{"id":191,"date":"2005-04-04T17:37:09","date_gmt":"2005-04-04T07:37:09","guid":{"rendered":"http:\/\/michaelnielsen.org\/?p=191"},"modified":"2005-04-04T17:37:09","modified_gmt":"2005-04-04T07:37:09","slug":"electrons-as-geometry","status":"publish","type":"post","link":"https:\/\/michaelnielsen.org\/blog\/electrons-as-geometry\/","title":{"rendered":"Electrons as geometry"},"content":{"rendered":"<p>(<b>Attention conservation notice (hat tip to <a href=\"http:\/\/www.cscs.umich.edu\/~crshalizi\/weblog\/\">Cosma<\/a> for the term):<\/b> This post requires some familiarity with Maxwell&#8217;s equations to make much sense.)<\/p>\n<p>A recent <a href=\"http:\/\/dabacon.org\/pontiff\/index.php?p=871#comments\">post<\/a> by Dave Bacon reminds me of a beautiful old idea by John Wheeler for explaining the electron (and other charged particles) as a combination of non-trivial geometry, and the free electromagnetic field.<\/p>\n<p>Suppose we start with ordinary flat spacetime.  Now insert a pair of tiny little punctures, and a little tube connecting those punctures.  The tube and the punctures will be used to represent an electron \/ positron pair.<\/p>\n<p>Now suppose that we have a divergence-free electric field going into one puncture, passing through the tube, and out the other end of the tube.<\/p>\n<p>From the point of view of an observer in the bulk, who is unaware of the puncture, it will look like the electric field has non-zero divergence around each puncture, i.e., it the punctures look like charges.<\/p>\n<p>There are several beautiful things about this picture:<\/p>\n<ul>\n<li> The charges of the two punctures are equal and opposite.\n<\/li>\n<li> It puts the electric and magnetic fields on an equal footing &#8211; there is no charge for either.\n<\/li>\n<\/ul>\n<p>Unfortunately, the idea leaves us wondering (a) why we don&#8217;t see magnetic charge in the bulk; (b) why charge is quantized ; and (c) what the dynamics of the tubes is supposed to be.<\/p>\n<p>Still, I really like the idea as a simple example of how non-trivial geometries can give rise to interesting physical phenomena.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>(Attention conservation notice (hat tip to Cosma for the term): This post requires some familiarity with Maxwell&#8217;s equations to make much sense.) A recent post by Dave Bacon reminds me of a beautiful old idea by John Wheeler for explaining the electron (and other charged particles) as a combination of non-trivial geometry, and the free&hellip; <a class=\"more-link\" href=\"https:\/\/michaelnielsen.org\/blog\/electrons-as-geometry\/\">Continue reading <span class=\"screen-reader-text\">Electrons as geometry<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-191","post","type-post","status-publish","format-standard","hentry","category-3","entry"],"_links":{"self":[{"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/posts\/191","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/comments?post=191"}],"version-history":[{"count":0,"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/posts\/191\/revisions"}],"wp:attachment":[{"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/media?parent=191"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/categories?post=191"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/tags?post=191"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}