{"id":631,"date":"2026-06-27T11:22:28","date_gmt":"2026-06-27T11:22:28","guid":{"rendered":"https:\/\/timeforsanity.com\/qm\/?page_id=631"},"modified":"2026-06-27T13:18:28","modified_gmt":"2026-06-27T13:18:28","slug":"05-01-feynman-diagrams","status":"publish","type":"page","link":"https:\/\/timeforsanity.com\/qm\/?page_id=631","title":{"rendered":"05.01 Feynman diagrams"},"content":{"rendered":"\n<p class=\"qm-chapter wp-block-paragraph\">Chapter 5 &#8211; Interactions<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Feynman diagrams<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Richard Feynman created diagrams showing particle interactions. They have time along one axis and show particles interacting at vertices along the time line. Here is a simple diagram:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"380\" height=\"194\" src=\"https:\/\/timeforsanity.com\/qm\/wp-content\/uploads\/2026\/06\/Interaction-1.jpg\" alt=\"\" class=\"wp-image-632\" srcset=\"https:\/\/timeforsanity.com\/qm\/wp-content\/uploads\/2026\/06\/Interaction-1.jpg 380w, https:\/\/timeforsanity.com\/qm\/wp-content\/uploads\/2026\/06\/Interaction-1-300x153.jpg 300w\" sizes=\"auto, (max-width: 380px) 100vw, 380px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">This starts with an electron and a positron (that is an anti-electron which is labeled as a with a bar over it). By convention, anti-particles have arrows going backwards.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>At the first vertex, the particles are annihilated and a photon is generated. Photons are shown with wavy lines.<\/li>\n\n\n\n<li>At the second vertex the photon changes to an electron and positron.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Note: The resulting particles did not exist before the interaction and are spontaneously created<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Diagrams can be rotated<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A rotated diagram shows an equally valid interaction. The new direction of the arrows can cause particles and anti-particles to be swapped.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"304\" height=\"388\" src=\"https:\/\/timeforsanity.com\/qm\/wp-content\/uploads\/2026\/06\/Interaction-2.jpg\" alt=\"\" class=\"wp-image-633\" srcset=\"https:\/\/timeforsanity.com\/qm\/wp-content\/uploads\/2026\/06\/Interaction-2.jpg 304w, https:\/\/timeforsanity.com\/qm\/wp-content\/uploads\/2026\/06\/Interaction-2-235x300.jpg 235w\" sizes=\"auto, (max-width: 304px) 100vw, 304px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">This rotated version of the last diagram describes a different interaction between an electron and a positron.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A positron changes to a positron and a photon<\/li>\n\n\n\n<li>An electron absorbs the photon to give a new electron<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">More than just pictures<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Feynman diagrams give a formal way of calculating the probability of an outcome by considering the infinite variations that achieve a result and adding them up!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"864\" height=\"294\" src=\"https:\/\/timeforsanity.com\/qm\/wp-content\/uploads\/2026\/06\/Interaction-3.jpg\" alt=\"\" class=\"wp-image-634\" srcset=\"https:\/\/timeforsanity.com\/qm\/wp-content\/uploads\/2026\/06\/Interaction-3.jpg 864w, https:\/\/timeforsanity.com\/qm\/wp-content\/uploads\/2026\/06\/Interaction-3-300x102.jpg 300w, https:\/\/timeforsanity.com\/qm\/wp-content\/uploads\/2026\/06\/Interaction-3-768x261.jpg 768w\" sizes=\"auto, (max-width: 864px) 100vw, 864px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">How can an infinite number of variations be added up?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Infinite series can be summed if the values go down rapidly. For exaample:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">    1 + 1\/2 + 1\/4 + 1\/8 + 1\/16 + &#8230;.. = 2.0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Each extra level of complexity in the Feynman diagram reduces contribution by the fine structure constant (about 1\/137). To see how quickly this converged consider adding an infinite number of terms:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">     1 + 1\/137 + 1\/137<sup>2<\/sup> + 1\/137<sup>3<\/sup> + &#8230;. = 1.00735294<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If we just stop after two terms we get the answer correct to 6 decimal places:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">     1 + 1\/137 + 1\/137<sup>2<\/sup>  = 1.00735255<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This allows the probabilities of different interactions to be calculated without really having to look at all infinite number of variations<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/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>Feynman diagrams are used to calculate probabilities for particle interactions<\/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=617\" data-type=\"page\" data-id=\"617\">Gauge invariance<\/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=638\" data-type=\"page\" data-id=\"638\">Virtual particles<\/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 5 &#8211; Interactions Feynman diagrams Richard Feynman created diagrams showing particle interactions. They have time along one axis and show particles interacting at vertices along the time line. Here is a simple diagram: This starts with an electron and a positron (that is an anti-electron which is labeled as a with a bar over &#8230; <a title=\"05.01 Feynman diagrams\" class=\"read-more\" href=\"https:\/\/timeforsanity.com\/qm\/?page_id=631\" aria-label=\"Read more about 05.01 Feynman diagrams\">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-631","page","type-page","status-publish"],"_links":{"self":[{"href":"https:\/\/timeforsanity.com\/qm\/index.php?rest_route=\/wp\/v2\/pages\/631","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=631"}],"version-history":[{"count":4,"href":"https:\/\/timeforsanity.com\/qm\/index.php?rest_route=\/wp\/v2\/pages\/631\/revisions"}],"predecessor-version":[{"id":690,"href":"https:\/\/timeforsanity.com\/qm\/index.php?rest_route=\/wp\/v2\/pages\/631\/revisions\/690"}],"wp:attachment":[{"href":"https:\/\/timeforsanity.com\/qm\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=631"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}