{"id":715,"date":"2026-06-27T14:24:03","date_gmt":"2026-06-27T14:24:03","guid":{"rendered":"https:\/\/timeforsanity.com\/qm\/?page_id=715"},"modified":"2026-06-28T13:34:20","modified_gmt":"2026-06-28T13:34:20","slug":"06-04-the-bell-test","status":"publish","type":"page","link":"https:\/\/timeforsanity.com\/qm\/?page_id=715","title":{"rendered":"06.03 The Bell test"},"content":{"rendered":"\n<p class=\"qm-chapter wp-block-paragraph\">Chapter 6 &#8211; Entanglement<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">The Bell test<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In 1964 John Bell used the way polarization rotates a wave function to test entanglement.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Start by sending two entangled particles with opposite but unknown spin axes to aligned polarizers. Each has 50% probability of passing through the polarizers. This is expected!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"872\" height=\"140\" src=\"https:\/\/timeforsanity.com\/qm\/wp-content\/uploads\/2026\/06\/Entanglement-10.jpg\" alt=\"\" class=\"wp-image-716\" srcset=\"https:\/\/timeforsanity.com\/qm\/wp-content\/uploads\/2026\/06\/Entanglement-10.jpg 872w, https:\/\/timeforsanity.com\/qm\/wp-content\/uploads\/2026\/06\/Entanglement-10-300x48.jpg 300w, https:\/\/timeforsanity.com\/qm\/wp-content\/uploads\/2026\/06\/Entanglement-10-768x123.jpg 768w\" sizes=\"auto, (max-width: 872px) 100vw, 872px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now slightly rotate the axis of one polarizer while particles are traveling. If the particles were independent, they would still have 50% chance of passing through the polarizers. The odds change with entanglement because the first that passes through its polarizer changes the wave function for the other.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"912\" height=\"166\" src=\"https:\/\/timeforsanity.com\/qm\/wp-content\/uploads\/2026\/06\/Entanglement-11.jpg\" alt=\"\" class=\"wp-image-717\" srcset=\"https:\/\/timeforsanity.com\/qm\/wp-content\/uploads\/2026\/06\/Entanglement-11.jpg 912w, https:\/\/timeforsanity.com\/qm\/wp-content\/uploads\/2026\/06\/Entanglement-11-300x55.jpg 300w, https:\/\/timeforsanity.com\/qm\/wp-content\/uploads\/2026\/06\/Entanglement-11-768x140.jpg 768w\" sizes=\"auto, (max-width: 912px) 100vw, 912px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Bell used this to create an experiment where multiple tests are run to see the probability of the results at the two polarizers matching. If the orientation of the polarizer are set after the particles leave the source but before they reach the polarizer, he was able to develop a test that confirmed no hidden variables can explain the entangled result.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">These tests were run with increasing complexity between 1972 and 2010 by Alain Aspect, John Clauser, and Anton Zeilinger. The testing of Bell\u2019s theorem proved nature cannot be explained by local hidden variables<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Most physicists interpret this result as confirming quantum particles do not possess specific, predefined properties (like a definite spin or position) prior to measurement. Instead, they exist in a probabilistic state defined by a wave function. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">There really is <em>\u201cspooky action at a distance<\/em>&#8221; but Einstein didn\u2019t live to see this confirmed.<\/p>\n\n\n\n<div class=\"wp-block-group qm-big-idea\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"qm-big-idea-title wp-block-paragraph\">Big Idea<\/p>\n\n\n\n<p class=\"qm-big-idea-text wp-block-paragraph\"><strong><strong><strong><strong>The Bell test shows hidden variable can&#8217;t explain entanglement <\/strong><\/strong><\/strong><\/strong><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group qm-nav\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group is-content-justification-center is-layout-flex wp-container-core-group-is-layout-de391324 wp-block-group-is-layout-flex\">\n<div class=\"wp-block-group qm-nav-title\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"qm-nav-title wp-block-paragraph\">Back<\/p>\n\n\n\n<p class=\"qm-nav-link wp-block-paragraph\"><a href=\"https:\/\/timeforsanity.com\/qm\/?page_id=706\" data-type=\"page\" data-id=\"706\">Polarization<\/a><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"qm-nav-title wp-block-paragraph\">Overview<\/p>\n\n\n\n<p class=\"qm-nav-link wp-block-paragraph\"><a href=\"https:\/\/timeforsanity.com\/qm\/?page_id=70\" data-type=\"page\" data-id=\"70\">Contents<\/a><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"qm-nav-title wp-block-paragraph\">Next<\/p>\n\n\n\n<p class=\"qm-nav-link wp-block-paragraph\"><a href=\"https:\/\/timeforsanity.com\/qm\/?page_id=725\" data-type=\"page\" data-id=\"725\">Quantum computers<\/a><\/p>\n<\/div><\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Chapter 6 &#8211; Entanglement The Bell test In 1964 John Bell used the way polarization rotates a wave function to test entanglement. Start by sending two entangled particles with opposite but unknown spin axes to aligned polarizers. Each has 50% probability of passing through the polarizers. This is expected! Now slightly rotate the axis of &#8230; <a title=\"06.03 The Bell test\" class=\"read-more\" href=\"https:\/\/timeforsanity.com\/qm\/?page_id=715\" aria-label=\"Read more about 06.03 The Bell test\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-715","page","type-page","status-publish"],"_links":{"self":[{"href":"https:\/\/timeforsanity.com\/qm\/index.php?rest_route=\/wp\/v2\/pages\/715","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/timeforsanity.com\/qm\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/timeforsanity.com\/qm\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/timeforsanity.com\/qm\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/timeforsanity.com\/qm\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=715"}],"version-history":[{"count":10,"href":"https:\/\/timeforsanity.com\/qm\/index.php?rest_route=\/wp\/v2\/pages\/715\/revisions"}],"predecessor-version":[{"id":954,"href":"https:\/\/timeforsanity.com\/qm\/index.php?rest_route=\/wp\/v2\/pages\/715\/revisions\/954"}],"wp:attachment":[{"href":"https:\/\/timeforsanity.com\/qm\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=715"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}