{"id":13853,"date":"2021-11-25T09:00:56","date_gmt":"2021-11-25T17:00:56","guid":{"rendered":"https:\/\/www.preposterousuniverse.com\/blog\/?p=13853"},"modified":"2021-11-25T09:01:03","modified_gmt":"2021-11-25T17:01:03","slug":"thanksgiving-16","status":"publish","type":"post","link":"https:\/\/preposterousuniverse.com\/blog\/2021\/11\/25\/thanksgiving-16\/","title":{"rendered":"Thanksgiving"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><meta charset=\"utf-8\">This year we give thanks for something we&#8217;ve all heard of, but maybe don&#8217;t appreciate as much as we should: electromagnetism. (We&#8217;ve previously given thanks for the <a href=\"http:\/\/preposterousuniverse.com\/blog\/2006\/11\/23\/thanksgiving\/\">Standard Model Lagrangian<\/a>, <a href=\"http:\/\/preposterousuniverse.com\/blog\/2007\/11\/22\/thanksgiving-2\/\">Hubble&#8217;s Law<\/a>, the <a href=\"http:\/\/preposterousuniverse.com\/blog\/2008\/11\/27\/thanksgiving-3\/\">Spin-Statistics Theorem<\/a>, <a href=\"http:\/\/preposterousuniverse.com\/blog\/2009\/11\/26\/thanksgiving-4\/\">conservation of momentum<\/a>, <a href=\"http:\/\/preposterousuniverse.com\/blog\/2010\/11\/25\/thanksgiving-5\/\">effective field theory<\/a>, <a href=\"http:\/\/preposterousuniverse.com\/blog\/2011\/11\/24\/thanksgiving-6\/\">the error bar<\/a>, <a href=\"https:\/\/www.preposterousuniverse.com\/blog\/2012\/11\/22\/thanksgiving-7\/\">gauge symmetry<\/a>, <a href=\"https:\/\/www.preposterousuniverse.com\/blog\/2013\/11\/28\/thanksgiving-8\/\">Landauer&#8217;s Principle<\/a>, the <a href=\"https:\/\/www.preposterousuniverse.com\/blog\/2014\/11\/27\/thanksgiving-9\/\">Fourier Transform<\/a>, <a href=\"https:\/\/www.preposterousuniverse.com\/blog\/2015\/11\/26\/thanksgiving-10\/\">Riemannian Geometry<\/a>, <a href=\"https:\/\/www.preposterousuniverse.com\/blog\/2016\/11\/24\/thanksgiving-11\/\">the speed of light<\/a>, <a href=\"https:\/\/www.preposterousuniverse.com\/blog\/2017\/11\/23\/thanksgiving-12\/\">the Jarzynski equality<\/a>, <a href=\"https:\/\/www.preposterousuniverse.com\/blog\/2018\/11\/22\/thanksgiving-13\/\">the moons of Jupiter<\/a>, <a href=\"https:\/\/www.preposterousuniverse.com\/blog\/2019\/11\/28\/thanksgiving-14\/\">space<\/a>, and <a href=\"https:\/\/www.preposterousuniverse.com\/blog\/2020\/11\/26\/thanksgiving-15\/\">black hole entropy<\/a>.)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Physicists like to say there are four forces of nature: <a href=\"https:\/\/en.wikipedia.org\/wiki\/Gravity\">gravitation<\/a>, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Electromagnetism\">electromagnetism<\/a>, the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Strong_interaction\">strong<\/a> nuclear force, and the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Weak_interaction\">weak<\/a> nuclear force. That&#8217;s a somewhat sloppy and old-fashioned way of talking. In the old days it made sense to distinguish between &#8220;matter,&#8221; in the form of particles or fluids or something like that, and &#8220;forces,&#8221; which pushed around the matter. These days we know it&#8217;s all just <a href=\"https:\/\/en.wikipedia.org\/wiki\/Quantum_field_theory\">quantum fields<\/a>, and both matter and forces arise from the behavior of quantum fields interacting with each other. There is an important distinction between fermions and bosons, which almost maps onto the old-fashioned matter\/force distinction, but not quite. If it did, we&#8217;d have to include the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Higgs_boson\">Higgs<\/a> force among the fundamental forces, but nobody is really inclined to do that.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The real reason we stick with the traditional four forces is that (unlike the Higgs) they are all mediated by a particular kind of bosonic quantum field, called <a href=\"https:\/\/en.wikipedia.org\/wiki\/Gauge_theory\">gauge fields. <\/a>There&#8217;s a lot of technical stuff that goes into explaining what that means, but the basic idea is that the gauge fields help us compare other fields at different points in space, when those fields are invariant under a certain kind of symmetry. For more details, check out this video from the<a href=\"https:\/\/www.youtube.com\/playlist?list=PLrxfgDEc2NxZJcWcrxH3jyjUUrJlnoyzX\"> Biggest Ideas in the Universe<\/a> series (but you might need to go back to pick up some of the prerequisites).<\/p>\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"lyte-wrapper\" title=\"The Biggest Ideas in the Universe | 15. Gauge Theory\" style=\"width:640px;max-width:100%;margin:5px;\"><div class=\"lyMe\" id=\"WYL_AuqKsBQnE2A\" itemprop=\"video\" itemscope itemtype=\"https:\/\/schema.org\/VideoObject\"><div><meta itemprop=\"thumbnailUrl\" content=\"https:\/\/i.ytimg.com\/vi\/AuqKsBQnE2A\/hqdefault.jpg\" \/><meta itemprop=\"embedURL\" content=\"https:\/\/www.youtube.com\/embed\/AuqKsBQnE2A\" \/><meta itemprop=\"duration\" content=\"PT1H17M58S\" \/><meta itemprop=\"uploadDate\" content=\"2020-06-30T14:37:20Z\" \/><\/div><div id=\"lyte_AuqKsBQnE2A\" data-src=\"https:\/\/i.ytimg.com\/vi\/AuqKsBQnE2A\/hqdefault.jpg\" class=\"pL\"><div class=\"tC\"><div class=\"tT\" itemprop=\"name\">The Biggest Ideas in the Universe | 15. Gauge Theory<\/div><\/div><div class=\"play\"><\/div><div class=\"ctrl\"><div class=\"Lctrl\"><\/div><div class=\"Rctrl\"><\/div><\/div><\/div><noscript><a href=\"https:\/\/youtu.be\/AuqKsBQnE2A\" rel=\"nofollow\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i.ytimg.com\/vi\/AuqKsBQnE2A\/0.jpg\" alt=\"The Biggest Ideas in the Universe | 15. Gauge Theory\" width=\"640\" height=\"340\" \/><br \/>Watch this video on YouTube<\/a><\/noscript><meta itemprop=\"description\" content=\"The Biggest Ideas in the Universe is a series of videos where I talk informally about some of the fundamental concepts that help us understand our natural world. Exceedingly casual, not overly polished, and meant for absolutely everybody. This is Idea #15, &quot;Gauge Theory.&quot; Here is where the last couple of ideas come together, and we see how geometry and symmetry underlie the fundamental forces of nature as they are currently understood. My web page: http:\/\/www.preposterousuniverse.com\/ My YouTube channel: https:\/\/www.youtube.com\/c\/seancarroll Mindscape podcast: http:\/\/www.preposterousuniverse.com\/podcast The Biggest Ideas playlist: https:\/\/www.youtube.com\/playlist?list=PLrxfgDEc2NxZJcWcrxH3jyjUUrJlnoyzX Blog posts for the series: http:\/\/www.preposterousuniverse.com\/blog\/category\/biggest-ideas-in-the-universe\/ Background image: http:\/\/www.desktopwallpaperhd.net\/blue-fractal-mirror-nice-background-wallpapers-84056.html #science #physics #ideas #universe #learning #cosmology #philosophy #math #gaugetheory #symmetry\"><\/div><\/div><div class=\"lL\" style=\"max-width:100%;width:640px;margin:5px;\"><\/div><figcaption><\/figcaption><\/figure>\n\n\n<p class=\"wp-block-paragraph\">All of which is just throat-clearing to say: there are four forces, but they&#8217;re all different in important ways, and electromagnetism is special. All the forces play some kind of role in accounting for the world around us, but electromagnetism is responsible for almost all of the &#8220;interestingness&#8221; of the world of our experience. Let&#8217;s see why.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">When you have a force carried by a gauge field, one of the first questions to ask is what <a href=\"https:\/\/arxiv.org\/abs\/1211.2843\">phase<\/a> the field is in (in whatever physical situation you care about). This is &#8220;phase&#8221; in the same sense as &#8220;phase of matter,&#8221; e.g. solid, liquid, gas, etc. In the case of gauge theories, we can think about the different phases in terms of what happens to <a href=\"https:\/\/en.wikipedia.org\/wiki\/Line_of_force\">lines of force<\/a> &#8212; the imaginary paths through space that we would draw to be parallel to the direction of the force exerted at each point.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The simplest thing that lines of force can do is just to extend away from a source, traveling forever through space until they hit some other source. (For electromagnetism, a &#8220;source&#8221; is just a charged particle.) That corresponds to field being in the <strong>Coulomb phase<\/strong>. Infinitely-stretching lines of force dilute in density as the area through which they are passing increases. In three dimensions of space, that corresponds to spheres we draw around the source, whose area goes up as the distance squared. The magnitude of the force therefore goes as the inverse of the square &#8212; the famous <strong>inverse square law<\/strong>. In the real world, both gravity and electromagnetism are in the Coulomb phase, and exhibit inverse-square laws.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">But there are other phases. There is the <strong>confined<\/strong> phase, where lines of force get all tangled up with each other. There is also the <strong>Higgs<\/strong> phase, where the lines of force are gradually absorbed into some surrounding field (the Higgs field!). In the real world, the strong nuclear force is in the confined phase, and the weak nuclear force is in the Higgs phase. As a result, neither force extends farther than subatomic distances.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><a href=\"https:\/\/www.preposterousuniverse.com\/blog\/wp-content\/uploads\/2021\/11\/phases.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.preposterousuniverse.com\/blog\/wp-content\/uploads\/2021\/11\/phases-1024x435.png\" alt=\"Phases of gauge fields.\" class=\"wp-image-13857\" width=\"512\" height=\"218\" srcset=\"https:\/\/preposterousuniverse.com\/blog\/wp-content\/uploads\/2021\/11\/phases-1024x435.png 1024w, https:\/\/preposterousuniverse.com\/blog\/wp-content\/uploads\/2021\/11\/phases-300x127.png 300w, https:\/\/preposterousuniverse.com\/blog\/wp-content\/uploads\/2021\/11\/phases-768x326.png 768w, https:\/\/preposterousuniverse.com\/blog\/wp-content\/uploads\/2021\/11\/phases-1536x652.png 1536w, https:\/\/preposterousuniverse.com\/blog\/wp-content\/uploads\/2021\/11\/phases-2048x870.png 2048w, https:\/\/preposterousuniverse.com\/blog\/wp-content\/uploads\/2021\/11\/phases-150x64.png 150w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/a><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">So there are four gauge forces that push around particles, but only two of them are &#8220;long-range&#8221; forces in the Coulomb phase. The short-range strong and weak forces are important for explaining the structure of protons and neutrons and nuclei, but once you understand what <a href=\"https:\/\/en.wikipedia.org\/wiki\/Stable_nuclide\">stable nuclei<\/a> there are, there work is essentially done, as far as accounting for the everyday world is concerned. (You still need them to explain fusion inside stars, so here we&#8217;re just thinking of life here on Earth.) The way that those nuclei come together with electrons to make atoms and molecules and larger structures is all explained by the long-range forces, electromagnetism and gravity.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">But electromagnetism and gravity aren&#8217;t quite equal here. Gravity is important, obviously, but it&#8217;s also pretty simple: everything attracts everything else. (We&#8217;re ignoring cosmology etc, focusing in on life here on Earth.) That&#8217;s nice &#8212; it&#8217;s good that we stay attached to the ground, rather than floating away &#8212; but it&#8217;s not a recipe for intricate complexity. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To get complexity, you need to be able to manipulate matter in delicate ways with your force. Gravity isn&#8217;t up to the task &#8212; it just attracts. Electromagentism, on the other hand, is exactly what the doctor ordered. Unlike gravity, where the &#8220;charge&#8221; is just mass and all masses are positive, electromagnetism has both positive and negative charges. Like charges repel, and opposite charges attract. So by deftly arranging collections of positively and negatively charged particles, you can manipulate matter in whatever way you like.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">That pinpoint control over pushing and pulling is crucial for the existence of complex structures in the universe, including you and me.  Nuclei join with electrons to make atoms because of electromagnetism. Atoms come together to make molecules because of electromagnetism. Molecules interact with each other in different ways because of electromagnetism. All of the chemical processes in your body, not to mention in the world immediately around you, can ultimately be traced to electromagnetism at work.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Electromagnetism doesn&#8217;t get all the credit for the structure of matter. A crucial role is played by the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Pauli_exclusion_principle\">Pauli exclusion principle<\/a>, which prohibits two electrons from inhabiting exactly the same state. That&#8217;s ultimately what gives matter its size &#8212; why objects are solid, etc. But without the electromagnetic interplay between atoms of different sizes and numbers of electrons, matter would be solid but inert, just sitting still without doing anything interesting. It&#8217;s electromagnetism that allows energy to move from place to place between atoms, both via electricity (electrons in motion, pushed by electromagnetic fields) and radiation (vibrations in the electromagnetic fields themselves).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So we should count ourselves lucky that we live in a world where at least one fundamental force is both in the Coulomb phase and has opposite charges, and give appropriate thanks. It&#8217;s what makes the world interesting.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This year we give thanks for something we&#8217;ve all heard of, but maybe don&#8217;t appreciate as much as we should: electromagnetism. (We&#8217;ve previously given thanks for the Standard Model Lagrangian, Hubble&#8217;s Law, the Spin-Statistics Theorem, conservation of momentum, effective field theory, the error bar, gauge symmetry, Landauer&#8217;s Principle, the Fourier Transform, Riemannian Geometry, the speed [&hellip;]<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-13853","post","type-post","status-publish","format-standard","hentry","category-miscellany"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/posts\/13853","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/comments?post=13853"}],"version-history":[{"count":5,"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/posts\/13853\/revisions"}],"predecessor-version":[{"id":13860,"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/posts\/13853\/revisions\/13860"}],"wp:attachment":[{"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/media?parent=13853"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/categories?post=13853"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/tags?post=13853"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}