{"id":224771,"date":"2025-11-09T05:11:33","date_gmt":"2025-11-09T11:11:33","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2025\/11\/physicists-take-the-imaginary-numbers-out-of-quantum-mechanics"},"modified":"2025-11-09T05:11:33","modified_gmt":"2025-11-09T11:11:33","slug":"physicists-take-the-imaginary-numbers-out-of-quantum-mechanics","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2025\/11\/physicists-take-the-imaginary-numbers-out-of-quantum-mechanics","title":{"rendered":"Physicists Take the Imaginary Numbers Out of Quantum Mechanics"},"content":{"rendered":"<p><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/physicists-take-the-imaginary-numbers-out-of-quantum-mechanics.jpg\"><\/a><\/p>\n<p>A century ago, the strange behavior of atoms and elementary particles led physicists to formulate a new theory of nature. That theory, quantum mechanics, found immediate success, proving its worth with accurate calculations of hydrogen\u2019s emission and absorption of light. There was, however, a snag. The central equation of quantum mechanics featured the imaginary number <em>i<\/em>, the square root of \u22121.<\/p>\n<p>Physicists knew <em>i<\/em> was a mathematical fiction. Real physical quantities like mass and momentum never yield a negative amount when squared. Yet this unreal number that behaves as <em>i<\/em><sup>2<\/sup> = \u22121 seemed to sit at the heart of the quantum world.<\/p>\n<p>After deriving the <em>i<\/em>-riddled equation \u2014 essentially the law of motion for quantum entities \u2014 Erwin Schr\u00f6dinger expressed the hope that it would be replaced by an entirely real version. (\u201cThere is undoubtedly a certain crudeness at the moment\u201d in the equation\u2019s form, he wrote in 1926.) Schr\u00f6dinger\u2019s distaste notwithstanding, <em>i<\/em> stuck around, and new generations of physicists took up his equation without much concern.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A century ago, the strange behavior of atoms and elementary particles led physicists to formulate a new theory of nature. That theory, quantum mechanics, found immediate success, proving its worth with accurate calculations of hydrogen\u2019s emission and absorption of light. There was, however, a snag. The central equation of quantum mechanics featured the imaginary number [\u2026]<\/p>\n","protected":false},"author":709,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[41,2229,48,1617],"tags":[],"class_list":["post-224771","post","type-post","status-publish","format-standard","hentry","category-information-science","category-mathematics","category-particle-physics","category-quantum-physics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/224771","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/709"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=224771"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/224771\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=224771"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=224771"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=224771"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}