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</button> <ul id="toc-The_"Paradox"_paper-sublist" class="vector-toc-list"> <li id="toc-Bohr's_reply" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bohr's_reply"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Bohr's reply</span> </div> </a> <ul id="toc-Bohr's_reply-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Einstein's_own_argument" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Einstein's_own_argument"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Einstein's own argument</span> </div> </a> <ul id="toc-Einstein's_own_argument-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Later_developments" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Later_developments"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Later developments</span> </div> </a> <button aria-controls="toc-Later_developments-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 Later developments subsection</span> </button> <ul id="toc-Later_developments-sublist" class="vector-toc-list"> <li id="toc-Bohm's_variant" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bohm's_variant"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Bohm's variant</span> </div> </a> <ul id="toc-Bohm's_variant-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bell's_theorem" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bell's_theorem"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Bell's theorem</span> </div> </a> <ul id="toc-Bell's_theorem-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Steering" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Steering"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Steering</span> </div> </a> <ul id="toc-Steering-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Locality" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Locality"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Locality</span> </div> </a> <ul id="toc-Locality-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mathematical_formulation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mathematical_formulation"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Mathematical formulation</span> </div> </a> <ul id="toc-Mathematical_formulation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span 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-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-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">8</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-Selected_papers" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Selected_papers"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Selected papers</span> </div> </a> <ul id="toc-Selected_papers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Books" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Books"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2</span> <span>Books</span> </div> </a> <ul id="toc-Books-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">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </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">Einstein–Podolsky–Rosen paradox</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 41 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-41" 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">41 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D9%81%D8%A7%D8%B1%D9%82%D8%A9_%D8%A5%D9%8A_%D8%A8%D9%8A_%D8%A2%D8%B1" title="مفارقة إي بي آر – Arabic" lang="ar" hreflang="ar" data-title="مفارقة إي بي آر" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/EPR_paradoksu" title="EPR paradoksu – Azerbaijani" lang="az" hreflang="az" data-title="EPR paradoksu" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%86%E0%A6%87%E0%A6%A8%E0%A6%B8%E0%A7%8D%E0%A6%9F%E0%A6%BE%E0%A6%87%E0%A6%A8%E2%80%93%E0%A6%AA%E0%A7%8B%E0%A6%A1%E0%A6%B2%E0%A6%B8%E0%A7%8D%E0%A6%95%E0%A6%BF%E2%80%93%E0%A6%B0%E0%A7%8B%E0%A6%9C%E0%A7%87%E0%A6%A8_%E0%A6%AA%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%B0%E0%A6%BE%E0%A6%A1%E0%A6%95%E0%A7%8D%E0%A6%B8" title="আইনস্টাইন–পোডলস্কি–রোজেন প্যারাডক্স – Bangla" lang="bn" hreflang="bn" data-title="আইনস্টাইন–পোডলস্কি–রোজেন প্যারাডক্স" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D0%B0%D1%80%D0%B0%D0%B4%D0%BE%D0%BA%D1%81_%D0%BD%D0%B0_%D0%90%D0%B9%D0%BD%D1%89%D0%B0%D0%B9%D0%BD_%E2%80%93_%D0%9F%D0%BE%D0%B4%D0%BE%D0%BB%D1%81%D0%BA%D0%B8_%E2%80%93_%D0%A0%D0%BE%D0%B7%D0%B5%D0%BD" title="Парадокс на Айнщайн – Подолски – Розен – Bulgarian" lang="bg" hreflang="bg" data-title="Парадокс на Айнщайн – Подолски – Розен" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Paradoxa_EPR" title="Paradoxa EPR – Catalan" lang="ca" hreflang="ca" data-title="Paradoxa EPR" 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/EPR_paradox" title="EPR paradox – Czech" lang="cs" hreflang="cs" data-title="EPR paradox" 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/EPR-paradokset" title="EPR-paradokset – Danish" lang="da" hreflang="da" data-title="EPR-paradokset" 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/Einstein-Podolsky-Rosen-Paradoxon" title="Einstein-Podolsky-Rosen-Paradoxon – German" lang="de" hreflang="de" data-title="Einstein-Podolsky-Rosen-Paradoxon" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CE%B1%CF%81%CE%AC%CE%B4%CE%BF%CE%BE%CE%BF_EPR" title="Παράδοξο EPR – Greek" lang="el" hreflang="el" data-title="Παράδοξο EPR" 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/Paradoja_EPR" title="Paradoja EPR – Spanish" lang="es" hreflang="es" data-title="Paradoja EPR" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/EPR_paradokso" title="EPR paradokso – Esperanto" lang="eo" hreflang="eo" data-title="EPR paradokso" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/EPR_paradoxa" title="EPR paradoxa – Basque" lang="eu" hreflang="eu" data-title="EPR paradoxa" 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/%D9%BE%D8%A7%D8%B1%D8%A7%D8%AF%D9%88%DA%A9%D8%B3_%D8%A7%DB%8C%E2%80%8C%D9%BE%DB%8C%E2%80%8C%D8%A2%D8%B1" title="پارادوکس ای‌پی‌آر – Persian" lang="fa" hreflang="fa" data-title="پارادوکس ای‌پی‌آر" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Paradoxe_EPR" title="Paradoxe EPR – French" lang="fr" hreflang="fr" data-title="Paradoxe EPR" 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/Paradoxo_EPR" title="Paradoxo EPR – Galician" lang="gl" hreflang="gl" data-title="Paradoxo EPR" 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/EPR_%EC%97%AD%EC%84%A4" title="EPR 역설 – Korean" lang="ko" hreflang="ko" data-title="EPR 역설" 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%B7%D5%B5%D5%B6%D5%B7%D5%BF%D5%A5%D5%B5%D5%B6-%D5%8A%D5%B8%D5%A4%D5%B8%D5%AC%D5%BD%D5%AF%D5%AB-%D5%8C%D5%B8%D5%A6%D5%A5%D5%B6%D5%AB_%D5%BA%D5%A1%D6%80%D5%A1%D5%A4%D5%B8%D6%84%D5%BD" title="Էյնշտեյն-Պոդոլսկի-Ռոզենի պարադոքս – Armenian" lang="hy" hreflang="hy" data-title="Էյնշտեյն-Պոդոլսկի-Ռոզենի պարադոքս" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hr badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://hr.wikipedia.org/wiki/EPR_paradoks" title="EPR paradoks – Croatian" lang="hr" hreflang="hr" data-title="EPR paradoks" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Paradoks_EPR" title="Paradoks EPR – Indonesian" lang="id" hreflang="id" data-title="Paradoks EPR" 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/Paradosso_di_Einstein-Podolsky-Rosen" title="Paradosso di Einstein-Podolsky-Rosen – Italian" lang="it" hreflang="it" data-title="Paradosso di Einstein-Podolsky-Rosen" 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%94%D7%A4%D7%A8%D7%93%D7%95%D7%A7%D7%A1_%D7%A9%D7%9C_%D7%90%D7%99%D7%99%D7%A0%D7%A9%D7%98%D7%99%D7%99%D7%9F-%D7%A4%D7%95%D7%93%D7%95%D7%9C%D7%A1%D7%A7%D7%99-%D7%A8%D7%95%D7%96%D7%9F" title="הפרדוקס של איינשטיין-פודולסקי-רוזן – Hebrew" lang="he" hreflang="he" data-title="הפרדוקס של איינשטיין-פודולסקי-רוזן" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/EPR-paradoxon" title="EPR-paradoxon – Hungarian" lang="hu" hreflang="hu" data-title="EPR-paradoxon" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/EPR-paradox" title="EPR-paradox – Dutch" lang="nl" hreflang="nl" data-title="EPR-paradox" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A2%E3%82%A4%E3%83%B3%E3%82%B7%E3%83%A5%E3%82%BF%E3%82%A4%E3%83%B3%EF%BC%9D%E3%83%9D%E3%83%89%E3%83%AB%E3%82%B9%E3%82%AD%E3%83%BC%EF%BC%9D%E3%83%AD%E3%83%BC%E3%82%BC%E3%83%B3%E3%81%AE%E3%83%91%E3%83%A9%E3%83%89%E3%83%83%E3%82%AF%E3%82%B9" title="アインシュタイン＝ポドルスキー＝ローゼンのパラドックス – Japanese" lang="ja" hreflang="ja" data-title="アインシュタイン＝ポドルスキー＝ローゼンのパラドックス" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/EPR-paradokset" title="EPR-paradokset – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="EPR-paradokset" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Einstein%E2%80%93Podolsky%E2%80%93Rosen-paradokset" title="Einstein–Podolsky–Rosen-paradokset – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Einstein–Podolsky–Rosen-paradokset" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Paradoks_EPR" title="Paradoks EPR – Polish" lang="pl" hreflang="pl" data-title="Paradoks EPR" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Paradoxo_EPR" title="Paradoxo EPR – Portuguese" lang="pt" hreflang="pt" data-title="Paradoxo EPR" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Paradoxul_EPR" title="Paradoxul EPR – Romanian" lang="ro" hreflang="ro" data-title="Paradoxul EPR" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D0%B0%D1%80%D0%B0%D0%B4%D0%BE%D0%BA%D1%81_%D0%AD%D0%B9%D0%BD%D1%88%D1%82%D0%B5%D0%B9%D0%BD%D0%B0_%E2%80%94_%D0%9F%D0%BE%D0%B4%D0%BE%D0%BB%D1%8C%D1%81%D0%BA%D0%BE%D0%B3%D0%BE_%E2%80%94_%D0%A0%D0%BE%D0%B7%D0%B5%D0%BD%D0%B0" title="Парадокс Эйнштейна — Подольского — Розена – Russian" lang="ru" hreflang="ru" data-title="Парадокс Эйнштейна — Подольского — Розена" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/EPR_paradox" title="EPR paradox – Simple English" lang="en-simple" hreflang="en-simple" data-title="EPR paradox" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link 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.sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><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"><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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><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 mw-collapsed"><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 href="/wiki/Double-slit_experiment" title="Double-slit experiment">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 class="mw-selflink selflink">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> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Albert_Einstein,_by_Doris_Ulmann.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/09/Albert_Einstein%2C_by_Doris_Ulmann.jpg/200px-Albert_Einstein%2C_by_Doris_Ulmann.jpg" decoding="async" width="200" height="265" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/09/Albert_Einstein%2C_by_Doris_Ulmann.jpg/300px-Albert_Einstein%2C_by_Doris_Ulmann.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/09/Albert_Einstein%2C_by_Doris_Ulmann.jpg/400px-Albert_Einstein%2C_by_Doris_Ulmann.jpg 2x" data-file-width="870" data-file-height="1154" /></a><figcaption><a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a></figcaption></figure> <p>The <b>Einstein–Podolsky–Rosen</b> (<b>EPR</b>) <b>paradox</b> is a <a href="/wiki/Thought_experiment" title="Thought experiment">thought experiment</a> proposed by physicists <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>, <a href="/wiki/Boris_Podolsky" title="Boris Podolsky">Boris Podolsky</a> and <a href="/wiki/Nathan_Rosen" title="Nathan Rosen">Nathan Rosen</a> which argues that the description of physical reality provided by <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a> is incomplete.<sup id="cite_ref-EPR_1-0" class="reference"><a href="#cite_note-EPR-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> In a 1935 paper titled "Can Quantum-Mechanical Description of Physical Reality be Considered Complete?", they argued for the existence of "elements of reality" that were not part of quantum theory, and speculated that it should be possible to construct a theory containing these <a href="/wiki/Hidden-variable_theory" title="Hidden-variable theory">hidden variables</a>. Resolutions of the paradox have important implications for the <a href="/wiki/Interpretation_of_quantum_mechanics" class="mw-redirect" title="Interpretation of quantum mechanics">interpretation of quantum mechanics</a>. </p><p>The thought experiment involves a pair of particles prepared in what would later become known as an <a href="/wiki/Quantum_entanglement" title="Quantum entanglement">entangled</a> <a href="/wiki/Quantum_state" title="Quantum state">state</a>. Einstein, Podolsky, and Rosen pointed out that, in this state, if the position of the first particle were measured, the result of measuring the position of the second particle could be predicted. If instead the momentum of the first particle were measured, then the result of measuring the momentum of the second particle could be predicted. They argued that no action taken on the first particle could instantaneously affect the other, since this would involve information being transmitted faster than light, which is impossible according to the <a href="/wiki/Theory_of_relativity" title="Theory of relativity">theory of relativity</a>. They invoked a principle, later known as the "EPR criterion of reality", positing that: "If, without in any way disturbing a system, we can predict with certainty (i.e., with <a href="/wiki/Probability" title="Probability">probability</a> equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity." From this, they inferred that the second particle must have a definite value of both position and of momentum prior to either quantity being measured. But quantum mechanics considers these two observables <a href="/wiki/Observable#Incompatibility_of_observables_in_quantum_mechanics" title="Observable">incompatible</a> and thus does not associate simultaneous values for both to any system. Einstein, Podolsky, and Rosen therefore concluded that quantum theory does not provide a complete description of reality.<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> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="The_"Paradox"_paper"><span id="The_.22Paradox.22_paper"></span>The "Paradox" paper</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox&action=edit&section=1" title="Edit section: The "Paradox" paper"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The term "Einstein–Podolsky–Rosen paradox" or "EPR" arose from a paper written in 1934 after Einstein joined the <a href="/wiki/Institute_for_Advanced_Study" title="Institute for Advanced Study">Institute for Advanced Study</a>, having <a href="/wiki/Albert_Einstein#1933:_Emigration_to_the_US" title="Albert Einstein">fled the rise of Nazi Germany</a>.<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-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The original paper<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> purports to describe what must happen to "two systems I and II, which we permit to interact", and after some time "we suppose that there is no longer any interaction between the two parts." The EPR description involves "two particles, A and B, [which] interact briefly and then move off in opposite directions."<sup id="cite_ref-Kumar2011_6-0" class="reference"><a href="#cite_note-Kumar2011-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> According to <a href="/wiki/Heisenberg%27s_uncertainty_principle" class="mw-redirect" title="Heisenberg's uncertainty principle">Heisenberg's uncertainty principle</a>, it is impossible to measure both the momentum and the position of particle B exactly; however, it is possible to measure the exact position of particle A. By calculation, therefore, with the exact position of particle A known, the exact position of particle B can be known. Alternatively, the exact momentum of particle A can be measured, so the exact momentum of particle B can be worked out. As <a href="/wiki/Manjit_Kumar" title="Manjit Kumar">Manjit Kumar</a> writes, "EPR argued that they had proved that ... [particle] B can have simultaneously exact values of position and momentum. ... Particle B has a position that is real and a momentum that is real. EPR appeared to have contrived a means to establish the exact values of <i>either</i> the momentum <i>or</i> the position of B due to measurements made on particle A, without the slightest possibility of particle B being physically disturbed."<sup id="cite_ref-Kumar2011_6-1" class="reference"><a href="#cite_note-Kumar2011-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>EPR tried to set up a paradox to question the range of true application of quantum mechanics: Quantum theory predicts that both values cannot be known for a particle, and yet the EPR thought experiment purports to show that they must all have determinate values. The EPR paper says: "We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete."<sup id="cite_ref-Kumar2011_6-2" class="reference"><a href="#cite_note-Kumar2011-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> The EPR paper ends by saying: "While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible." The 1935 EPR paper condensed the philosophical discussion into a physical argument. The authors claim that given a specific experiment, in which the outcome of a measurement is known before the measurement takes place, there must exist something in the real world, an "element of reality", that determines the measurement outcome. They postulate that these elements of reality are, in modern terminology, <a href="/wiki/Principle_of_locality" title="Principle of locality">local</a>, in the sense that each belongs to a certain point in <a href="/wiki/Spacetime" title="Spacetime">spacetime</a>. Each element may, again in modern terminology, only be influenced by events which are located in the backward <a href="/wiki/Light_cone" title="Light cone">light cone</a> of its point in spacetime (i.e. in the past). These claims are founded on assumptions about nature that constitute what is now known as <b>local realism</b>.<sup id="cite_ref-Jaeger2014_7-0" class="reference"><a href="#cite_note-Jaeger2014-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:NYT_May_4,_1935.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/NYT_May_4%2C_1935.jpg/250px-NYT_May_4%2C_1935.jpg" decoding="async" width="250" height="299" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/NYT_May_4%2C_1935.jpg/375px-NYT_May_4%2C_1935.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/NYT_May_4%2C_1935.jpg/500px-NYT_May_4%2C_1935.jpg 2x" data-file-width="569" data-file-height="680" /></a><figcaption>Article headline regarding the EPR paradox paper in the May 4, 1935, issue of <i><a href="/wiki/The_New_York_Times" title="The New York Times">The New York Times</a></i></figcaption></figure> <p>Though the EPR paper has often been taken as an exact expression of Einstein's views, it was primarily authored by Podolsky, based on discussions at the <a href="/wiki/Institute_for_Advanced_Study" title="Institute for Advanced Study">Institute for Advanced Study</a> with Einstein and Rosen. Einstein later expressed to <a href="/wiki/Erwin_Schr%C3%B6dinger" title="Erwin Schrödinger">Erwin Schrödinger</a> that, "it did not come out as well as I had originally wanted; rather, the essential thing was, so to speak, smothered by the formalism."<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Einstein would later go on to present an individual account of his local realist ideas.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Shortly before the EPR paper appeared in the <i><a href="/wiki/Physical_Review" title="Physical Review">Physical Review</a>,</i> <i><a href="/wiki/The_New_York_Times" title="The New York Times">The New York Times</a></i> ran a news story about it, under the headline "Einstein Attacks Quantum Theory".<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> The story, which quoted Podolsky, irritated Einstein, who wrote to the <i>Times,</i> "Any information upon which the article 'Einstein Attacks Quantum Theory' in your issue of May 4 is based was given to you without authority. It is my invariable practice to discuss scientific matters only in the appropriate forum and I deprecate advance publication of any announcement in regard to such matters in the secular press."<sup id="cite_ref-jammer1974_11-0" class="reference"><a href="#cite_note-jammer1974-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 189">: 189 </span></sup> </p><p>The <i>Times</i> story also sought out comment from physicist <a href="/wiki/Edward_Condon" title="Edward Condon">Edward Condon</a>, who said, "Of course, a great deal of the argument hinges on just what meaning is to be attached to the word 'reality' in physics."<sup id="cite_ref-jammer1974_11-1" class="reference"><a href="#cite_note-jammer1974-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 189">: 189 </span></sup> The physicist and historian <a href="/wiki/Max_Jammer" title="Max Jammer">Max Jammer</a> later noted, "[I]t remains a historical fact that the earliest criticism of the EPR paper — moreover, a criticism which correctly saw in Einstein's conception of physical reality the key problem of the whole issue — appeared in a daily newspaper prior to the publication of the criticized paper itself."<sup id="cite_ref-jammer1974_11-2" class="reference"><a href="#cite_note-jammer1974-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 190">: 190 </span></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Bohr's_reply"><span id="Bohr.27s_reply"></span>Bohr's reply</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox&action=edit&section=2" title="Edit section: Bohr's reply"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The publication of the paper prompted a response by <a href="/wiki/Niels_Bohr" title="Niels Bohr">Niels Bohr</a>, which he published in the same journal (<i><a href="/wiki/Physical_Review" title="Physical Review">Physical Review</a></i>), in the same year, using the same title.<sup id="cite_ref-Bohr1935_12-0" class="reference"><a href="#cite_note-Bohr1935-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> (This exchange was only one chapter in <a href="/wiki/Bohr%E2%80%93Einstein_debates" title="Bohr–Einstein debates">a prolonged debate between Bohr and Einstein</a> about the nature of quantum reality.) He argued that EPR had reasoned fallaciously. Bohr said measurements of position and of momentum are <a href="/wiki/Complementarity_(physics)" title="Complementarity (physics)">complementary</a>, meaning the choice to measure one excludes the possibility of measuring the other. Consequently, a fact deduced regarding one arrangement of laboratory apparatus could not be combined with a fact deduced by means of the other, and so, the inference of predetermined position and momentum values for the second particle was not valid. Bohr concluded that EPR's "arguments do not justify their conclusion that the quantum description turns out to be essentially incomplete." </p> <div class="mw-heading mw-heading3"><h3 id="Einstein's_own_argument"><span id="Einstein.27s_own_argument"></span>Einstein's own argument</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox&action=edit&section=3" title="Edit section: Einstein's own argument"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In his own publications and correspondence, Einstein indicated that he was not satisfied with the EPR paper and that Rosen had authored most of it. He later used a different argument to insist that quantum mechanics is an incomplete theory.<sup id="cite_ref-:0_13-0" class="reference"><a href="#cite_note-:0-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-howard_14-0" class="reference"><a href="#cite_note-howard-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 83ff">: 83ff </span></sup> He explicitly de-emphasized EPR's attribution of "elements of reality" to the position and momentum of particle B, saying that "I couldn't care less" whether the resulting states of particle B allowed one to predict the position and momentum with certainty.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> </p><p>For Einstein, the crucial part of the argument was the demonstration of <a href="/wiki/Quantum_nonlocality" title="Quantum nonlocality">nonlocality</a>, that the choice of measurement done in particle A, either position or momentum, would lead to <i>two different</i> quantum states of particle B. He argued that, because of locality, the real state of particle B could not depend on which kind of measurement was done in A and that the quantum states therefore cannot be in one-to-one correspondence with the real states.<sup id="cite_ref-:0_13-1" class="reference"><a href="#cite_note-:0-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Einstein struggled unsuccessfully for the rest of his life to find a theory that could better comply with his idea of locality. </p> <div class="mw-heading mw-heading2"><h2 id="Later_developments">Later developments</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox&action=edit&section=4" title="Edit section: Later developments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Bohm's_variant"><span id="Bohm.27s_variant"></span>Bohm's variant</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox&action=edit&section=5" title="Edit section: Bohm's variant"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1951, <a href="/wiki/David_Bohm" title="David Bohm">David Bohm</a> proposed a variant of the EPR thought experiment in which the measurements have discrete ranges of possible outcomes, unlike the position and momentum measurements considered by EPR.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> The EPR–Bohm thought experiment can be explained using electron–<a href="/wiki/Positron" title="Positron">positron</a> pairs. Suppose we have a source that emits electron–positron pairs, with the electron sent to destination <i>A</i>, where there is an observer named <a href="/wiki/Alice_and_Bob" title="Alice and Bob">Alice</a>, and the positron sent to destination <i>B</i>, where there is an observer named <a href="/wiki/Alice_and_Bob" title="Alice and Bob">Bob</a>. According to quantum mechanics, we can arrange our source so that each emitted pair occupies a quantum state called a <a href="/wiki/Spin_singlet" class="mw-redirect" title="Spin singlet">spin singlet</a>. The particles are thus said to be <a href="/wiki/Quantum_entanglement" title="Quantum entanglement">entangled</a>. This can be viewed as a <a href="/wiki/Quantum_superposition" title="Quantum superposition">quantum superposition</a> of two states, which we call state I and state II. In state I, the electron has <a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</a> pointing upward along the <i>z</i>-axis (<i>+z</i>) and the positron has spin pointing downward along the <i>z</i>-axis (−<i>z</i>). In state II, the electron has spin −<i>z</i> and the positron has spin +<i>z</i>. Because it is in a superposition of states, it is impossible without measuring to know the definite state of spin of either particle in the spin singlet.<sup id="cite_ref-Griffiths2004_21-0" class="reference"><a href="#cite_note-Griffiths2004-21"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 421–422">: 421–422 </span></sup> </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:EPR_illustration.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/EPR_illustration.svg/500px-EPR_illustration.svg.png" decoding="async" width="500" height="166" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/EPR_illustration.svg/750px-EPR_illustration.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/57/EPR_illustration.svg/1000px-EPR_illustration.svg.png 2x" data-file-width="628" data-file-height="208" /></a><figcaption>The EPR thought experiment, performed with electron–positron pairs. A source (center) sends particles toward two observers, electrons to Alice (left) and positrons to Bob (right), who can perform spin measurements.</figcaption></figure> <p>Alice now measures the spin along the <i>z</i>-axis. She can obtain one of two possible outcomes: +<i>z</i> or −<i>z</i>. Suppose she gets +<i>z</i>. Informally speaking, the quantum state of the system <a href="/wiki/Wavefunction_collapse" class="mw-redirect" title="Wavefunction collapse">collapses</a> into state I. The quantum state determines the probable outcomes of any measurement performed on the system. In this case, if Bob subsequently measures spin along the <i>z</i>-axis, there is 100% probability that he will obtain −<i>z</i>. Similarly, if Alice gets −<i>z</i>, Bob will get +<i>z</i>. There is nothing special about choosing the <i>z</i>-axis: according to quantum mechanics the spin singlet state may equally well be expressed as a superposition of spin states pointing in the <i>x</i> direction.<sup id="cite_ref-Laloe_22-0" class="reference"><a href="#cite_note-Laloe-22"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 318">: 318 </span></sup> </p><p>Whatever axis their spins are measured along, they are always found to be opposite. In quantum mechanics, the <i>x</i>-spin and <i>z</i>-spin are "incompatible observables", meaning the <a href="/wiki/Uncertainty_principle" title="Uncertainty principle">Heisenberg uncertainty principle</a> applies to alternating measurements of them: a quantum state cannot possess a definite value for both of these variables. Suppose Alice measures the <i>z</i>-spin and obtains <i>+z</i>, so that the quantum state collapses into state I. Now, instead of measuring the <i>z</i>-spin as well, Bob measures the <i>x</i>-spin. According to quantum mechanics, when the system is in state I, Bob's <i>x</i>-spin measurement will have a 50% probability of producing +<i>x</i> and a 50% probability of -<i>x</i>. It is impossible to predict which outcome will appear until Bob actually <i>performs</i> the measurement. Therefore, Bob's positron will have a definite spin when measured along the same axis as Alice's electron, but when measured in the perpendicular axis its spin will be uniformly random. It seems as if information has propagated (faster than light) from Alice's apparatus to make Bob's positron assume a definite spin in the appropriate axis. </p> <div class="mw-heading mw-heading3"><h3 id="Bell's_theorem"><span id="Bell.27s_theorem"></span>Bell's theorem</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox&action=edit&section=6" title="Edit section: Bell's theorem"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Bell%27s_theorem" title="Bell's theorem">Bell's theorem</a></div> <p>In 1964, <a href="/wiki/John_Stewart_Bell" title="John Stewart Bell">John Stewart Bell</a> published a paper<sup id="cite_ref-Bell1964_23-0" class="reference"><a href="#cite_note-Bell1964-23"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> investigating the puzzling situation at that time: on one hand, the EPR paradox purportedly showed that quantum mechanics was nonlocal, and suggested that a hidden-variable theory could heal this nonlocality. On the other hand, David Bohm had recently developed the first successful hidden-variable theory, but it had a grossly nonlocal character.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> Bell set out to investigate whether it was indeed possible to solve the nonlocality problem with hidden variables, and found out that first, the correlations shown in both EPR's and Bohm's versions of the paradox could indeed be explained in a local way with hidden variables, and second, that the correlations shown in his own variant of the paradox couldn't be explained by <i>any</i> local hidden-variable theory. This second result became known as the Bell theorem. </p><p>To understand the first result, consider the following toy hidden-variable theory introduced later by J.J. Sakurai:<sup id="cite_ref-Sakurai_26-0" class="reference"><a href="#cite_note-Sakurai-26"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 239–240">: 239–240 </span></sup> in it, quantum spin-singlet states emitted by the source are actually approximate descriptions for "true" physical states possessing definite values for the <i>z</i>-spin and <i>x</i>-spin. In these "true" states, the positron going to Bob always has spin values opposite to the electron going to Alice, but the values are otherwise completely random. For example, the first pair emitted by the source might be "(+<i>z</i>, −<i>x</i>) to Alice and (−<i>z</i>, +<i>x</i>) to Bob", the next pair "(−<i>z</i>, −<i>x</i>) to Alice and (+<i>z</i>, +<i>x</i>) to Bob", and so forth. Therefore, if Bob's measurement axis is aligned with Alice's, he will necessarily get the opposite of whatever Alice gets; otherwise, he will get "+" and "−" with equal probability. </p><p>Bell showed, however, that such models can only reproduce the singlet correlations when Alice and Bob make measurements on the same axis or on perpendicular axes. As soon as other angles between their axes are allowed, local hidden-variable theories become unable to reproduce the quantum mechanical correlations. This difference, expressed using inequalities known as "<a href="/wiki/Bell%27s_inequalities" class="mw-redirect" title="Bell's inequalities">Bell's inequalities</a>", is in principle experimentally testable. After the publication of Bell's paper, a variety of <a href="/wiki/Bell_test" title="Bell test">experiments to test Bell's inequalities</a> were carried out, notably by the group of <a href="/wiki/Alain_Aspect" title="Alain Aspect">Alain Aspect</a> in the 1980s;<sup id="cite_ref-Aspect1999_27-0" class="reference"><a href="#cite_note-Aspect1999-27"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> all experiments conducted to date have found behavior in line with the predictions of quantum mechanics. The present view of the situation is that quantum mechanics flatly contradicts Einstein's philosophical postulate that any acceptable physical theory must fulfill "local realism". The fact that quantum mechanics violates Bell inequalities indicates that any hidden-variable theory underlying quantum mechanics must be non-local; whether this should be taken to imply that quantum mechanics <i>itself</i> is non-local is a matter of continuing debate.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Steering">Steering</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox&action=edit&section=7" title="Edit section: Steering"><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/Quantum_steering" title="Quantum steering">Quantum steering</a></div> <p>Inspired by Schrödinger's treatment of the EPR paradox back in 1935,<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Howard_M._Wiseman" title="Howard M. Wiseman">Howard M. Wiseman</a> et al. formalised it in 2007 as the phenomenon of quantum steering.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> They defined steering as the situation where Alice's measurements on a part of an entangled state <i>steer</i> Bob's part of the state. That is, Bob's observations cannot be explained by a <i>local hidden state</i> model, where Bob would have a fixed quantum state in his side, that is classically correlated but otherwise independent of Alice's. </p> <div class="mw-heading mw-heading2"><h2 id="Locality">Locality</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox&action=edit&section=8" title="Edit section: Locality"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i><a href="/wiki/Principle_of_locality" title="Principle of locality">Locality</a></i> has several different meanings in physics. EPR describe the principle of locality as asserting that physical processes occurring at one place should have no immediate effect on the elements of reality at another location. At first sight, this appears to be a reasonable assumption to make, as it seems to be a consequence of <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a>, which states that energy can never be transmitted faster than the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a> without violating <a href="/wiki/Causality_(physics)" title="Causality (physics)">causality</a>;<sup id="cite_ref-Griffiths2004_21-1" class="reference"><a href="#cite_note-Griffiths2004-21"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 427–428">: 427–428 </span></sup><sup id="cite_ref-Blaylock_33-0" class="reference"><a href="#cite_note-Blaylock-33"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> however, it turns out that the usual rules for combining quantum mechanical and classical descriptions violate EPR's principle of locality without violating special relativity or causality.<sup id="cite_ref-Griffiths2004_21-2" class="reference"><a href="#cite_note-Griffiths2004-21"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 427–428">: 427–428 </span></sup><sup id="cite_ref-Blaylock_33-1" class="reference"><a href="#cite_note-Blaylock-33"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> Causality is preserved because there is no way for Alice to transmit messages (i.e., information) to Bob by manipulating her measurement axis. Whichever axis she uses, she has a 50% probability of obtaining "+" and 50% probability of obtaining "−", completely at <a href="/wiki/Randomness" title="Randomness">random</a>; according to quantum mechanics, it is fundamentally impossible for her to influence what result she gets. Furthermore, Bob is able to perform his measurement only <i>once</i>: there is a fundamental property of quantum mechanics, the <a href="/wiki/No-cloning_theorem" title="No-cloning theorem">no-cloning theorem</a>, which makes it impossible for him to make an arbitrary number of copies of the electron he receives, perform a spin measurement on each, and look at the statistical distribution of the results. Therefore, in the one measurement he is allowed to make, there is a 50% probability of getting "+" and 50% of getting "−", regardless of whether or not his axis is aligned with Alice's. </p><p>As a summary, the results of the EPR thought experiment do not contradict the predictions of special relativity. Neither the EPR paradox nor any quantum experiment demonstrates that <a href="/wiki/Faster-than-light_communication" class="mw-redirect" title="Faster-than-light communication">superluminal signaling</a> is possible; however, the principle of locality appeals powerfully to physical intuition, and Einstein, Podolsky and Rosen were unwilling to abandon it. Einstein derided the quantum mechanical predictions as "<a href="/wiki/Action_at_a_distance_(physics)" class="mw-redirect" title="Action at a distance (physics)">spooky action at a distance</a>".<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>b<span class="cite-bracket">]</span></a></sup> The conclusion they drew was that quantum mechanics is not a complete theory.<sup id="cite_ref-Bell1981_36-0" class="reference"><a href="#cite_note-Bell1981-36"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Mathematical_formulation">Mathematical formulation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox&action=edit&section=9" title="Edit section: Mathematical formulation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Bohm's variant of the EPR paradox can be expressed mathematically using the <a href="/wiki/Spin_(physics)" title="Spin (physics)">quantum mechanical formulation of spin</a>. The spin degree of freedom for an electron is associated with a two-dimensional complex <a href="/wiki/Vector_space" title="Vector space">vector space</a> <i>V</i>, with each quantum state corresponding to a vector in that space. The operators corresponding to the spin along the <i>x</i>, <i>y</i>, and <i>z</i> direction, denoted <i>S<sub>x</sub></i>, <i>S<sub>y</sub></i>, and <i>S<sub>z</sub></i> respectively, can be represented using the <a href="/wiki/Pauli_matrices" title="Pauli matrices">Pauli matrices</a>:<sup id="cite_ref-Sakurai_26-1" class="reference"><a href="#cite_note-Sakurai-26"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 9">: 9 </span></sup> <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 S_{x}={\frac {\hbar }{2}}{\begin{bmatrix}0&1\\1&0\end{bmatrix}},\quad S_{y}={\frac {\hbar }{2}}{\begin{bmatrix}0&-i\\i&0\end{bmatrix}},\quad S_{z}={\frac {\hbar }{2}}{\begin{bmatrix}1&0\\0&-1\end{bmatrix}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mo>,</mo> <mspace width="1em" /> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <mi>i</mi> </mtd> </mtr> <mtr> <mtd> <mi>i</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mo>,</mo> <mspace width="1em" /> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{x}={\frac {\hbar }{2}}{\begin{bmatrix}0&1\\1&0\end{bmatrix}},\quad S_{y}={\frac {\hbar }{2}}{\begin{bmatrix}0&-i\\i&0\end{bmatrix}},\quad S_{z}={\frac {\hbar }{2}}{\begin{bmatrix}1&0\\0&-1\end{bmatrix}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa529fb32fbcac2730d19b3f24d2b4a32b78be7c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:57.399ex; height:6.176ex;" alt="{\displaystyle S_{x}={\frac {\hbar }{2}}{\begin{bmatrix}0&1\\1&0\end{bmatrix}},\quad S_{y}={\frac {\hbar }{2}}{\begin{bmatrix}0&-i\\i&0\end{bmatrix}},\quad S_{z}={\frac {\hbar }{2}}{\begin{bmatrix}1&0\\0&-1\end{bmatrix}},}"></span> where <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 \hbar }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi class="MJX-variant">ℏ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \hbar }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de68de3a92517953436c93b5a76461d49160cc41" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.306ex; height:2.176ex;" alt="{\displaystyle \hbar }"></span> is the <a href="/wiki/Reduced_Planck_constant" class="mw-redirect" title="Reduced Planck constant">reduced Planck constant</a> (or the Planck constant divided by 2π). </p><p>The <a href="/wiki/Eigenstate" class="mw-redirect" title="Eigenstate">eigenstates</a> of <i>S<sub>z</sub></i> are represented as <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 \left|+z\right\rangle \leftrightarrow {\begin{bmatrix}1\\0\end{bmatrix}},\quad \left|-z\right\rangle \leftrightarrow {\begin{bmatrix}0\\1\end{bmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mrow> <mo>+</mo> <mi>z</mi> </mrow> <mo>⟩</mo> </mrow> <mo stretchy="false">↔</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mo>,</mo> <mspace width="1em" /> <mrow> <mo>|</mo> <mrow> <mo>−</mo> <mi>z</mi> </mrow> <mo>⟩</mo> </mrow> <mo stretchy="false">↔</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left|+z\right\rangle \leftrightarrow {\begin{bmatrix}1\\0\end{bmatrix}},\quad \left|-z\right\rangle \leftrightarrow {\begin{bmatrix}0\\1\end{bmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e72169fb4f44e1f4a749d2c9e5689fd5d05708ca" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:28.218ex; height:6.176ex;" alt="{\displaystyle \left|+z\right\rangle \leftrightarrow {\begin{bmatrix}1\\0\end{bmatrix}},\quad \left|-z\right\rangle \leftrightarrow {\begin{bmatrix}0\\1\end{bmatrix}}}"></span> and the eigenstates of <i>S<sub>x</sub></i> are represented as <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 \left|+x\right\rangle \leftrightarrow {\frac {1}{\sqrt {2}}}{\begin{bmatrix}1\\1\end{bmatrix}},\quad \left|-x\right\rangle \leftrightarrow {\frac {1}{\sqrt {2}}}{\begin{bmatrix}1\\-1\end{bmatrix}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mrow> <mo>+</mo> <mi>x</mi> </mrow> <mo>⟩</mo> </mrow> <mo stretchy="false">↔</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mo>,</mo> <mspace width="1em" /> <mrow> <mo>|</mo> <mrow> <mo>−</mo> <mi>x</mi> </mrow> <mo>⟩</mo> </mrow> <mo stretchy="false">↔</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>1</mn> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left|+x\right\rangle \leftrightarrow {\frac {1}{\sqrt {2}}}{\begin{bmatrix}1\\1\end{bmatrix}},\quad \left|-x\right\rangle \leftrightarrow {\frac {1}{\sqrt {2}}}{\begin{bmatrix}1\\-1\end{bmatrix}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/354a05d64729c3ab3ce32c837393af9085a8a60b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:39.025ex; height:6.509ex;" alt="{\displaystyle \left|+x\right\rangle \leftrightarrow {\frac {1}{\sqrt {2}}}{\begin{bmatrix}1\\1\end{bmatrix}},\quad \left|-x\right\rangle \leftrightarrow {\frac {1}{\sqrt {2}}}{\begin{bmatrix}1\\-1\end{bmatrix}}.}"></span> </p><p>The vector space of the electron-positron pair is <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 V\otimes V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>⊗</mo> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V\otimes V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52a1c6efb27fb1c61db37781404942628dca7f8b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.415ex; height:2.343ex;" alt="{\displaystyle V\otimes V}"></span>, the <a href="/wiki/Tensor_product" title="Tensor product">tensor product</a> of the electron's and positron's vector spaces. The spin singlet state is <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 \left|\psi \right\rangle ={\frac {1}{\sqrt {2}}}{\biggl (}\left|+z\right\rangle \otimes \left|-z\right\rangle -\left|-z\right\rangle \otimes \left|+z\right\rangle {\biggr )},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mi>ψ</mi> <mo>⟩</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> </mrow> <mrow> <mo>|</mo> <mrow> <mo>+</mo> <mi>z</mi> </mrow> <mo>⟩</mo> </mrow> <mo>⊗</mo> <mrow> <mo>|</mo> <mrow> <mo>−</mo> <mi>z</mi> </mrow> <mo>⟩</mo> </mrow> <mo>−</mo> <mrow> <mo>|</mo> <mrow> <mo>−</mo> <mi>z</mi> </mrow> <mo>⟩</mo> </mrow> <mo>⊗</mo> <mrow> <mo>|</mo> <mrow> <mo>+</mo> <mi>z</mi> </mrow> <mo>⟩</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left|\psi \right\rangle ={\frac {1}{\sqrt {2}}}{\biggl (}\left|+z\right\rangle \otimes \left|-z\right\rangle -\left|-z\right\rangle \otimes \left|+z\right\rangle {\biggr )},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e47af4dc241ad7fc422a04acb79bec4758abae43" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:41.252ex; height:6.509ex;" alt="{\displaystyle \left|\psi \right\rangle ={\frac {1}{\sqrt {2}}}{\biggl (}\left|+z\right\rangle \otimes \left|-z\right\rangle -\left|-z\right\rangle \otimes \left|+z\right\rangle {\biggr )},}"></span> where the two terms on the right hand side are what we have referred to as state I and state II above. </p><p>From the above equations, it can be shown that the spin singlet can also be written as <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 \left|\psi \right\rangle =-{\frac {1}{\sqrt {2}}}{\biggl (}\left|+x\right\rangle \otimes \left|-x\right\rangle -\left|-x\right\rangle \otimes \left|+x\right\rangle {\biggr )},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mi>ψ</mi> <mo>⟩</mo> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> </mrow> <mrow> <mo>|</mo> <mrow> <mo>+</mo> <mi>x</mi> </mrow> <mo>⟩</mo> </mrow> <mo>⊗</mo> <mrow> <mo>|</mo> <mrow> <mo>−</mo> <mi>x</mi> </mrow> <mo>⟩</mo> </mrow> <mo>−</mo> <mrow> <mo>|</mo> <mrow> <mo>−</mo> <mi>x</mi> </mrow> <mo>⟩</mo> </mrow> <mo>⊗</mo> <mrow> <mo>|</mo> <mrow> <mo>+</mo> <mi>x</mi> </mrow> <mo>⟩</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left|\psi \right\rangle =-{\frac {1}{\sqrt {2}}}{\biggl (}\left|+x\right\rangle \otimes \left|-x\right\rangle -\left|-x\right\rangle \otimes \left|+x\right\rangle {\biggr )},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a693d7627cadd7aad671d4eaa547c1b5edc54a3" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:44.026ex; height:6.509ex;" alt="{\displaystyle \left|\psi \right\rangle =-{\frac {1}{\sqrt {2}}}{\biggl (}\left|+x\right\rangle \otimes \left|-x\right\rangle -\left|-x\right\rangle \otimes \left|+x\right\rangle {\biggr )},}"></span> where the terms on the right hand side are what we have referred to as state Ia and state IIa. </p><p>To illustrate the paradox, we need to show that after Alice's measurement of <i>S<sub>z</sub></i> (or <i>S<sub>x</sub></i>), Bob's value of <i>S<sub>z</sub></i> (or <i>S<sub>x</sub></i>) is uniquely determined and Bob's value of <i>S<sub>x</sub></i> (or <i>S<sub>z</sub></i>) is uniformly random. This follows from the principles of <a href="/wiki/Measurement_in_quantum_mechanics" title="Measurement in quantum mechanics">measurement in quantum mechanics</a>. When <i>S</i><sub>z</sub> is measured, the system state <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 |\psi \rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\psi \rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc27f1893b769a08cd6b296e115a29e61cab675e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.065ex; height:2.843ex;" alt="{\displaystyle |\psi \rangle }"></span> collapses into an eigenvector of <i>S</i><sub>z</sub>. If the measurement result is <i>+z</i>, this means that immediately after measurement the system state collapses to <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 \left|+z\right\rangle \otimes \left|-z\right\rangle =\left|+z\right\rangle \otimes {\frac {\left|+x\right\rangle -\left|-x\right\rangle }{\sqrt {2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mrow> <mo>+</mo> <mi>z</mi> </mrow> <mo>⟩</mo> </mrow> <mo>⊗</mo> <mrow> <mo>|</mo> <mrow> <mo>−</mo> <mi>z</mi> </mrow> <mo>⟩</mo> </mrow> <mo>=</mo> <mrow> <mo>|</mo> <mrow> <mo>+</mo> <mi>z</mi> </mrow> <mo>⟩</mo> </mrow> <mo>⊗</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow> <mo>|</mo> <mrow> <mo>+</mo> <mi>x</mi> </mrow> <mo>⟩</mo> </mrow> <mo>−</mo> <mrow> <mo>|</mo> <mrow> <mo>−</mo> <mi>x</mi> </mrow> <mo>⟩</mo> </mrow> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left|+z\right\rangle \otimes \left|-z\right\rangle =\left|+z\right\rangle \otimes {\frac {\left|+x\right\rangle -\left|-x\right\rangle }{\sqrt {2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09a153ea74c9a501b5656de24883310c6bd5cc48" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:35.825ex; height:6.676ex;" alt="{\displaystyle \left|+z\right\rangle \otimes \left|-z\right\rangle =\left|+z\right\rangle \otimes {\frac {\left|+x\right\rangle -\left|-x\right\rangle }{\sqrt {2}}}.}"></span> </p><p>Similarly, if Alice's measurement result is −<i>z</i>, the state collapses to <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 \left|-z\right\rangle \otimes \left|+z\right\rangle =\left|-z\right\rangle \otimes {\frac {\left|+x\right\rangle +\left|-x\right\rangle }{\sqrt {2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mrow> <mo>−</mo> <mi>z</mi> </mrow> <mo>⟩</mo> </mrow> <mo>⊗</mo> <mrow> <mo>|</mo> <mrow> <mo>+</mo> <mi>z</mi> </mrow> <mo>⟩</mo> </mrow> <mo>=</mo> <mrow> <mo>|</mo> <mrow> <mo>−</mo> <mi>z</mi> </mrow> <mo>⟩</mo> </mrow> <mo>⊗</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow> <mo>|</mo> <mrow> <mo>+</mo> <mi>x</mi> </mrow> <mo>⟩</mo> </mrow> <mo>+</mo> <mrow> <mo>|</mo> <mrow> <mo>−</mo> <mi>x</mi> </mrow> <mo>⟩</mo> </mrow> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left|-z\right\rangle \otimes \left|+z\right\rangle =\left|-z\right\rangle \otimes {\frac {\left|+x\right\rangle +\left|-x\right\rangle }{\sqrt {2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04b944f187ca37665e654ee142421ae361b3d7bc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:35.825ex; height:6.676ex;" alt="{\displaystyle \left|-z\right\rangle \otimes \left|+z\right\rangle =\left|-z\right\rangle \otimes {\frac {\left|+x\right\rangle +\left|-x\right\rangle }{\sqrt {2}}}.}"></span> The left hand side of both equations show that the measurement of <i>S</i><sub>z</sub> on Bob's positron is now determined, it will be −<i>z</i> in the first case or +<i>z</i> in the second case. The right hand side of the equations show that the measurement of <i>S</i><sub>x</sub> on Bob's positron will return, in both cases, +<i>x</i> or -<i>x</i> with probability 1/2 each. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox&action=edit&section=10" 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: 21em;"> <ul><li><a href="/wiki/Aspect%27s_experiment" title="Aspect's experiment">Aspect's experiment</a></li> <li><a href="/wiki/Bohr%E2%80%93Einstein_debates#The_argument_of_EPR" title="Bohr–Einstein debates">Bohr-Einstein debates: The argument of EPR</a></li> <li><a href="/wiki/Coherence_(physics)" title="Coherence (physics)">Coherence</a></li> <li><a href="/wiki/Correlation_does_not_imply_causation" title="Correlation does not imply causation">Correlation does not imply causation</a></li> <li><a href="/wiki/CHSH_inequality" title="CHSH inequality">CHSH inequality</a></li> <li><a href="/wiki/ER_%3D_EPR" title="ER = EPR">ER = EPR</a></li> <li><a href="/wiki/GHZ_experiment" class="mw-redirect" title="GHZ experiment">GHZ experiment</a></li> <li><a href="/wiki/Measurement_problem" title="Measurement problem">Measurement problem</a></li> <li><a href="/wiki/Philosophy_of_information" title="Philosophy of information">Philosophy of information</a></li> <li><a href="/wiki/Philosophy_of_physics" title="Philosophy of physics">Philosophy of physics</a></li> <li><a href="/wiki/Popper%27s_experiment" title="Popper's experiment">Popper's experiment</a></li> <li><a href="/wiki/Superdeterminism" title="Superdeterminism">Superdeterminism</a></li> <li><a href="/wiki/Quantum_entanglement" title="Quantum entanglement">Quantum entanglement</a></li> <li><a href="/wiki/Quantum_information" title="Quantum information">Quantum information</a></li> <li><a href="/wiki/Quantum_pseudo-telepathy" title="Quantum pseudo-telepathy">Quantum pseudo-telepathy</a></li> <li><a href="/wiki/Quantum_teleportation" title="Quantum teleportation">Quantum teleportation</a></li> <li><a href="/wiki/Quantum_Zeno_effect" title="Quantum Zeno effect">Quantum Zeno effect</a></li> <li><a href="/wiki/Synchronicity" title="Synchronicity">Synchronicity</a></li> <li><a href="/wiki/John_Clive_Ward" title="John Clive Ward">Ward's probability amplitude</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox&action=edit&section=11" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width reflist-lower-alpha" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">"Ob die <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 \psi _{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi _{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ca3b90bba42c451129c4969322e175f5a1d3368" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.993ex; height:2.509ex;" alt="{\displaystyle \psi _{B}}"></span> und <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 \psi _{\underline {B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <munder> <mi>B</mi> <mo>_</mo> </munder> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi _{\underline {B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ac85b69ed41fe87eb9e663312424bc4d08f170e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.71ex; margin-bottom: -0.628ex; width:2.994ex; height:3.176ex;" alt="{\displaystyle \psi _{\underline {B}}}"></span> als Eigenfunktionen von Observabeln <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 B,{\underline {B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <munder> <mi>B</mi> <mo>_</mo> </munder> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B,{\underline {B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c588edf99b1de72e3be7aa7ab98e056c8772e9de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.511ex; margin-bottom: -0.827ex; width:4.564ex; height:3.176ex;" alt="{\displaystyle B,{\underline {B}}}"></span> aufgefasst werden können ist mir <i>wurst</i>>." Emphasis from the original. "Ist mir wurst" is a German expression that literally translates to "It is a sausage to me", but means "I couldn't care less". Letter from Einstein to Schrödinger, dated 19th June 1935.<sup id="cite_ref-howard_14-1" class="reference"><a href="#cite_note-howard-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></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">"Spukhaften Fernwirkung", in the German original. Used in a letter to <a href="/wiki/Max_Born" title="Max Born">Max Born</a> dated March 3, 1947.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup></span> </li> </ol></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=Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox&action=edit&section=12" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-EPR-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-EPR_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="CITEREFEinsteinB_PodolskyN_Rosen1935" class="citation journal cs1">Einstein, A; B Podolsky; N Rosen (1935-05-15). <a rel="nofollow" class="external text" href="https://cds.cern.ch/record/405662/files/PhysRev.47.777.pdf">"Can Quantum-Mechanical Description of Physical Reality be Considered Complete?"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Physical_Review" title="Physical Review">Physical Review</a></i>. <b>47</b> (10): 777–780. <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/1935PhRv...47..777E">1935PhRv...47..777E</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/10.1103%2FPhysRev.47.777">10.1103/PhysRev.47.777</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review&rft.atitle=Can+Quantum-Mechanical+Description+of+Physical+Reality+be+Considered+Complete%3F&rft.volume=47&rft.issue=10&rft.pages=777-780&rft.date=1935-05-15&rft_id=info%3Adoi%2F10.1103%2FPhysRev.47.777&rft_id=info%3Abibcode%2F1935PhRv...47..777E&rft.aulast=Einstein&rft.aufirst=A&rft.au=B+Podolsky&rft.au=N+Rosen&rft_id=https%3A%2F%2Fcds.cern.ch%2Frecord%2F405662%2Ffiles%2FPhysRev.47.777.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" 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="CITEREFPeres2002" class="citation book cs1"><a href="/wiki/Asher_Peres" title="Asher Peres">Peres, Asher</a> (2002). <a href="/wiki/Quantum_Theory:_Concepts_and_Methods" title="Quantum Theory: Concepts and Methods"><i>Quantum Theory: Concepts and Methods</i></a>. Kluwer. p. 149.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Theory%3A+Concepts+and+Methods&rft.pages=149&rft.pub=Kluwer&rft.date=2002&rft.aulast=Peres&rft.aufirst=Asher&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" 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="CITEREFRobinson2018" class="citation journal cs1">Robinson, Andrew (2018-04-30). <a rel="nofollow" class="external text" href="https://www.nature.com/articles/d41586-018-05004-4">"Did Einstein really say that?"</a>. <i>Nature</i>. <b>557</b> (7703): 30. <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/2018Natur.557...30R">2018Natur.557...30R</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%2Fd41586-018-05004-4">10.1038/d41586-018-05004-4</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:14013938">14013938</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=Did+Einstein+really+say+that%3F&rft.volume=557&rft.issue=7703&rft.pages=30&rft.date=2018-04-30&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A14013938%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1038%2Fd41586-018-05004-4&rft_id=info%3Abibcode%2F2018Natur.557...30R&rft.aulast=Robinson&rft.aufirst=Andrew&rft_id=https%3A%2F%2Fwww.nature.com%2Farticles%2Fd41586-018-05004-4&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLevenson1917" class="citation web cs1">Levenson, Thomas (9 June 1917). <a rel="nofollow" class="external text" href="https://www.theatlantic.com/science/archive/2017/06/einstein-germany-and-the-bomb/528534/">"The Scientist and the Fascist"</a>. <i>The Atlantic</i><span class="reference-accessdate">. Retrieved <span class="nowrap">28 June</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+Atlantic&rft.atitle=The+Scientist+and+the+Fascist&rft.date=1917-06-09&rft.aulast=Levenson&rft.aufirst=Thomas&rft_id=https%3A%2F%2Fwww.theatlantic.com%2Fscience%2Farchive%2F2017%2F06%2Feinstein-germany-and-the-bomb%2F528534%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEinsteinPodolskyRosen1935" class="citation journal cs1">Einstein, Albert; Podolsky, Boris; Rosen, Nathan (May 15, 1935). <a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.47.777">"Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?"</a>. <i>Physical Review</i>. <b>47</b> (10). Princeton, New Jersey: Institute for Advanced Study: 777–780. <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/1935PhRv...47..777E">1935PhRv...47..777E</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/10.1103%2FPhysRev.47.777">10.1103/PhysRev.47.777</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review&rft.atitle=Can+Quantum-Mechanical+Description+of+Physical+Reality+Be+Considered+Complete%3F&rft.volume=47&rft.issue=10&rft.pages=777-780&rft.date=1935-05-15&rft_id=info%3Adoi%2F10.1103%2FPhysRev.47.777&rft_id=info%3Abibcode%2F1935PhRv...47..777E&rft.aulast=Einstein&rft.aufirst=Albert&rft.au=Podolsky%2C+Boris&rft.au=Rosen%2C+Nathan&rft_id=https%3A%2F%2Fdoi.org%2F10.1103%252FPhysRev.47.777&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" class="Z3988"></span></span> </li> <li id="cite_note-Kumar2011-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-Kumar2011_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Kumar2011_6-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Kumar2011_6-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKumar2011" class="citation book cs1">Kumar, Manjit (2011). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/quantumeinsteinb00manj/page/305"><i>Quantum: Einstein, Bohr, and the Great Debate about the Nature of Reality</i></a></span> (Reprint ed.). W. W. Norton & Company. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/quantumeinsteinb00manj/page/305">305–306</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0393339888" title="Special:BookSources/978-0393339888"><bdi>978-0393339888</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">September 12,</span> 2021</span> – via Internet Archive.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum%3A+Einstein%2C+Bohr%2C+and+the+Great+Debate+about+the+Nature+of+Reality&rft.pages=305-306&rft.edition=Reprint&rft.pub=W.+W.+Norton+%26+Company&rft.date=2011&rft.isbn=978-0393339888&rft.aulast=Kumar&rft.aufirst=Manjit&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fquantumeinsteinb00manj%2Fpage%2F305&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" class="Z3988"></span></span> </li> <li id="cite_note-Jaeger2014-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-Jaeger2014_7-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJaeger2014" class="citation book cs1">Jaeger, Gregg (2014). <i>Quantum Objects</i>. Springer Verlag. pp. 9–15. <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%2F978-3-642-37629-0">10.1007/978-3-642-37629-0</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-642-37628-3" title="Special:BookSources/978-3-642-37628-3"><bdi>978-3-642-37628-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Objects&rft.pages=9-15&rft.pub=Springer+Verlag&rft.date=2014&rft_id=info%3Adoi%2F10.1007%2F978-3-642-37629-0&rft.isbn=978-3-642-37628-3&rft.aulast=Jaeger&rft.aufirst=Gregg&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaiser1994" class="citation journal cs1">Kaiser, David (1994). "Bringing the human actors back on stage: the personal context of the Einstein-Bohr debate". <i>British Journal for the History of Science</i>. <b>27</b> (2): 129–152. <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%2FS0007087400031861">10.1017/S0007087400031861</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/4027432">4027432</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:145143635">145143635</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=British+Journal+for+the+History+of+Science&rft.atitle=Bringing+the+human+actors+back+on+stage%3A+the+personal+context+of+the+Einstein-Bohr+debate&rft.volume=27&rft.issue=2&rft.pages=129-152&rft.date=1994&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A145143635%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F4027432%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1017%2FS0007087400031861&rft.aulast=Kaiser&rft.aufirst=David&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEinstein1936" class="citation journal cs1">Einstein, Albert (1936). "Physik und Realität". <i>Journal of the Franklin Institute</i>. <b>221</b> (3): 313–347. <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%2FS0016-0032%2836%2991045-1">10.1016/S0016-0032(36)91045-1</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+Franklin+Institute&rft.atitle=Physik+und+Realit%C3%A4t&rft.volume=221&rft.issue=3&rft.pages=313-347&rft.date=1936&rft_id=info%3Adoi%2F10.1016%2FS0016-0032%2836%2991045-1&rft.aulast=Einstein&rft.aufirst=Albert&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" class="Z3988"></span> English translation by Jean Piccard, pp 349–382 in the same issue, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><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%2FS0016-0032%2836%2991047-5">10.1016/S0016-0032(36)91047-5</a>).</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://www.nytimes.com/1935/05/04/archives/einstein-attacks-quantum-theory-scientist-and-two-colleagues-find.html">"Einstein Attacks Quantum Theory"</a>. <i><a href="/wiki/The_New_York_Times" title="The New York Times">The New York Times</a></i>. 4 May 1935. p. 11<span class="reference-accessdate">. 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"Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox". <i>Physical Review Letters</i>. <b>98</b> (14): 140402. <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/quant-ph/0612147">quant-ph/0612147</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/2007PhRvL..98n0402W">2007PhRvL..98n0402W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.98.140402">10.1103/PhysRevLett.98.140402</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/0031-9007">0031-9007</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/17501251">17501251</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:30078867">30078867</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Steering%2C+Entanglement%2C+Nonlocality%2C+and+the+Einstein-Podolsky-Rosen+Paradox&rft.volume=98&rft.issue=14&rft.pages=140402&rft.date=2007&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A30078867%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2007PhRvL..98n0402W&rft_id=info%3Aarxiv%2Fquant-ph%2F0612147&rft.issn=0031-9007&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.98.140402&rft_id=info%3Apmid%2F17501251&rft.aulast=Wiseman&rft.aufirst=H.+M.&rft.au=Jones%2C+S.+J.&rft.au=Doherty%2C+A.+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" class="Z3988"></span></span> </li> <li id="cite_note-Blaylock-33"><span class="mw-cite-backlink">^ <a href="#cite_ref-Blaylock_33-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Blaylock_33-1"><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="CITEREFBlaylock2010" class="citation journal cs1">Blaylock, Guy (January 2010). "The EPR paradox, Bell's inequality, and the question of locality". <i>American Journal of Physics</i>. <b>78</b> (1): 111–120. <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/0902.3827">0902.3827</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/2010AmJPh..78..111B">2010AmJPh..78..111B</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%2F1.3243279">10.1119/1.3243279</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:118520639">118520639</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=The+EPR+paradox%2C+Bell%27s+inequality%2C+and+the+question+of+locality&rft.volume=78&rft.issue=1&rft.pages=111-120&rft.date=2010-01&rft_id=info%3Aarxiv%2F0902.3827&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A118520639%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1119%2F1.3243279&rft_id=info%3Abibcode%2F2010AmJPh..78..111B&rft.aulast=Blaylock&rft.aufirst=Guy&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" class="Z3988"></span></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><i>Albert Einstein Max Born, Briefwechsel 1916-1955</i> (in German) (3 ed.). München: Langen Müller. 2005. p. 254.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Albert+Einstein+Max+Born%2C+Briefwechsel+1916-1955&rft.place=M%C3%BCnchen&rft.pages=254&rft.edition=3&rft.pub=Langen+M%C3%BCller&rft.date=2005&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" class="Z3988"></span></span> </li> <li id="cite_note-Bell1981-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-Bell1981_36-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBell1981" class="citation journal cs1">Bell, John (1981). <a rel="nofollow" class="external text" href="https://cds.cern.ch/record/142461?ln=en">"Bertlmann's socks and the nature of reality"</a>. <i>J. Physique Colloques</i>. <b>C22</b>: 41–62. <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/1988nbpw.conf..245B">1988nbpw.conf..245B</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J.+Physique+Colloques&rft.atitle=Bertlmann%27s+socks+and+the+nature+of+reality&rft.volume=C22&rft.pages=41-62&rft.date=1981&rft_id=info%3Abibcode%2F1988nbpw.conf..245B&rft.aulast=Bell&rft.aufirst=John&rft_id=https%3A%2F%2Fcds.cern.ch%2Frecord%2F142461%3Fln%3Den&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Selected_papers">Selected papers</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox&action=edit&section=13" title="Edit section: Selected papers"><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="CITEREFEberhard1977" class="citation journal cs1">Eberhard, P. H. (1977). "Bell's theorem without hidden variables". <i>Il Nuovo Cimento B</i>. Series 11. <b>38</b> (1): 75–80. <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/quant-ph/0010047">quant-ph/0010047</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/1977NCimB..38...75E">1977NCimB..38...75E</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%2Fbf02726212">10.1007/bf02726212</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/1826-9877">1826-9877</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:51759163">51759163</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Il+Nuovo+Cimento+B&rft.atitle=Bell%27s+theorem+without+hidden+variables&rft.volume=38&rft.issue=1&rft.pages=75-80&rft.date=1977&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A51759163%23id-name%3DS2CID&rft_id=info%3Abibcode%2F1977NCimB..38...75E&rft_id=info%3Aarxiv%2Fquant-ph%2F0010047&rft.issn=1826-9877&rft_id=info%3Adoi%2F10.1007%2Fbf02726212&rft.aulast=Eberhard&rft.aufirst=P.+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEberhard1978" class="citation journal cs1">Eberhard, P. H. (1978). <a rel="nofollow" class="external text" href="https://escholarship.org/uc/item/3nt850mv">"Bell's theorem and the different concepts of locality"</a>. <i>Il Nuovo Cimento B</i>. Series 11. <b>46</b> (2): 392–419. <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/1978NCimB..46..392E">1978NCimB..46..392E</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%2Fbf02728628">10.1007/bf02728628</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/1826-9877">1826-9877</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:118836806">118836806</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Il+Nuovo+Cimento+B&rft.atitle=Bell%27s+theorem+and+the+different+concepts+of+locality&rft.volume=46&rft.issue=2&rft.pages=392-419&rft.date=1978&rft_id=info%3Adoi%2F10.1007%2Fbf02728628&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A118836806%23id-name%3DS2CID&rft.issn=1826-9877&rft_id=info%3Abibcode%2F1978NCimB..46..392E&rft.aulast=Eberhard&rft.aufirst=P.+H.&rft_id=https%3A%2F%2Fescholarship.org%2Fuc%2Fitem%2F3nt850mv&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEinsteinPodolskyRosen1935" class="citation journal cs1">Einstein, A.; Podolsky, B.; Rosen, N. (1935-05-15). <a rel="nofollow" class="external text" href="https://cds.cern.ch/record/405662/files/PhysRev.47.777.pdf">"Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?"</a> <span class="cs1-format">(PDF)</span>. <i>Physical Review</i>. <b>47</b> (10): 777–780. <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/1935PhRv...47..777E">1935PhRv...47..777E</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/10.1103%2Fphysrev.47.777">10.1103/physrev.47.777</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/0031-899X">0031-899X</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review&rft.atitle=Can+Quantum-Mechanical+Description+of+Physical+Reality+Be+Considered+Complete%3F&rft.volume=47&rft.issue=10&rft.pages=777-780&rft.date=1935-05-15&rft.issn=0031-899X&rft_id=info%3Adoi%2F10.1103%2Fphysrev.47.777&rft_id=info%3Abibcode%2F1935PhRv...47..777E&rft.aulast=Einstein&rft.aufirst=A.&rft.au=Podolsky%2C+B.&rft.au=Rosen%2C+N.&rft_id=https%3A%2F%2Fcds.cern.ch%2Frecord%2F405662%2Ffiles%2FPhysRev.47.777.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFine1982" class="citation journal cs1">Fine, Arthur (1982-02-01). "Hidden Variables, Joint Probability, and the Bell Inequalities". <i>Physical Review Letters</i>. <b>48</b> (5): 291–295. <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/1982PhRvL..48..291F">1982PhRvL..48..291F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2Fphysrevlett.48.291">10.1103/physrevlett.48.291</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/0031-9007">0031-9007</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Hidden+Variables%2C+Joint+Probability%2C+and+the+Bell+Inequalities&rft.volume=48&rft.issue=5&rft.pages=291-295&rft.date=1982-02-01&rft.issn=0031-9007&rft_id=info%3Adoi%2F10.1103%2Fphysrevlett.48.291&rft_id=info%3Abibcode%2F1982PhRvL..48..291F&rft.aulast=Fine&rft.aufirst=Arthur&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" class="Z3988"></span></li> <li>A. Fine, <i>Do Correlations need to be explained?</i>, in <i>Philosophical Consequences of Quantum Theory: Reflections on Bell's Theorem</i>, edited by Cushing & McMullin (University of Notre Dame Press, 1986).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHardy1993" class="citation journal cs1">Hardy, Lucien (1993-09-13). "Nonlocality for two particles without inequalities for almost all entangled states". <i>Physical Review Letters</i>. <b>71</b> (11): 1665–1668. <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/1993PhRvL..71.1665H">1993PhRvL..71.1665H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2Fphysrevlett.71.1665">10.1103/physrevlett.71.1665</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/0031-9007">0031-9007</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/10054467">10054467</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Nonlocality+for+two+particles+without+inequalities+for+almost+all+entangled+states&rft.volume=71&rft.issue=11&rft.pages=1665-1668&rft.date=1993-09-13&rft_id=info%3Adoi%2F10.1103%2Fphysrevlett.71.1665&rft.issn=0031-9007&rft_id=info%3Apmid%2F10054467&rft_id=info%3Abibcode%2F1993PhRvL..71.1665H&rft.aulast=Hardy&rft.aufirst=Lucien&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" class="Z3988"></span></li> <li>M. Mizuki, <i>A classical interpretation of Bell's inequality</i>. Annales de la Fondation Louis de Broglie <b>26</b> 683 (2001)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPeres2005" class="citation journal cs1"><a href="/wiki/Asher_Peres" title="Asher Peres">Peres, Asher</a> (2005). "Einstein, Podolsky, Rosen, and Shannon". <i>Foundations of Physics</i>. <b>35</b> (3): 511–514. <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/quant-ph/0310010">quant-ph/0310010</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/2005FoPh...35..511P">2005FoPh...35..511P</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%2Fs10701-004-1986-6">10.1007/s10701-004-1986-6</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/0015-9018">0015-9018</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:119556878">119556878</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Foundations+of+Physics&rft.atitle=Einstein%2C+Podolsky%2C+Rosen%2C+and+Shannon&rft.volume=35&rft.issue=3&rft.pages=511-514&rft.date=2005&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119556878%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2005FoPh...35..511P&rft_id=info%3Aarxiv%2Fquant-ph%2F0310010&rft.issn=0015-9018&rft_id=info%3Adoi%2F10.1007%2Fs10701-004-1986-6&rft.aulast=Peres&rft.aufirst=Asher&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" class="Z3988"></span></li> <li>P. Pluch, "Theory for Quantum Probability", PhD Thesis University of Klagenfurt (2006)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRoweKielpinskiMeyerSackett2001" class="citation journal cs1">Rowe, M. A.; Kielpinski, D.; Meyer, V.; Sackett, C. A.; Itano, W. M.; Monroe, C.; Wineland, D. J. (2001). "Experimental violation of a Bell's inequality with efficient detection". <i>Nature</i>. <b>409</b> (6822): 791–794. <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/2001Natur.409..791R">2001Natur.409..791R</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%2F35057215">10.1038/35057215</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/2027.42%2F62731">2027.42/62731</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/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/11236986">11236986</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:205014115">205014115</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=Experimental+violation+of+a+Bell%27s+inequality+with+efficient+detection&rft.volume=409&rft.issue=6822&rft.pages=791-794&rft.date=2001&rft_id=info%3Ahdl%2F2027.42%2F62731&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A205014115%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2001Natur.409..791R&rft.issn=0028-0836&rft_id=info%3Adoi%2F10.1038%2F35057215&rft_id=info%3Apmid%2F11236986&rft.aulast=Rowe&rft.aufirst=M.+A.&rft.au=Kielpinski%2C+D.&rft.au=Meyer%2C+V.&rft.au=Sackett%2C+C.+A.&rft.au=Itano%2C+W.+M.&rft.au=Monroe%2C+C.&rft.au=Wineland%2C+D.+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSmerlakRovelli2007" class="citation journal cs1">Smerlak, Matteo; Rovelli, Carlo (2007-02-03). "Relational EPR". <i>Foundations of Physics</i>. <b>37</b> (3): 427–445. <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/quant-ph/0604064">quant-ph/0604064</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/2007FoPh...37..427S">2007FoPh...37..427S</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%2Fs10701-007-9105-0">10.1007/s10701-007-9105-0</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/0015-9018">0015-9018</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:11816650">11816650</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Foundations+of+Physics&rft.atitle=Relational+EPR&rft.volume=37&rft.issue=3&rft.pages=427-445&rft.date=2007-02-03&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A11816650%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2007FoPh...37..427S&rft_id=info%3Aarxiv%2Fquant-ph%2F0604064&rft.issn=0015-9018&rft_id=info%3Adoi%2F10.1007%2Fs10701-007-9105-0&rft.aulast=Smerlak&rft.aufirst=Matteo&rft.au=Rovelli%2C+Carlo&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEinstein%E2%80%93Podolsky%E2%80%93Rosen+paradox" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading3"><h3 id="Books">Books</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox&action=edit&section=14" title="Edit section: Books"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/John_S._Bell" class="mw-redirect" title="John S. Bell">Bell, John S.</a> (1987). <i>Speakable and Unspeakable in Quantum Mechanics</i>. Cambridge University Press. <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/0-521-36869-3" title="Special:BookSources/0-521-36869-3">0-521-36869-3</a>.</li> <li><a href="/wiki/Arthur_Fine" title="Arthur Fine">Fine, Arthur</a> (1996). <i>The Shaky Game: Einstein, Realism and the Quantum Theory</i>. 2nd ed. Univ. of Chicago Press.</li> <li><a href="/wiki/John_Gribbin" title="John Gribbin">Gribbin, John</a> (1984). <i>In Search of Schrödinger's Cat</i>. Black Swan. <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/978-0-552-12555-0" title="Special:BookSources/978-0-552-12555-0">978-0-552-12555-0</a></li> <li><a href="/w/index.php?title=Leon_Leaderman&action=edit&redlink=1" class="new" title="Leon Leaderman (page does not exist)">Leaderman, Leon</a>; <a href="/wiki/Dick_Teresi" title="Dick Teresi">Teresi, Dick</a> (1993). <i>The God Particle: If the Universe Is the Answer, What Is the Question?</i> Houghton Mifflin Company, pp. 21, 187–189.</li> <li><a href="/wiki/Franco_Selleri" title="Franco Selleri">Selleri, Franco</a> (1988). <i>Quantum Mechanics Versus Local Realism: The Einstein–Podolsky–Rosen Paradox</i>. New York: Plenum Press. <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/0-306-42739-7" title="Special:BookSources/0-306-42739-7">0-306-42739-7</a>.</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=Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox&action=edit&section=15" 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 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title="q:Special:Search/Einstein–Podolsky–Rosen paradox">Einstein–Podolsky–Rosen paradox</a></b></i>.</div></div> </div> <ul><li>Stanford Encyclopedia of Philosophy: The Einstein–Podolsky–Rosen Argument in Quantum Theory; <a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/qt-epr/#1.2">1.2 The argument in the text</a></li> <li><i><a href="/wiki/Internet_Encyclopedia_of_Philosophy" title="Internet Encyclopedia of Philosophy">Internet Encyclopedia of Philosophy</a></i>: "<a rel="nofollow" class="external text" href="http://www.iep.utm.edu/epr/">The Einstein-Podolsky-Rosen Argument and the Bell Inequalities</a>"</li> <li><i><a href="/wiki/Stanford_Encyclopedia_of_Philosophy" title="Stanford Encyclopedia of Philosophy">Stanford Encyclopedia of Philosophy</a></i>: <a href="/wiki/Abner_Shimony" title="Abner Shimony">Abner Shimony</a> (2019) "<a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/bell-theorem/">Bell's Theorem</a>"</li> <li><a rel="nofollow" class="external text" href="http://www.drchinese.com/David/EPR_Bell_Aspect.htm">EPR, Bell & Aspect: The Original References</a></li> <li><a rel="nofollow" class="external text" href="http://math.ucr.edu/home/baez/physics/Quantum/bells_inequality.html">Does Bell's Inequality Principle rule out local theories of quantum mechanics?</a> from the Usenet Physics FAQ</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20061115193609/http://www.research.ibm.com/journal/rd/481/brassard.html">Theoretical use of EPR in teleportation</a></li> <li><a rel="nofollow" class="external text" href="http://www.dhushara.com/book/quantcos/aq/qcrypt.htm">Effective use of EPR in cryptography</a></li> <li><a rel="nofollow" class="external text" href="http://www.QuantumLab.de/">EPR experiment with single photons interactive</a></li> <li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=ta09WXiUqcQ">Spooky Actions At A Distance?: Oppenheimer Lecture by Prof. Mermin</a></li> <li><a rel="nofollow" class="external text" href="http://www.drchinese.com/David/EPR.pdf">Original paper</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 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title="General relativity">General relativity</a></li></ul></li> <li><a href="/wiki/Mass%E2%80%93energy_equivalence" title="Mass–energy equivalence">Mass–energy equivalence (E=mc<sup>2</sup>)</a></li> <li><a href="/wiki/Brownian_motion" title="Brownian motion">Brownian motion</a></li> <li><a href="/wiki/Photoelectric_effect" title="Photoelectric effect">Photoelectric effect</a></li> <li><a href="/wiki/Einstein_coefficients" title="Einstein coefficients">Einstein coefficients</a></li> <li><a href="/wiki/Einstein_solid" title="Einstein solid">Einstein solid</a></li> <li><a href="/wiki/Equivalence_principle" title="Equivalence principle">Equivalence principle</a></li> <li><a href="/wiki/Einstein_field_equations" title="Einstein field equations">Einstein field equations</a></li> <li><a href="/wiki/Einstein_radius" title="Einstein radius">Einstein radius</a></li> <li><a href="/wiki/Einstein_relation_(kinetic_theory)" title="Einstein relation (kinetic theory)">Einstein relation (kinetic theory)</a></li> <li><a href="/wiki/Cosmological_constant" title="Cosmological constant">Cosmological constant</a></li> <li><a href="/wiki/Bose%E2%80%93Einstein_condensate" title="Bose–Einstein condensate">Bose–Einstein condensate</a></li> <li><a href="/wiki/Bose%E2%80%93Einstein_statistics" title="Bose–Einstein statistics">Bose–Einstein statistics</a></li> <li><a href="/wiki/Bose%E2%80%93Einstein_correlations" title="Bose–Einstein correlations">Bose–Einstein correlations</a></li> <li><a href="/wiki/Einstein%E2%80%93Cartan_theory" title="Einstein–Cartan theory">Einstein–Cartan theory</a></li> <li><a href="/wiki/Einstein%E2%80%93Infeld%E2%80%93Hoffmann_equations" title="Einstein–Infeld–Hoffmann equations">Einstein–Infeld–Hoffmann equations</a></li> <li><a href="/wiki/Einstein%E2%80%93de_Haas_effect" title="Einstein–de Haas effect">Einstein–de Haas effect</a></li> <li><a href="/wiki/EPR_paradox" class="mw-redirect" title="EPR paradox">EPR paradox</a></li> <li><a href="/wiki/Bohr%E2%80%93Einstein_debates" title="Bohr–Einstein debates">Bohr–Einstein debates</a></li> <li><a href="/wiki/Teleparallelism" title="Teleparallelism">Teleparallelism</a></li> <li><a href="/wiki/Einstein%27s_thought_experiments" title="Einstein's thought experiments">Thought experiments</a></li> <li><a href="/wiki/Einstein%27s_unsuccessful_investigations" title="Einstein's unsuccessful investigations">Unsuccessful investigations</a></li> <li><a href="/wiki/Wave%E2%80%93particle_duality" title="Wave–particle duality">Wave–particle duality</a></li> <li><a href="/wiki/Gravitational_wave" title="Gravitational wave">Gravitational wave</a></li> <li><a href="/wiki/Tea_leaf_paradox" title="Tea leaf paradox">Tea leaf paradox</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_scientific_publications_by_Albert_Einstein" title="List of scientific publications by Albert Einstein">Works</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Annus_mirabilis_papers" title="Annus mirabilis papers"><i>Annus mirabilis</i> papers</a> (1905)</li> <li>"<a href="/wiki/%C3%9Cber_die_von_der_molekularkinetischen_Theorie_der_W%C3%A4rme_geforderte_Bewegung_von_in_ruhenden_Fl%C3%BCssigkeiten_suspendierten_Teilchen" title="Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen">Investigations on the Theory of Brownian Movement</a>" (1905)</li> <li><i><a href="/wiki/Relativity:_The_Special_and_the_General_Theory" title="Relativity: The Special and the General Theory">Relativity: The Special and the General Theory</a></i> (1916)</li> <li><i><a href="/wiki/The_Meaning_of_Relativity" title="The Meaning of Relativity">The Meaning of Relativity</a></i> (1922)</li> <li><i><a href="/wiki/The_World_as_I_See_It_(book)" title="The World as I See It (book)">The World as I See It</a></i> (1934)</li> <li><i><a href="/wiki/The_Evolution_of_Physics" title="The Evolution of Physics">The Evolution of Physics</a></i> (1938)</li> <li>"<a href="/wiki/Why_Socialism%3F" title="Why Socialism?">Why Socialism?</a>" (1949)</li> <li><a href="/wiki/Russell%E2%80%93Einstein_Manifesto" title="Russell–Einstein Manifesto">Russell–Einstein Manifesto</a> (1955)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Albert_Einstein_in_popular_culture" title="Albert Einstein in popular culture">In popular<br />culture</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Die_Grundlagen_der_Einsteinschen_Relativit%C3%A4ts-Theorie" title="Die Grundlagen der Einsteinschen Relativitäts-Theorie">Die Grundlagen der Einsteinschen Relativitäts-Theorie</a></i> (1922 documentary)</li> <li><i><a href="/wiki/The_Einstein_Theory_of_Relativity" title="The Einstein Theory of Relativity">The Einstein Theory of Relativity</a></i> (1923 documentary)</li> <li><i><a href="/wiki/Relics:_Einstein%27s_Brain" title="Relics: Einstein's Brain">Relics: Einstein's Brain</a></i> (1994 documentary)</li> <li><i><a href="/wiki/Insignificance_(film)" title="Insignificance (film)">Insignificance</a></i> (1985 film)</li> <li><i><a href="/wiki/Young_Einstein" title="Young Einstein">Young Einstein</a></i> (1988 film)</li> <li><i><a href="/wiki/Picasso_at_the_Lapin_Agile" title="Picasso at the Lapin Agile">Picasso at the Lapin Agile</a></i> (1993 play)</li> <li><i><a href="/wiki/I.Q._(film)" title="I.Q. (film)">I.Q.</a></i> (1994 film)</li> <li><i><a href="/wiki/Einstein%27s_Gift" title="Einstein's Gift">Einstein's Gift</a></i> (2003 play)</li> <li><i><a href="/wiki/Einstein_and_Eddington" title="Einstein and Eddington">Einstein and Eddington</a></i> (2008 TV film)</li> <li><i><a href="/wiki/Genius_(American_TV_series)" title="Genius (American TV series)">Genius</a></i> (2017 series)</li> <li><i><a href="/wiki/Oppenheimer_(film)" title="Oppenheimer (film)">Oppenheimer</a></i> (2023 film)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Prizes</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Albert_Einstein_Award" title="Albert Einstein Award">Albert Einstein Award</a></li> <li><a href="/wiki/Albert_Einstein_Medal" title="Albert Einstein Medal">Albert Einstein Medal</a></li> <li><a href="/wiki/Kalinga_Prize" title="Kalinga Prize">Kalinga Prize</a></li> <li><a href="/wiki/Albert_Einstein_Peace_Prize" title="Albert Einstein Peace Prize">Albert Einstein Peace Prize</a></li> <li><a href="/wiki/Albert_Einstein_World_Award_of_Science" title="Albert Einstein World Award of Science">Albert Einstein World Award of Science</a></li> <li><a href="/wiki/Einstein_Prize_for_Laser_Science" title="Einstein Prize for Laser Science">Einstein Prize for Laser Science</a></li> <li><a href="/wiki/Einstein_Prize_(APS)" title="Einstein Prize (APS)">Einstein Prize (APS)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Books about<br />Einstein</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Albert_Einstein:_Creator_and_Rebel" title="Albert Einstein: Creator and Rebel">Albert Einstein: Creator and Rebel</a></i></li> <li><i><a href="/wiki/Einstein_and_Religion" title="Einstein and Religion">Einstein and Religion</a></i></li> <li><i><a href="/wiki/Einstein_for_Beginners" title="Einstein for Beginners">Einstein for Beginners</a></i></li> <li><i><a href="/wiki/Einstein:_His_Life_and_Universe" title="Einstein: His Life and Universe">Einstein: His Life and Universe</a></i></li> <li><i><a href="/wiki/Einstein%27s_Cosmos" title="Einstein's Cosmos">Einstein's Cosmos</a></i></li> <li><i><a href="/wiki/I_Am_Albert_Einstein" title="I Am Albert Einstein">I Am Albert Einstein</a></i></li> <li><i><a href="/wiki/Introducing_Relativity" title="Introducing Relativity">Introducing Relativity</a></i></li> <li><i><a href="/wiki/Subtle_is_the_Lord" title="Subtle is the Lord">Subtle is the Lord</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Einstein_family" title="Einstein family">Family</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mileva_Mari%C4%87" title="Mileva Marić">Mileva Marić</a> (first wife)</li> <li><a href="/wiki/Elsa_Einstein" title="Elsa Einstein">Elsa Einstein</a> (second wife; cousin)</li> <li><a href="/wiki/Lieserl_Einstein" class="mw-redirect" title="Lieserl Einstein">Lieserl Einstein</a> (daughter)</li> <li><a href="/wiki/Hans_Albert_Einstein" title="Hans Albert Einstein">Hans Albert Einstein</a> (son)</li> <li><a href="/wiki/Pauline_Koch" class="mw-redirect" title="Pauline Koch">Pauline Koch</a> (mother)</li> <li><a href="/wiki/Hermann_Einstein" class="mw-redirect" title="Hermann Einstein">Hermann Einstein</a> (father)</li> <li><a href="/wiki/Maja_Einstein" title="Maja Einstein">Maja Einstein</a> (sister)</li> <li><a href="/wiki/Einstein_family#Eduard_"Tete"_Einstein_(Albert's_second_son)" title="Einstein family">Eduard Einstein</a> (son)</li> <li><a href="/wiki/Murder_of_the_family_of_Robert_Einstein" title="Murder of the family of Robert Einstein">Robert Einstein</a> (cousin)</li> <li><a href="/wiki/Bernhard_Caesar_Einstein" title="Bernhard Caesar Einstein">Bernhard Caesar Einstein</a> (grandson)</li> <li><a href="/wiki/Evelyn_Einstein" title="Evelyn Einstein">Evelyn Einstein</a> (granddaughter)</li> <li><a href="/wiki/Thomas_Martin_Einstein" class="mw-redirect" title="Thomas Martin Einstein">Thomas Martin Einstein</a> (great-grandson)</li> <li><a href="/wiki/Siegbert_Einstein" title="Siegbert Einstein">Siegbert Einstein</a> (distant cousin)</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-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_awards_and_honors_received_by_Albert_Einstein" title="List of awards and honors received by Albert Einstein">Awards and honors</a></li> <li><a href="/wiki/Brain_of_Albert_Einstein" title="Brain of Albert Einstein">Brain</a></li> <li><a href="/wiki/Albert_Einstein_House" title="Albert Einstein House">House</a></li> <li><a href="/wiki/Albert_Einstein_Memorial" title="Albert Einstein Memorial">Memorial</a></li> <li><a href="/wiki/Political_views_of_Albert_Einstein" title="Political views of Albert Einstein">Political views</a></li> <li><a href="/wiki/Religious_and_philosophical_views_of_Albert_Einstein" title="Religious and philosophical views of Albert Einstein">Religious views</a></li> <li><a href="/wiki/List_of_things_named_after_Albert_Einstein" title="List of things named after Albert Einstein">Things named after</a></li> <li><a href="/wiki/Einstein%E2%80%93Oppenheimer_relationship" title="Einstein–Oppenheimer relationship">Einstein–Oppenheimer relationship</a></li> <li><a href="/wiki/Albert_Einstein_Archives" title="Albert Einstein Archives">Albert Einstein Archives</a></li> <li><a href="/wiki/Einstein%27s_Blackboard" title="Einstein's Blackboard">Einstein's Blackboard</a></li> <li><a href="/wiki/Einstein_Papers_Project" title="Einstein Papers Project">Einstein Papers Project</a></li> <li><a href="/wiki/Einstein_refrigerator" title="Einstein refrigerator">Einstein refrigerator</a></li> <li><a href="/wiki/Einsteinhaus" title="Einsteinhaus">Einsteinhaus</a></li> <li><a href="/wiki/Einsteinium" title="Einsteinium">Einsteinium</a></li> <li><a href="/wiki/Max_Talmey" title="Max Talmey">Max Talmey</a></li> <li><a href="/wiki/Emergency_Committee_of_Atomic_Scientists" title="Emergency Committee of Atomic Scientists">Emergency Committee of Atomic Scientists</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow hlist" 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, 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