{"id":820,"date":"2021-11-14T11:07:32","date_gmt":"2021-11-14T16:07:32","guid":{"rendered":"http:\/\/www.fruechtetheory.com\/blog\/?p=820"},"modified":"2021-12-23T11:59:40","modified_gmt":"2021-12-23T16:59:40","slug":"greatest-lower-bound","status":"publish","type":"post","link":"https:\/\/www.fruechtetheory.com\/blog\/2021\/11\/14\/greatest-lower-bound\/","title":{"rendered":"Greatest Lower Bound"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">One would guess that the particle physicists and quantum field theorists may like a 1.3335 x 10<sup>-15<\/sup> m diameter of a free electron, because it is closer to a point particle than many estimates of the diameter.&nbsp; It is possible that 1.3335 x 10<sup>-15<\/sup> m is also the limit inferior of the sequence S<sub>137<\/sub> to S<sub>n<\/sub> in an atomic orbital.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The maximum diameter, on the other hand, will depend on the element and on the orbital.&nbsp; At a spin flip, electrons in all orbitals may reduce to 1.3335 x 10<sup>-15<\/sup> m, before taking off on a new trajectory and increasing in diameter again.&nbsp; We cannot speak of a limit superior of the sequence of diameters of the electron in an atomic orbital nevertheless.&nbsp; That will depend on the direction of electron travel, and on whether the atom is at the surface of the earth, or at some other planet.&nbsp; For the latter, it depends on the density of the gravitational field.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We may also ask whether 1.3335 x 10<sup>-15<\/sup> m is the greatest lower bound at all locations in the universe.\u00a0 This raises the question of whether the fine structure constant is a universal constant, or whether or not the Coulomb gauge is the same everywhere.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>One would guess that the particle physicists and quantum field theorists may like a 1.3335 x 10-15 m diameter of a free electron, because it is closer to a point particle than many estimates of the diameter.&nbsp; It is possible that 1.3335 x 10-15 m is also the limit inferior of the sequence S137 to [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,7,18,5],"tags":[],"class_list":["post-820","post","type-post","status-publish","format-standard","hentry","category-astrophysics","category-classical-electrodynamics","category-mathematics","category-quantum-mechanics"],"_links":{"self":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/820","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=820"}],"version-history":[{"count":4,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/820\/revisions"}],"predecessor-version":[{"id":830,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/820\/revisions\/830"}],"wp:attachment":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/media?parent=820"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/categories?post=820"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/tags?post=820"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}