolution.</div></div></div></div></div> <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=Double-slit_experiment&action=edit&section=20" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 26em;"> <ul><li><a href="/wiki/Aharonov-Bohm_effect" class="mw-redirect" title="Aharonov-Bohm effect">Aharonov-Bohm effect</a></li> <li><a href="/wiki/Complementarity_(physics)" title="Complementarity (physics)">Complementarity (physics)</a></li> <li><a href="/wiki/Delayed-choice_quantum_eraser" title="Delayed-choice quantum eraser">Delayed-choice quantum eraser</a></li> <li><a href="/wiki/Diffraction_from_slits" title="Diffraction from slits">Diffraction from slits</a></li> <li><a href="/wiki/Dual-polarization_interferometry" title="Dual-polarization interferometry">Dual-polarization interferometry</a></li> <li><a href="/wiki/Elitzur%E2%80%93Vaidman_bomb_tester" title="Elitzur–Vaidman bomb tester">Elitzur–Vaidman bomb tester</a></li> <li><a href="/wiki/N-slit_interferometer" title="N-slit interferometer">N-slit interferometer</a></li> <li><a href="/wiki/Matter_wave" title="Matter wave">Matter wave</a></li> <li><a href="/wiki/Photon_polarization" title="Photon polarization">Photon polarization</a></li> <li><a href="/wiki/Quantum_coherence" class="mw-redirect" title="Quantum coherence">Quantum coherence</a></li> <li><a href="/wiki/Schr%C3%B6dinger%27s_cat" title="Schrödinger's cat">Schrödinger's cat</a></li> <li><a href="/wiki/Young%27s_interference_experiment" title="Young's interference experiment">Young's interference experiment</a></li> <li><a href="/wiki/Measurement_problem" title="Measurement problem">Measurement problem</a></li> <li><a href="/wiki/Hydrodynamic_quantum_analogs" title="Hydrodynamic quantum analogs">Hydrodynamic quantum analogs</a></li> <li><a href="/wiki/Pilot_wave_theory" title="Pilot wave theory">Pilot wave theory</a></li></ul> </div> <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=Double-slit_experiment&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"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-The_Bakerian_lecture-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-The_Bakerian_lecture_1-0">^</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="CITEREFYoung1804" class="citation journal cs1">Young, Thomas (1804). <a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frstl.1804.0001">"The Bakerian lecture. Experiments and calculation relative to physical optics"</a>. <i>Philosophical Transactions of the Royal Society of London</i>. <b>94</b>: 1–16. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frstl.1804.0001">10.1098/rstl.1804.0001</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:110408369">110408369</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Transactions+of+the+Royal+Society+of+London&rft.atitle=The+Bakerian+lecture.+Experiments+and+calculation+relative+to+physical+optics.&rft.volume=94&rft.pages=1-16&rft.date=1804&rft_id=info%3Adoi%2F10.1098%2Frstl.1804.0001&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A110408369%23id-name%3DS2CID&rft.aulast=Young&rft.aufirst=Thomas&rft_id=https%3A%2F%2Fdoi.org%2F10.1098%252Frstl.1804.0001&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNavarro2010" class="citation journal cs1">Navarro, Jaume (2010). <a rel="nofollow" class="external text" href="https://www.cambridge.org/core/product/identifier/S0007087410000026/type/journal_article">"Electron diffraction chez Thomson: early responses to quantum physics in Britain"</a>. <i>The British Journal for the History of Science</i>. <b>43</b> (2): 245–275. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS0007087410000026">10.1017/S0007087410000026</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0007-0874">0007-0874</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:171025814">171025814</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+British+Journal+for+the+History+of+Science&rft.atitle=Electron+diffraction+chez+Thomson%3A+early+responses+to+quantum+physics+in+Britain&rft.volume=43&rft.issue=2&rft.pages=245-275&rft.date=2010&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A171025814%23id-name%3DS2CID&rft.issn=0007-0874&rft_id=info%3Adoi%2F10.1017%2FS0007087410000026&rft.aulast=Navarro&rft.aufirst=Jaume&rft_id=https%3A%2F%2Fwww.cambridge.org%2Fcore%2Fproduct%2Fidentifier%2FS0007087410000026%2Ftype%2Fjournal_article&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" 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="CITEREFThomsonReid1927" class="citation journal cs1">Thomson, G. P.; Reid, A. (1927). <a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F119890a0">"Diffraction of Cathode Rays by a Thin Film"</a>. <i>Nature</i>. <b>119</b> (3007): 890. <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/1927Natur.119Q.890T">1927Natur.119Q.890T</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F119890a0">10.1038/119890a0</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0028-0836">0028-0836</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4122313">4122313</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Diffraction+of+Cathode+Rays+by+a+Thin+Film&rft.volume=119&rft.issue=3007&rft.pages=890&rft.date=1927&rft_id=info%3Adoi%2F10.1038%2F119890a0&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4122313%23id-name%3DS2CID&rft.issn=0028-0836&rft_id=info%3Abibcode%2F1927Natur.119Q.890T&rft.aulast=Thomson&rft.aufirst=G.+P.&rft.au=Reid%2C+A.&rft_id=https%3A%2F%2Fdoi.org%2F10.1038%252F119890a0&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-medium.com-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-medium.com_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-medium.com_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">"<a rel="nofollow" class="external text" href="https://medium.com/the-physics-arxiv-blog/462c39db8e7b">Physicists Smash Record For Wave–Particle Duality</a>"</span> </li> <li id="cite_note-Eibenberger_2013_pp._14696–14700-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-Eibenberger_2013_pp._14696–14700_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Eibenberger_2013_pp._14696–14700_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEibenberger2013" class="citation journal cs1">Eibenberger, Sandra; et al. (2013). "Matter-wave interference with particles selected from a molecular library with masses exceeding 10000 amu". <i><a href="/wiki/Physical_Chemistry_Chemical_Physics" title="Physical Chemistry Chemical Physics">Physical Chemistry Chemical Physics</a></i>. <b>15</b> (35): 14696–14700. <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/1310.8343">1310.8343</a></span>. <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/2013PCCP...1514696E">2013PCCP...1514696E</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1039%2FC3CP51500A">10.1039/C3CP51500A</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/23900710">23900710</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:3944699">3944699</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Chemistry+Chemical+Physics&rft.atitle=Matter-wave+interference+with+particles+selected+from+a+molecular+library+with+masses+exceeding+10000+amu&rft.volume=15&rft.issue=35&rft.pages=14696-14700&rft.date=2013&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A3944699%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2013PCCP...1514696E&rft_id=info%3Aarxiv%2F1310.8343&rft_id=info%3Apmid%2F23900710&rft_id=info%3Adoi%2F10.1039%2FC3CP51500A&rft.aulast=Eibenberger&rft.aufirst=Sandra&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" 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">While there is no doubt that Young's demonstration of optical interference, using sunlight, pinholes and cards, played a vital part in the acceptance of the wave theory of light, there is some question as to whether he ever actually performed a double-slit interference experiment. <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRobinson2006" class="citation book cs1">Robinson, Andrew (2006). <a rel="nofollow" class="external text" href="https://archive.org/details/lastmanwhoknewev00robi/page/123"><i>The Last Man Who Knew Everything</i></a>. New York, NY: Pi Press. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/lastmanwhoknewev00robi/page/123">123–124</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-134304-7" title="Special:BookSources/978-0-13-134304-7"><bdi>978-0-13-134304-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Last+Man+Who+Knew+Everything&rft.place=New+York%2C+NY&rft.pages=123-124&rft.pub=Pi+Press&rft.date=2006&rft.isbn=978-0-13-134304-7&rft.aulast=Robinson&rft.aufirst=Andrew&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Flastmanwhoknewev00robi%2Fpage%2F123&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></li></ul> </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="CITEREFKipnis1991" class="citation book cs1">Kipnis, Naum S. (1991). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=e7fvAAAAMAAJ"><i>History of the Principle of Interference of Light</i></a>. Springer. p. 65. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8176-2316-6" title="Special:BookSources/978-0-8176-2316-6"><bdi>978-0-8176-2316-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=History+of+the+Principle+of+Interference+of+Light&rft.pages=65&rft.pub=Springer&rft.date=1991&rft.isbn=978-0-8176-2316-6&rft.aulast=Kipnis&rft.aufirst=Naum+S.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3De7fvAAAAMAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-Lederman-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-Lederman_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Lederman_8-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLedermanChristopher_T._Hill2011" class="citation book cs1">Lederman, Leon M.; Christopher T. Hill (2011). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=qY_yOwHg_WYC&pg=PA102"><i>Quantum Physics for Poets</i></a>. US: Prometheus Books. pp. 102–111. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-61614-281-0" title="Special:BookSources/978-1-61614-281-0"><bdi>978-1-61614-281-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Physics+for+Poets&rft.place=US&rft.pages=102-111&rft.pub=Prometheus+Books&rft.date=2011&rft.isbn=978-1-61614-281-0&rft.aulast=Lederman&rft.aufirst=Leon+M.&rft.au=Christopher+T.+Hill&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DqY_yOwHg_WYC%26pg%3DPA102&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-Feynman-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-Feynman_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Feynman_9-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Feynman_9-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Feynman_9-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Feynman_9-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-Feynman_9-5"><sup><i><b>f</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFeynmanRobert_B._LeightonMatthew_Sands1965" class="citation book cs1">Feynman, Richard P.; Robert B. Leighton; Matthew Sands (1965). <a href="/wiki/The_Feynman_Lectures_on_Physics" title="The Feynman Lectures on Physics"><i>The Feynman Lectures on Physics, Vol. 3</i></a>. Addison-Wesley. pp. 1.1–1.8. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-201-02118-9" title="Special:BookSources/978-0-201-02118-9"><bdi>978-0-201-02118-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Feynman+Lectures+on+Physics%2C+Vol.+3&rft.pages=1.1-1.8&rft.pub=Addison-Wesley&rft.date=1965&rft.isbn=978-0-201-02118-9&rft.aulast=Feynman&rft.aufirst=Richard+P.&rft.au=Robert+B.+Leighton&rft.au=Matthew+Sands&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" 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">Feynman, 1965, p. 1.5</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="CITEREFDarling2007" class="citation encyclopaedia cs1"><a href="/wiki/David_Darling_(astronomer)" class="mw-redirect" title="David Darling (astronomer)">Darling, David</a> (2007). <a rel="nofollow" class="external text" href="http://www.daviddarling.info/encyclopedia/W/wave-particle_duality.html">"Wave–Particle Duality"</a>. <i>The Internet Encyclopedia of Science</i>. The Worlds of David Darling<span class="reference-accessdate">. Retrieved <span class="nowrap">18 October</span> 2008</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Wave%E2%80%93Particle+Duality&rft.btitle=The+Internet+Encyclopedia+of+Science&rft.pub=The+Worlds+of+David+Darling&rft.date=2007&rft.aulast=Darling&rft.aufirst=David&rft_id=http%3A%2F%2Fwww.daviddarling.info%2Fencyclopedia%2FW%2Fwave-particle_duality.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" 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">Feynman, 1965, p. 1.7</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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLeon_LedermanChristopher_T._Hill2011" class="citation book cs1">Leon Lederman; Christopher T. Hill (27 September 2011). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=qY_yOwHg_WYC&pg=PA109"><i>Quantum Physics for Poets</i></a>. Prometheus Books, Publishers. p. 109. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-61614-281-0" title="Special:BookSources/978-1-61614-281-0"><bdi>978-1-61614-281-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Physics+for+Poets&rft.pages=109&rft.pub=Prometheus+Books%2C+Publishers&rft.date=2011-09-27&rft.isbn=978-1-61614-281-0&rft.au=Leon+Lederman&rft.au=Christopher+T.+Hill&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DqY_yOwHg_WYC%26pg%3DPA109&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-Müller-Kirsten-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-Müller-Kirsten_14-0">^</a></b></span> <span class="reference-text">"<i>...if in a double-slit experiment, the detectors which register outcoming photons are placed immediately behind the diaphragm with two slits: A photon is registered in one detector, not in both...</i>" <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMüller-Kirsten2006" class="citation book cs1">Müller-Kirsten, H. J. W. (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=p1_Z81Le58MC&pg=PA14"><i>Introduction to Quantum Mechanics: Schrödinger Equation and Path Integral</i></a>. US: World Scientific. p. 14. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-981-2566911" title="Special:BookSources/978-981-2566911"><bdi>978-981-2566911</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Quantum+Mechanics%3A+Schr%C3%B6dinger+Equation+and+Path+Integral&rft.place=US&rft.pages=14&rft.pub=World+Scientific&rft.date=2006&rft.isbn=978-981-2566911&rft.aulast=M%C3%BCller-Kirsten&rft.aufirst=H.+J.+W.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dp1_Z81Le58MC%26pg%3DPA14&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-Plotnitsky-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-Plotnitsky_15-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPlotnitsky2012" class="citation book cs1">Plotnitsky, Arkady (2012). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=dmdUp97S4AYC&pg=PA75"><i>Niels Bohr and Complementarity: An Introduction</i></a>. US: Springer. pp. 75–76. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4614-4517-3" title="Special:BookSources/978-1-4614-4517-3"><bdi>978-1-4614-4517-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Niels+Bohr+and+Complementarity%3A+An+Introduction&rft.place=US&rft.pages=75-76&rft.pub=Springer&rft.date=2012&rft.isbn=978-1-4614-4517-3&rft.aulast=Plotnitsky&rft.aufirst=Arkady&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DdmdUp97S4AYC%26pg%3DPA75&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-Rae-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-Rae_16-0">^</a></b></span> <span class="reference-text">"<i>It seems that light passes through one slit or the other in the form of photons if we set up an experiment to detect which slit the photon passes, but passes through both slits in the form of a wave if we perform an interference experiment.</i>" <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRae2004" class="citation book cs1">Rae, Alastair I.M. (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=FVtMqukQ6g4C&pg=PA9"><i>Quantum Physics: Illusion Or Reality?</i></a>. UK: Cambridge University Press. pp. 9–10. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-139-45527-5" title="Special:BookSources/978-1-139-45527-5"><bdi>978-1-139-45527-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Physics%3A+Illusion+Or+Reality%3F&rft.place=UK&rft.pages=9-10&rft.pub=Cambridge+University+Press&rft.date=2004&rft.isbn=978-1-139-45527-5&rft.aulast=Rae&rft.aufirst=Alastair+I.M.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DFVtMqukQ6g4C%26pg%3DPA9&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">Feynman, <i><a href="/wiki/The_Feynman_Lectures_on_Physics" title="The Feynman Lectures on Physics">The Feynman Lectures on Physics</a></i>, <b>3</b>:Quantum Mechanics p.1-1 "There is one lucky break, however— electrons behave just like light".</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text">See: <a href="/wiki/Davisson%E2%80%93Germer_experiment" title="Davisson–Germer experiment">Davisson–Germer experiment</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavisson1928" class="citation journal cs1">Davisson, C. J (1928). "The diffraction of electrons by a crystal of nickel". <i><a href="/wiki/Bell_System_Technical_Journal" class="mw-redirect" title="Bell System Technical Journal">Bell System Technical Journal</a></i>. <b>7</b>: 90–105. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fj.1538-7305.1928.tb00342.x">10.1002/j.1538-7305.1928.tb00342.x</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bell+System+Technical+Journal&rft.atitle=The+diffraction+of+electrons+by+a+crystal+of+nickel&rft.volume=7&rft.pages=90-105&rft.date=1928&rft_id=info%3Adoi%2F10.1002%2Fj.1538-7305.1928.tb00342.x&rft.aulast=Davisson&rft.aufirst=C.+J&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-Yaakov_Y._Fein_1242–1245-19"><span class="mw-cite-backlink">^ <a href="#cite_ref-Yaakov_Y._Fein_1242–1245_19-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Yaakov_Y._Fein_1242–1245_19-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFYaakov_Y._FeinPhilipp_GeyerPatrick_ZwickFilip_Kiałka2019" class="citation journal cs1">Yaakov Y. Fein; Philipp Geyer; Patrick Zwick; Filip Kiałka; Sebastian Pedalino; Marcel Mayor; Stefan Gerlich; Markus Arndt (September 2019). "Quantum superposition of molecules beyond 25 kDa". <i>Nature Physics</i>. <b>15</b> (12): 1242–1245. <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/2019NatPh..15.1242F">2019NatPh..15.1242F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fs41567-019-0663-9">10.1038/s41567-019-0663-9</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:203638258">203638258</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature+Physics&rft.atitle=Quantum+superposition+of+molecules+beyond+25+kDa&rft.volume=15&rft.issue=12&rft.pages=1242-1245&rft.date=2019-09&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A203638258%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1038%2Fs41567-019-0663-9&rft_id=info%3Abibcode%2F2019NatPh..15.1242F&rft.au=Yaakov+Y.+Fein&rft.au=Philipp+Geyer&rft.au=Patrick+Zwick&rft.au=Filip+Kia%C5%82ka&rft.au=Sebastian+Pedalino&rft.au=Marcel+Mayor&rft.au=Stefan+Gerlich&rft.au=Markus+Arndt&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><a href="/wiki/Charles_Sanders_Peirce" title="Charles Sanders Peirce">Charles Sanders Peirce</a> first proposed the use of this effect as an artifact-independent reference standard for <a href="/wiki/Length" title="Length">length</a> <ul><li>C.S. Peirce (July 1879). "Note on the Progress of Experiments for Comparing a Wave-length with a Meter". <i>American Journal of Science</i>, as referenced by Crease, Robert P. (2011). <i>World in the Balance: The historic quest for an absolute system of measurement</i>. New York: W.W. Norton. p. 317. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-393-07298-3" title="Special:BookSources/978-0-393-07298-3">978-0-393-07298-3</a>. p. 203.</li></ul> </span></li> <li id="cite_note-Greene_1999-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-Greene_1999_21-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGreene1999" class="citation book cs1"><a href="/wiki/Brian_Greene" title="Brian Greene">Greene, Brian</a> (1999). <a rel="nofollow" class="external text" href="https://archive.org/details/elegantuniverses0000gree/page/97"><i>The Elegant Universe: Super Strings, Hidden Dimensions, and the Quest for the Ultimate Theory</i></a>. New York: W.W. Norton. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/elegantuniverses0000gree/page/97">97–109</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-393-04688-5" title="Special:BookSources/978-0-393-04688-5"><bdi>978-0-393-04688-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Elegant+Universe%3A+Super+Strings%2C+Hidden+Dimensions%2C+and+the+Quest+for+the+Ultimate+Theory&rft.place=New+York&rft.pages=97-109&rft.pub=W.W.+Norton&rft.date=1999&rft.isbn=978-0-393-04688-5&rft.aulast=Greene&rft.aufirst=Brian&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Felegantuniverses0000gree%2Fpage%2F97&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text">Feynman, 1965, chapter 3</span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSir_Geoffrey1909" class="citation journal cs1"><a href="/wiki/Geoffrey_Ingram_Taylor" class="mw-redirect" title="Geoffrey Ingram Taylor">Sir Geoffrey, Ingram Taylor</a> (1909). "Interference Fringes with Feeble Light". <i>Prof. Cam. Phil. Soc</i>. <b>15</b>: 114.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Prof.+Cam.+Phil.+Soc.&rft.atitle=Interference+Fringes+with+Feeble+Light&rft.volume=15&rft.pages=114&rft.date=1909&rft.aulast=Sir+Geoffrey&rft.aufirst=Ingram+Taylor&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJönsson1961" class="citation journal cs1 cs1-prop-foreign-lang-source">Jönsson, Claus (1 August 1961). "Elektroneninterferenzen an mehreren künstlich hergestellten Feinspalten". <i>Zeitschrift für Physik</i> (in German). <b>161</b> (4): 454–474. <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/1961ZPhy..161..454J">1961ZPhy..161..454J</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01342460">10.1007/BF01342460</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0044-3328">0044-3328</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:121659705">121659705</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Zeitschrift+f%C3%BCr+Physik&rft.atitle=Elektroneninterferenzen+an+mehreren+k%C3%BCnstlich+hergestellten+Feinspalten&rft.volume=161&rft.issue=4&rft.pages=454-474&rft.date=1961-08-01&rft_id=info%3Adoi%2F10.1007%2FBF01342460&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A121659705%23id-name%3DS2CID&rft.issn=0044-3328&rft_id=info%3Abibcode%2F1961ZPhy..161..454J&rft.aulast=J%C3%B6nsson&rft.aufirst=Claus&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJönsson1974" class="citation journal cs1">Jönsson, Claus (1 January 1974). "Electron Diffraction at Multiple Slits". <i>American Journal of Physics</i>. <b>42</b> (1): 4–11. <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/1974AmJPh..42....4J">1974AmJPh..42....4J</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%2F1.1987592">10.1119/1.1987592</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0002-9505">0002-9505</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=Electron+Diffraction+at+Multiple+Slits&rft.volume=42&rft.issue=1&rft.pages=4-11&rft.date=1974-01-01&rft.issn=0002-9505&rft_id=info%3Adoi%2F10.1119%2F1.1987592&rft_id=info%3Abibcode%2F1974AmJPh..42....4J&rft.aulast=J%C3%B6nsson&rft.aufirst=Claus&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMerliMissiroliPozzi1976" class="citation journal cs1">Merli, P G; Missiroli, G F; Pozzi, G (1976). "On the statistical aspect of electron interference phenomena". <i>American Journal of Physics</i>. <b>44</b> (3): 306–307. <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/1976AmJPh..44..306M">1976AmJPh..44..306M</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%2F1.10184">10.1119/1.10184</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=On+the+statistical+aspect+of+electron+interference+phenomena&rft.volume=44&rft.issue=3&rft.pages=306-307&rft.date=1976&rft_id=info%3Adoi%2F10.1119%2F1.10184&rft_id=info%3Abibcode%2F1976AmJPh..44..306M&rft.aulast=Merli&rft.aufirst=P+G&rft.au=Missiroli%2C+G+F&rft.au=Pozzi%2C+G&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRosa2012" class="citation journal cs1">Rosa, R (2012). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4617474">"The Merli–Missiroli–Pozzi Two-Slit Electron-Interference Experiment"</a>. <i>Physics in Perspective</i>. <b>14</b> (2): 178–194. <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/2012PhP....14..178R">2012PhP....14..178R</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs00016-011-0079-0">10.1007/s00016-011-0079-0</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4617474">4617474</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/26525832">26525832</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+in+Perspective&rft.atitle=The+Merli%E2%80%93Missiroli%E2%80%93Pozzi+Two-Slit+Electron-Interference+Experiment&rft.volume=14&rft.issue=2&rft.pages=178-194&rft.date=2012&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC4617474%23id-name%3DPMC&rft_id=info%3Apmid%2F26525832&rft_id=info%3Adoi%2F10.1007%2Fs00016-011-0079-0&rft_id=info%3Abibcode%2F2012PhP....14..178R&rft.aulast=Rosa&rft.aufirst=R&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC4617474&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://physicsworld.com/a/the-double-slit-experiment/">"The most beautiful experiment"</a>. Physics World 2002 <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210524080643/https://physicsworld.com/a/the-double-slit-experiment/">Archived</a> 24 May 2021 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></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="CITEREFSteedsMerliPozziMissiroli2003" class="citation journal cs1">Steeds, John; Merli, Pier Giorgio; Pozzi, Giulio; Missiroli, GianFranco; Tonomura, Akira (2003). <a rel="nofollow" class="external text" href="https://iopscience.iop.org/article/10.1088/2058-7058/16/5/24">"The double-slit experiment with single electrons"</a>. <i>Physics World</i>. <b>16</b> (5): 20–21. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F2058-7058%2F16%2F5%2F24">10.1088/2058-7058/16/5/24</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0953-8585">0953-8585</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+World&rft.atitle=The+double-slit+experiment+with+single+electrons&rft.volume=16&rft.issue=5&rft.pages=20-21&rft.date=2003&rft_id=info%3Adoi%2F10.1088%2F2058-7058%2F16%2F5%2F24&rft.issn=0953-8585&rft.aulast=Steeds&rft.aufirst=John&rft.au=Merli%2C+Pier+Giorgio&rft.au=Pozzi%2C+Giulio&rft.au=Missiroli%2C+GianFranco&rft.au=Tonomura%2C+Akira&rft_id=https%3A%2F%2Fiopscience.iop.org%2Farticle%2F10.1088%2F2058-7058%2F16%2F5%2F24&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFrabboniGabrielliCarlo_GazzadiGiorgi2012" class="citation journal cs1">Frabboni, Stefano; Gabrielli, Alessandro; Carlo Gazzadi, Gian; Giorgi, Filippo; Matteucci, Giorgio; Pozzi, Giulio; Cesari, Nicola Semprini; Villa, Mauro; Zoccoli, Antonio (May 2012). "The Young-Feynman two-slits experiment with single electrons: Build-up of the interference pattern and arrival-time distribution using a fast-readout pixel detector". <i>Ultramicroscopy</i>. <b>116</b>: 73–76. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.ultramic.2012.03.017">10.1016/j.ultramic.2012.03.017</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0304-3991">0304-3991</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Ultramicroscopy&rft.atitle=The+Young-Feynman+two-slits+experiment+with+single+electrons%3A+Build-up+of+the+interference+pattern+and+arrival-time+distribution+using+a+fast-readout+pixel+detector&rft.volume=116&rft.pages=73-76&rft.date=2012-05&rft_id=info%3Adoi%2F10.1016%2Fj.ultramic.2012.03.017&rft.issn=0304-3991&rft.aulast=Frabboni&rft.aufirst=Stefano&rft.au=Gabrielli%2C+Alessandro&rft.au=Carlo+Gazzadi%2C+Gian&rft.au=Giorgi%2C+Filippo&rft.au=Matteucci%2C+Giorgio&rft.au=Pozzi%2C+Giulio&rft.au=Cesari%2C+Nicola+Semprini&rft.au=Villa%2C+Mauro&rft.au=Zoccoli%2C+Antonio&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCowley1995" class="citation book cs1">Cowley, J. 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(2017). <i>High-resolution electron microscopy</i> (Fourth edition, first published in paperback ed.). 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IOP Publishing: 033018. <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/1210.6243">1210.6243</a></span>. <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/2013NJPh...15c3018B">2013NJPh...15c3018B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F1367-2630%2F15%2F3%2F033018">10.1088/1367-2630/15/3/033018</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1367-2630">1367-2630</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:832961">832961</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=New+Journal+of+Physics&rft.atitle=Controlled+double-slit+electron+diffraction&rft.volume=15&rft.issue=3&rft.pages=033018&rft.date=2013-03-13&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A832961%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2013NJPh...15c3018B&rft_id=info%3Aarxiv%2F1210.6243&rft.issn=1367-2630&rft_id=info%3Adoi%2F10.1088%2F1367-2630%2F15%2F3%2F033018&rft.aulast=Bach&rft.aufirst=Roger&rft.au=Pope%2C+Damian&rft.au=Liou%2C+Sy-Hwang&rft.au=Batelaan%2C+Herman&rft_id=https%3A%2F%2Fiopscience.iop.org%2Farticle%2F10.1088%2F1367-2630%2F15%2F3%2F033018&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGreene2007" class="citation book cs1">Greene, Brian (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=DNd2K6mxLpIC&pg=PA90"><i>The Fabric of the Cosmos: Space, Time, and the Texture of Reality</i></a>. Random House LLC. p. 90. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-307-42853-0" title="Special:BookSources/978-0-307-42853-0"><bdi>978-0-307-42853-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Fabric+of+the+Cosmos%3A+Space%2C+Time%2C+and+the+Texture+of+Reality&rft.pages=90&rft.pub=Random+House+LLC&rft.date=2007&rft.isbn=978-0-307-42853-0&rft.aulast=Greene&rft.aufirst=Brian&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DDNd2K6mxLpIC%26pg%3DPA90&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-Ananthaswamy-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-Ananthaswamy_36-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAnanthaswamy2018" class="citation book cs1">Ananthaswamy, Anil (2018). <i>Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality</i>. 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(2015). "Niels Bohr as Philosopher of Experiment: Does Decoherence Theory Challenge Bohr's Doctrine of Classical Concepts?". <i><a href="/wiki/Studies_in_History_and_Philosophy_of_Modern_Physics" class="mw-redirect" title="Studies in History and Philosophy of Modern Physics">Studies in History and Philosophy of Modern Physics</a></i>. <b>49</b>: 73–83. <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/1502.06547">1502.06547</a></span>. <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/2015SHPMP..49...73C">2015SHPMP..49...73C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.shpsb.2015.01.005">10.1016/j.shpsb.2015.01.005</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:27697360">27697360</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Studies+in+History+and+Philosophy+of+Modern+Physics&rft.atitle=Niels+Bohr+as+Philosopher+of+Experiment%3A+Does+Decoherence+Theory+Challenge+Bohr%27s+Doctrine+of+Classical+Concepts%3F&rft.volume=49&rft.pages=73-83&rft.date=2015&rft_id=info%3Aarxiv%2F1502.06547&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A27697360%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.shpsb.2015.01.005&rft_id=info%3Abibcode%2F2015SHPMP..49...73C&rft.aulast=Camilleri&rft.aufirst=K.&rft.au=Schlosshauer%2C+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-88"><span class="mw-cite-backlink"><b><a href="#cite_ref-88">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFScheibe1973" class="citation book cs1"><a href="/wiki/Erhard_Scheibe" title="Erhard Scheibe">Scheibe, Erhard</a> (1973). <i>The Logical Analysis of Quantum Mechanics</i>. Pergamon Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-08-017158-6" title="Special:BookSources/978-0-08-017158-6"><bdi>978-0-08-017158-6</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/799397091">799397091</a>. <q>[T]here is no point in looking for <i>the</i> Copenhagen interpretation as a unified and consistent logical structure. Terms such as "Copenhagen interpretation" or "Copenhagen school" are based on the history of the development of quantum mechanics; they form a simplified and often convenient way of referring to the ideas of a number of physicists who played an important role in the establishment of quantum mechanics, and who were collaborators of Bohr's at his Institute or took part in the discussions during the crucial years. On closer inspection, one sees quite easily that these ideas are divergent in detail and that in particular the views of Bohr, the spiritual leader of the school, form a separate entity which can now be understood only by a thorough study of as many as possible of the relevant publications by Bohr himself.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Logical+Analysis+of+Quantum+Mechanics&rft.pub=Pergamon+Press&rft.date=1973&rft_id=info%3Aoclcnum%2F799397091&rft.isbn=978-0-08-017158-6&rft.aulast=Scheibe&rft.aufirst=Erhard&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-Mermin_2017-89"><span class="mw-cite-backlink"><b><a href="#cite_ref-Mermin_2017_89-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMermin2017" class="citation book cs1">Mermin, N. 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"A correlation between the compton wavelength and the de Broglie wavelength". <i>Physics Letters A</i>. <b>114</b> (4): 179–182. <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/1986PhLA..114..179M">1986PhLA..114..179M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0375-9601%2886%2990200-8">10.1016/0375-9601(86)90200-8</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0375-9601">0375-9601</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Letters+A&rft.atitle=A+correlation+between+the+compton+wavelength+and+the+de+Broglie+wavelength&rft.volume=114&rft.issue=4&rft.pages=179-182&rft.date=1986&rft.issn=0375-9601&rft_id=info%3Adoi%2F10.1016%2F0375-9601%2886%2990200-8&rft_id=info%3Abibcode%2F1986PhLA..114..179M&rft.aulast=Mukhopadhyay&rft.aufirst=P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> <li id="cite_note-110"><span class="mw-cite-backlink"><b><a href="#cite_ref-110">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFElbaz1985" class="citation journal cs1">Elbaz, Claude (1985). "On de Broglie waves and Compton waves of massive particles". <i>Physics Letters A</i>. <b>109</b> (1–2): 7–8. <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/1985PhLA..109....7E">1985PhLA..109....7E</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0375-9601%2885%2990379-2">10.1016/0375-9601(85)90379-2</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0375-9601">0375-9601</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Letters+A&rft.atitle=On+de+Broglie+waves+and+Compton+waves+of+massive+particles&rft.volume=109&rft.issue=1%E2%80%932&rft.pages=7-8&rft.date=1985&rft.issn=0375-9601&rft_id=info%3Adoi%2F10.1016%2F0375-9601%2885%2990379-2&rft_id=info%3Abibcode%2F1985PhLA..109....7E&rft.aulast=Elbaz&rft.aufirst=Claude&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Further_reading">Further reading</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=22" 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="CITEREFAl-Khalili2003" class="citation book cs1"><a href="/wiki/Jim_Al-Khalili" title="Jim Al-Khalili">Al-Khalili, Jim</a> (2003). <i>Quantum: A Guide for the Perplexed</i>. London: Weidenfeld & Nicolson. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-297-84305-4" title="Special:BookSources/978-0-297-84305-4"><bdi>978-0-297-84305-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum%3A+A+Guide+for+the+Perplexed&rft.place=London&rft.pub=Weidenfeld+%26+Nicolson&rft.date=2003&rft.isbn=978-0-297-84305-4&rft.aulast=Al-Khalili&rft.aufirst=Jim&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAnanthaswamy2018" class="citation book cs1"><a href="/wiki/Anil_Ananthaswamy" title="Anil Ananthaswamy">Ananthaswamy, Anil</a> (2018). <i>Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality</i>. Dutton/Penguin. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-101-98609-7" title="Special:BookSources/978-1-101-98609-7"><bdi>978-1-101-98609-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Through+Two+Doors+at+Once%3A+The+Elegant+Experiment+That+Captures+the+Enigma+of+Our+Quantum+Reality&rft.pub=Dutton%2FPenguin&rft.date=2018&rft.isbn=978-1-101-98609-7&rft.aulast=Ananthaswamy&rft.aufirst=Anil&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFeynman1988" class="citation book cs1">Feynman, Richard P. (1988). <a rel="nofollow" class="external text" href="https://archive.org/details/qedstrangetheory00feyn"><i>QED: The Strange Theory of Light and Matter</i></a>. Princeton University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-02417-2" title="Special:BookSources/978-0-691-02417-2"><bdi>978-0-691-02417-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=QED%3A+The+Strange+Theory+of+Light+and+Matter&rft.pub=Princeton+University+Press&rft.date=1988&rft.isbn=978-0-691-02417-2&rft.aulast=Feynman&rft.aufirst=Richard+P.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fqedstrangetheory00feyn&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFrank1957" class="citation book cs1">Frank, Philipp (1957). <i>Philosophy of Science</i>. Prentice-Hall.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Philosophy+of+Science&rft.pub=Prentice-Hall&rft.date=1957&rft.aulast=Frank&rft.aufirst=Philipp&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFrenchTaylor1978" class="citation book cs1">French, A.P.; Taylor, Edwin F. (1978). <i>An Introduction to Quantum Physics</i>. Norton. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-393-09106-9" title="Special:BookSources/978-0-393-09106-9"><bdi>978-0-393-09106-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Introduction+to+Quantum+Physics&rft.pub=Norton&rft.date=1978&rft.isbn=978-0-393-09106-9&rft.aulast=French&rft.aufirst=A.P.&rft.au=Taylor%2C+Edwin+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGreene2000" class="citation book cs1">Greene, Brian (2000). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/elegantuniverses0000gree"><i>The Elegant Universe</i></a></span>. Vintage. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-375-70811-4" title="Special:BookSources/978-0-375-70811-4"><bdi>978-0-375-70811-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Elegant+Universe&rft.pub=Vintage&rft.date=2000&rft.isbn=978-0-375-70811-4&rft.aulast=Greene&rft.aufirst=Brian&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Felegantuniverses0000gree&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGreene2005" class="citation book cs1">Greene, Brian (2005). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/fabricofcosmossp00gree"><i>The Fabric of the Cosmos</i></a></span>. Vintage. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-375-72720-7" title="Special:BookSources/978-0-375-72720-7"><bdi>978-0-375-72720-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Fabric+of+the+Cosmos&rft.pub=Vintage&rft.date=2005&rft.isbn=978-0-375-72720-7&rft.aulast=Greene&rft.aufirst=Brian&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ffabricofcosmossp00gree&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGribbin1999" class="citation book cs1"><a href="/wiki/John_Gribbin" title="John Gribbin">Gribbin, John</a> (1999). <i>Q is for Quantum: Particle Physics from A to Z</i>. Weidenfeld & Nicolson. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7538-0685-2" title="Special:BookSources/978-0-7538-0685-2"><bdi>978-0-7538-0685-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Q+is+for+Quantum%3A+Particle+Physics+from+A+to+Z&rft.pub=Weidenfeld+%26+Nicolson&rft.date=1999&rft.isbn=978-0-7538-0685-2&rft.aulast=Gribbin&rft.aufirst=John&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHey2003" class="citation book cs1">Hey, Tony (2003). <i>The New Quantum Universe</i>. Cambridge University Press. <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/2003nqu..book.....H">2003nqu..book.....H</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-56457-1" title="Special:BookSources/978-0-521-56457-1"><bdi>978-0-521-56457-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+New+Quantum+Universe&rft.pub=Cambridge+University+Press&rft.date=2003&rft_id=info%3Abibcode%2F2003nqu..book.....H&rft.isbn=978-0-521-56457-1&rft.aulast=Hey&rft.aufirst=Tony&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSears1949" class="citation book cs1">Sears, Francis Weston (1949). <i>Optics</i>. Addison Wesley.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Optics&rft.pub=Addison+Wesley&rft.date=1949&rft.aulast=Sears&rft.aufirst=Francis+Weston&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTipler2004" class="citation book cs1">Tipler, Paul (2004). <i>Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics</i> (5th ed.). W. H. Freeman. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7167-0810-0" title="Special:BookSources/978-0-7167-0810-0"><bdi>978-0-7167-0810-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics+for+Scientists+and+Engineers%3A+Electricity%2C+Magnetism%2C+Light%2C+and+Elementary+Modern+Physics&rft.edition=5th&rft.pub=W.+H.+Freeman&rft.date=2004&rft.isbn=978-0-7167-0810-0&rft.aulast=Tipler&rft.aufirst=Paul&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-slit+experiment" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=23" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Double-slit_experiments" class="extiw" title="commons:Category:Double-slit experiments">Double-slit experiments</a></span>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://youtube.com/watch?v=1rYF72PXVks">Double slit interference lecture</a> by <a href="/wiki/Walter_Lewin" title="Walter Lewin">Walter Lewin</a> of MIT</li></ul> <div class="mw-heading mw-heading3"><h3 id="Interactive_animations">Interactive animations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=24" title="Edit section: Interactive animations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.acoustics.salford.ac.uk/feschools/waves/diffract3.htm">Huygens and interference</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20071028092236/http://www.acoustics.salford.ac.uk/feschools/waves/diffract3.htm">Archived</a> 28 October 2007 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Single_particle_experiments">Single particle experiments</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=25" title="Edit section: Single particle experiments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://l-esperimento-piu-bello-della-fisica.bo.imm.cnr.it/english/index.html">Website with the movie and other information from the first single electron experiment by Merli, Missiroli, and Pozzi.</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20161109042639/http://www.hitachi.com/rd/research/em/movie.html">Movie showing single electron events build up to form an interference pattern in double-slit experiments. Several versions with and without narration (File size = 3.6 to 10.4 MB) (Movie Length = 1m 8s)</a></li> <li><a rel="nofollow" class="external text" href="http://www.vega.org.uk/video/programme/66">Freeview video 'Electron Waves Unveil the Microcosmos' A Royal Institution Discourse by Akira Tonomura provided by the Vega Science Trust</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110114170600/http://www.hitachi.com/rd/research/em/doubleslit.html">Hitachi website that provides background on Tonomura video and link to the video</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Hydrodynamic_analog">Hydrodynamic analog</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=26" title="Edit section: Hydrodynamic analog"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.physorg.com/news78650511.html">"Single-particle interference observed for macroscopic objects"</a></li> <li><a rel="nofollow" class="external text" href="http://www.annualreviews.org/doi/suppl/10.1146/annurev-fluid-010814-014506">Pilot-Wave Hydrodynamics: Supplemental Video</a></li> <li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=W9yWv5dqSKk"><i>Through the Wormhole</i>: Yves Couder . Explains Wave/Particle Duality via Silicon Droplets</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Computer_simulations">Computer simulations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-slit_experiment&action=edit&section=27" title="Edit section: Computer simulations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://vsg.quasihome.com/interf.htm">Java demonstration of Young's double slit interference</a></li> <li><a rel="nofollow" class="external text" href="http://demonstrations.wolfram.com/WaveParticleDualityInTheDoubleSlitExperiment/">A simulation that runs in Mathematica Player, in which the number of quantum particles, the frequency of the particles, and the slit separation can be independently varied</a></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 .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Quantum_mechanics" style="padding:3px"><table class="nowraplinks hlist 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:Quantum_mechanics_topics" title="Template:Quantum mechanics topics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Quantum_mechanics_topics" title="Template talk:Quantum mechanics topics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Quantum_mechanics_topics" title="Special:EditPage/Template:Quantum mechanics topics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Quantum_mechanics" style="font-size:114%;margin:0 4em"><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Background</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/Introduction_to_quantum_mechanics" title="Introduction to quantum mechanics">Introduction</a></li> <li><a href="/wiki/History_of_quantum_mechanics" title="History of quantum mechanics">History</a> <ul><li><a href="/wiki/Timeline_of_quantum_mechanics" title="Timeline of quantum mechanics">Timeline</a></li></ul></li> <li><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a></li> <li><a href="/wiki/Old_quantum_theory" title="Old quantum theory">Old quantum theory</a></li> <li><a href="/wiki/Glossary_of_elementary_quantum_mechanics" title="Glossary of elementary quantum mechanics">Glossary</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Fundamentals</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/Born_rule" title="Born rule">Born rule</a></li> <li><a href="/wiki/Bra%E2%80%93ket_notation" title="Bra–ket notation">Bra–ket notation</a></li> <li><a href="/wiki/Complementarity_(physics)" title="Complementarity (physics)"> Complementarity</a></li> <li><a href="/wiki/Density_matrix" title="Density matrix">Density matrix</a></li> <li><a href="/wiki/Energy_level" title="Energy level">Energy level</a> <ul><li><a href="/wiki/Ground_state" title="Ground state">Ground state</a></li> <li><a href="/wiki/Excited_state" title="Excited state">Excited state</a></li> <li><a href="/wiki/Degenerate_energy_levels" title="Degenerate energy levels">Degenerate levels</a></li> <li><a href="/wiki/Zero-point_energy" title="Zero-point energy">Zero-point energy</a></li></ul></li> <li><a href="/wiki/Quantum_entanglement" title="Quantum entanglement">Entanglement</a></li> <li><a href="/wiki/Hamiltonian_(quantum_mechanics)" title="Hamiltonian (quantum mechanics)">Hamiltonian</a></li> <li><a href="/wiki/Wave_interference" title="Wave interference">Interference</a></li> <li><a href="/wiki/Quantum_decoherence" title="Quantum decoherence">Decoherence</a></li> <li><a href="/wiki/Measurement_in_quantum_mechanics" title="Measurement in quantum mechanics">Measurement</a></li> <li><a href="/wiki/Quantum_nonlocality" title="Quantum nonlocality">Nonlocality</a></li> <li><a href="/wiki/Quantum_state" title="Quantum state">Quantum state</a></li> <li><a href="/wiki/Quantum_superposition" title="Quantum superposition">Superposition</a></li> <li><a href="/wiki/Quantum_tunnelling" title="Quantum tunnelling">Tunnelling</a></li> <li><a href="/wiki/Scattering_theory" class="mw-redirect" title="Scattering theory">Scattering theory</a></li> <li><a href="/wiki/Symmetry_in_quantum_mechanics" title="Symmetry in quantum mechanics">Symmetry in quantum mechanics</a></li> <li><a href="/wiki/Uncertainty_principle" title="Uncertainty principle">Uncertainty</a></li> <li><a href="/wiki/Wave_function" title="Wave function">Wave function</a> <ul><li><a href="/wiki/Wave_function_collapse" title="Wave function collapse">Collapse</a></li> <li><a href="/wiki/Wave%E2%80%93particle_duality" title="Wave–particle duality">Wave–particle duality</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Formulations</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/Mathematical_formulation_of_quantum_mechanics" title="Mathematical formulation of quantum mechanics">Formulations</a></li> <li><a href="/wiki/Heisenberg_picture" title="Heisenberg picture">Heisenberg</a></li> <li><a href="/wiki/Interaction_picture" title="Interaction picture">Interaction</a></li> <li><a href="/wiki/Matrix_mechanics" title="Matrix mechanics">Matrix mechanics</a></li> <li><a href="/wiki/Schr%C3%B6dinger_picture" title="Schrödinger picture">Schrödinger</a></li> <li><a href="/wiki/Path_integral_formulation" title="Path integral formulation">Path integral formulation</a></li> <li><a href="/wiki/Phase-space_formulation" title="Phase-space formulation">Phase space</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Equations</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/Klein%E2%80%93Gordon_equation" title="Klein–Gordon equation">Klein–Gordon</a></li> <li><a href="/wiki/Dirac_equation" title="Dirac equation">Dirac</a></li> <li><a href="/wiki/Weyl_equation" title="Weyl equation">Weyl</a></li> <li><a href="/wiki/Majorana_equation" title="Majorana equation">Majorana</a></li> <li><a href="/wiki/Rarita%E2%80%93Schwinger_equation" title="Rarita–Schwinger equation">Rarita–Schwinger</a></li> <li><a href="/wiki/Pauli_equation" title="Pauli equation">Pauli</a></li> <li><a href="/wiki/Rydberg_formula" title="Rydberg formula">Rydberg</a></li> <li><a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Interpretations_of_quantum_mechanics" title="Interpretations of quantum mechanics">Interpretations</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/Quantum_Bayesianism" title="Quantum Bayesianism">Bayesian</a></li> <li><a href="/wiki/Consistent_histories" title="Consistent histories">Consistent histories</a></li> <li><a href="/wiki/Copenhagen_interpretation" title="Copenhagen interpretation">Copenhagen</a></li> <li><a href="/wiki/De_Broglie%E2%80%93Bohm_theory" title="De Broglie–Bohm theory">de Broglie–Bohm</a></li> <li><a href="/wiki/Ensemble_interpretation" title="Ensemble interpretation">Ensemble</a></li> <li><a href="/wiki/Hidden-variable_theory" title="Hidden-variable theory">Hidden-variable</a> <ul><li><a href="/wiki/Local_hidden-variable_theory" title="Local hidden-variable theory">Local</a> <ul><li><a href="/wiki/Superdeterminism" title="Superdeterminism">Superdeterminism</a></li></ul></li></ul></li> <li><a href="/wiki/Many-worlds_interpretation" title="Many-worlds interpretation">Many-worlds</a></li> <li><a href="/wiki/Objective-collapse_theory" title="Objective-collapse theory">Objective collapse</a></li> <li><a href="/wiki/Quantum_logic" title="Quantum logic">Quantum logic</a></li> <li><a href="/wiki/Relational_quantum_mechanics" title="Relational quantum mechanics">Relational</a></li> <li><a href="/wiki/Transactional_interpretation" title="Transactional interpretation">Transactional</a></li> <li><a href="/wiki/Von_Neumann%E2%80%93Wigner_interpretation" title="Von Neumann–Wigner interpretation">Von Neumann–Wigner</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Experiments</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/Bell_test" title="Bell test">Bell test</a></li> <li><a href="/wiki/Davisson%E2%80%93Germer_experiment" title="Davisson–Germer experiment">Davisson–Germer</a></li> <li><a href="/wiki/Delayed-choice_quantum_eraser" title="Delayed-choice quantum eraser">Delayed-choice quantum eraser</a></li> <li><a class="mw-selflink selflink">Double-slit</a></li> <li><a href="/wiki/Franck%E2%80%93Hertz_experiment" title="Franck–Hertz experiment">Franck–Hertz</a></li> <li><a href="/wiki/Mach%E2%80%93Zehnder_interferometer" title="Mach–Zehnder interferometer">Mach–Zehnder interferometer</a></li> <li><a href="/wiki/Elitzur%E2%80%93Vaidman_bomb_tester" title="Elitzur–Vaidman bomb tester">Elitzur–Vaidman</a></li> <li><a href="/wiki/Popper%27s_experiment" title="Popper's experiment">Popper</a></li> <li><a href="/wiki/Quantum_eraser_experiment" title="Quantum eraser experiment">Quantum eraser</a></li> <li><a href="/wiki/Stern%E2%80%93Gerlach_experiment" title="Stern–Gerlach experiment">Stern–Gerlach</a></li> <li><a href="/wiki/Wheeler%27s_delayed-choice_experiment" title="Wheeler's delayed-choice experiment">Wheeler's delayed choice</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_nanoscience" class="mw-redirect" title="Quantum nanoscience">Science</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/Quantum_biology" title="Quantum biology">Quantum biology</a></li> <li><a href="/wiki/Quantum_chemistry" title="Quantum chemistry">Quantum chemistry</a></li> <li><a href="/wiki/Quantum_chaos" title="Quantum chaos">Quantum chaos</a></li> <li><a href="/wiki/Quantum_cosmology" title="Quantum cosmology">Quantum cosmology</a></li> <li><a href="/wiki/Quantum_differential_calculus" title="Quantum differential calculus">Quantum differential calculus</a></li> <li><a href="/wiki/Quantum_dynamics" title="Quantum dynamics">Quantum dynamics</a></li> <li><a href="/wiki/Quantum_geometry" title="Quantum geometry">Quantum geometry</a></li> <li><a href="/wiki/Measurement_problem" title="Measurement problem">Quantum measurement problem</a></li> <li><a href="/wiki/Quantum_mind" title="Quantum mind">Quantum mind</a></li> <li><a href="/wiki/Quantum_stochastic_calculus" title="Quantum stochastic calculus">Quantum stochastic calculus</a></li> <li><a href="/wiki/Quantum_spacetime" title="Quantum spacetime">Quantum spacetime</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_technology" class="mw-redirect" title="Quantum technology">Technology</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><a href="/wiki/Quantum_algorithm" title="Quantum algorithm">Quantum algorithms</a></li> <li><a href="/wiki/Quantum_amplifier" title="Quantum amplifier">Quantum amplifier</a></li> <li><a href="/wiki/Quantum_bus" title="Quantum bus">Quantum bus</a></li> <li><a href="/wiki/Quantum_cellular_automaton" title="Quantum cellular automaton">Quantum cellular automata</a> <ul><li><a href="/wiki/Quantum_finite_automaton" title="Quantum finite automaton">Quantum finite automata</a></li></ul></li> <li><a href="/wiki/Quantum_channel" title="Quantum channel">Quantum channel</a></li> <li><a href="/wiki/Quantum_circuit" title="Quantum circuit">Quantum circuit</a></li> <li><a href="/wiki/Quantum_complexity_theory" title="Quantum complexity theory">Quantum complexity theory</a></li> <li><a href="/wiki/Quantum_computing" title="Quantum computing">Quantum computing</a> <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/Quantum_cryptography" title="Quantum cryptography">Quantum cryptography</a></li> <li><a href="/wiki/Quantum_electronics" class="mw-redirect" title="Quantum electronics">Quantum electronics</a></li> <li><a href="/wiki/Quantum_error_correction" title="Quantum error correction">Quantum error correction</a></li> <li><a href="/wiki/Quantum_imaging" title="Quantum imaging">Quantum imaging</a></li> <li><a href="/wiki/Quantum_image_processing" title="Quantum image processing">Quantum image processing</a></li> <li><a href="/wiki/Quantum_information" title="Quantum information">Quantum information</a></li> <li><a href="/wiki/Quantum_key_distribution" title="Quantum key distribution">Quantum key distribution</a></li> <li><a href="/wiki/Quantum_logic" title="Quantum logic">Quantum logic</a></li> <li><a href="/wiki/Quantum_logic_gate" title="Quantum logic gate">Quantum logic gates</a></li> <li><a href="/wiki/Quantum_machine" title="Quantum machine">Quantum machine</a></li> <li><a href="/wiki/Quantum_machine_learning" title="Quantum machine learning">Quantum machine learning</a></li> <li><a href="/wiki/Quantum_metamaterial" title="Quantum metamaterial">Quantum metamaterial</a></li> <li><a href="/wiki/Quantum_metrology" title="Quantum metrology">Quantum metrology</a></li> <li><a href="/wiki/Quantum_network" title="Quantum network">Quantum network</a></li> <li><a href="/wiki/Quantum_neural_network" title="Quantum neural network">Quantum neural network</a></li> <li><a href="/wiki/Quantum_optics" title="Quantum optics">Quantum optics</a></li> <li><a href="/wiki/Quantum_programming" title="Quantum programming">Quantum programming</a></li> <li><a href="/wiki/Quantum_sensor" title="Quantum sensor">Quantum sensing</a></li> <li><a href="/wiki/Quantum_simulator" title="Quantum simulator">Quantum simulator</a></li> <li><a href="/wiki/Quantum_teleportation" title="Quantum teleportation">Quantum teleportation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Extensions</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/Quantum_fluctuation" title="Quantum fluctuation">Quantum fluctuation</a></li> <li><a href="/wiki/Casimir_effect" title="Casimir effect">Casimir effect</a></li> <li><a href="/wiki/Quantum_statistical_mechanics" title="Quantum statistical mechanics">Quantum statistical mechanics</a></li> <li><a href="/wiki/Quantum_field_theory" title="Quantum field theory">Quantum field theory</a> <ul><li><a href="/wiki/History_of_quantum_field_theory" title="History of quantum field theory">History</a></li></ul></li> <li><a href="/wiki/Quantum_gravity" title="Quantum gravity">Quantum gravity</a></li> <li><a href="/wiki/Relativistic_quantum_mechanics" title="Relativistic quantum mechanics">Relativistic quantum mechanics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</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/Schr%C3%B6dinger%27s_cat" title="Schrödinger's cat">Schrödinger's cat</a> <ul><li><a href="/wiki/Schr%C3%B6dinger%27s_cat_in_popular_culture" title="Schrödinger's cat in popular culture">in popular culture</a></li></ul></li> <li><a href="/wiki/Wigner%27s_friend" title="Wigner's friend">Wigner's friend</a></li> <li><a href="/wiki/Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox" title="Einstein–Podolsky–Rosen paradox">EPR paradox</a></li> <li><a href="/wiki/Quantum_mysticism" title="Quantum mysticism">Quantum mysticism</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><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:Quantum_mechanics" title="Category:Quantum mechanics">Category</a></li></ul> </div></td></tr></tbody></table></div> <style 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