{"id":4443,"date":"2024-09-22T17:58:40","date_gmt":"2024-09-22T17:58:40","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=4443"},"modified":"2024-09-22T17:58:41","modified_gmt":"2024-09-22T17:58:41","slug":"time-energy-uncertainty","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/09\/22\/time-energy-uncertainty\/","title":{"rendered":"TIME\u2013ENERGY UNCERTAINTY"},"content":{"rendered":"\n<p>Bohr realized that if there is an uncertainty relationship between momentum&nbsp;<em>p<\/em>&nbsp;and position&nbsp;<em>x<\/em>:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9781118170700\/files\/OEBPS\/images\/159-1.gif\" alt=\"equation\"\/><\/figure>\n\n\n\n<p>which comes from quantizing momentum as a function of wavelength:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9781118170700\/files\/OEBPS\/images\/159-2.gif\" alt=\"equation\"\/><\/figure>\n\n\n\n<p>A similar uncertainty principle must then exist between energy&nbsp;<em>E<\/em>&nbsp;and time&nbsp;<em>t<\/em>. This is because:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9781118170700\/files\/OEBPS\/images\/159-3.gif\" alt=\"equation\"\/><\/figure>\n\n\n\n<p>where frequency is the inverse of a time interval&nbsp;<em>f<\/em>&nbsp;= 1\/<em>t<\/em>, so:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9781118170700\/files\/OEBPS\/images\/159-4.gif\" alt=\"equation\"\/><\/figure>\n\n\n\n<p>Indeed, an identical relationship exists for the product of the&nbsp;<em>uncertainty<\/em>&nbsp;in the measurement of a particle\u2019s energy \u0394<em>E<\/em>, and the&nbsp;<em>uncertainty<\/em>&nbsp;in the measurement of the time \u0394<em>t<\/em>&nbsp;at which the particle possesses that energy. The formal derivation of this uncertainty relationship is more complex than deriving the uncertainty between measurements of position and momentum, so we will limit ourselves to stating it as:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9781118170700\/files\/OEBPS\/images\/159-5.gif\" alt=\"equation\"\/><\/figure>\n\n\n\n<p>Experimentally proving this form of the Uncertainty Principle is not easy. It requires ultrafast lasers and detectors that are beyond the reach of most casual experimenters\u2019 budgets. However, the uncertainty in frequency measurement of a signal as a function of the signal\u2019s duration is a convenient and educational model of the quantum time\u2013energy uncertainty relationship.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bohr realized that if there is an uncertainty relationship between momentum&nbsp;p&nbsp;and position&nbsp;x: which comes from quantizing momentum as a function of wavelength: A similar uncertainty principle must then exist between energy&nbsp;E&nbsp;and time&nbsp;t. This is because: where frequency is the inverse of a time interval&nbsp;f&nbsp;= 1\/t, so: Indeed, an identical relationship exists for the product of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":4193,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[516],"tags":[],"class_list":["post-4443","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-the-uncertainty-principle"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/09\/uncertainty.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4443","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=4443"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4443\/revisions"}],"predecessor-version":[{"id":4444,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4443\/revisions\/4444"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/4193"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=4443"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=4443"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=4443"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}