{"id":910,"date":"2022-10-05T11:51:00","date_gmt":"2022-10-05T16:51:00","guid":{"rendered":"http:\/\/www.fruechtetheory.com\/blog\/?p=910"},"modified":"2022-10-05T14:49:30","modified_gmt":"2022-10-05T19:49:30","slug":"the-vector-potential","status":"publish","type":"post","link":"https:\/\/www.fruechtetheory.com\/blog\/2022\/10\/05\/the-vector-potential\/","title":{"rendered":"The Vector Potential"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">In electrodynamics we find that \u201cA quantum-mechanical description of photons necessitates quantization of only the vector potential\u201d ([1], pg. 242), as in the summation of all the manifolds of gravitational fields at a given location. In a more densely packed summation of manifolds, the action of an electric charge will have a lesser rotational effect on the electric fields of the gamma rays than on a less dense field. The power of the rotation is the same in either field however, as long as we are referring to a gravitational field that is not too sparse for electric fields to propagate.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201cThe definition of <strong>B<\/strong> = \u2207 x <strong>A<\/strong> specifies the curl of <strong>A<\/strong>, but it doesn\u2019t say anything about the divergence \u2013 we are at liberty to pick that as we see fit, and zero is ordinarily the simplest choice.\u201d ([2], pg. 235) The reason we may pick the divergence as zero is that the manifolds \u201care frozen in time for phonon transmission\u201d:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.fruechtetheory.com\/blog\/2022\/03\/29\/transmission-of-the-coulomb-field\/\">https:\/\/www.fruechtetheory.com\/blog\/2022\/03\/29\/transmission-of-the-coulomb-field\/<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">As far as group action, Mackenzie [3] calls these \u201cgroupoids\u201d, such as an ellipsoid, a spheroid, or another 3-dimensional shape. The definition of a spheroid I find is that it is like a sphere, but not a perfect sphere, and in the present case we have \u201coscillations and accordion motion in multiple axes\u201d:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.fruechtetheory.com\/blog\/2022\/08\/27\/concentrated-group-action\/\">https:\/\/www.fruechtetheory.com\/blog\/2022\/08\/27\/concentrated-group-action\/<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">On a side note, though related to manifolds of gravitational fields, the Nobel Prize in Physics is being given this year for essentially this:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.fruechtetheory.com\/blog\/2014\/05\/30\/quantum-entanglement\/\">https:\/\/www.fruechtetheory.com\/blog\/2014\/05\/30\/quantum-entanglement\/<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[1] Jackson, J. D., \u201cClassical Electrodynamics, Third Edition\u201d, c. 1999 John David Jackson, John Wiley &amp; Sons, Inc<br>[2] Griffiths, David J., \u201cIntroduction to Electrodynamics, Third Edition\u201d, c. 1999, Prentice-Hall, Inc.<br>[3] Mackenzie, Kirill C. H., \u201cGeneral Theory of Lie Groupoids and Lie Algebroids\u201d, c. 2005 Kirill C. H. Mackenzie, London Mathematical Society<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In electrodynamics we find that \u201cA quantum-mechanical description of photons necessitates quantization of only the vector potential\u201d ([1], pg. 242), as in the summation of all the manifolds of gravitational fields at a given location. In a more densely packed summation of manifolds, the action of an electric charge will have a lesser rotational effect [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7,18,5],"tags":[],"class_list":["post-910","post","type-post","status-publish","format-standard","hentry","category-classical-electrodynamics","category-mathematics","category-quantum-mechanics"],"_links":{"self":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/910","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/comments?post=910"}],"version-history":[{"count":4,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/910\/revisions"}],"predecessor-version":[{"id":916,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/910\/revisions\/916"}],"wp:attachment":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/media?parent=910"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/categories?post=910"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/tags?post=910"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}