CINXE.COM

<!DOCTYPE html><html lang="en-US" class="html_boxed responsive av-preloader-disabled html_header_top html_logo_left html_main_nav_header html_menu_right html_custom html_header_sticky html_header_shrinking_disabled html_mobile_menu_phone html_header_searchicon html_content_align_center html_header_unstick_top_disabled html_header_stretch_disabled html_av-submenu-hidden html_av-submenu-display-click html_av-overlay-side html_av-overlay-side-classic html_av-submenu-noclone html_entry_id_21404 av-cookies-no-cookie-consent av-no-preview av-default-lightbox html_text_menu_active av-mobile-menu-switch-default"><head><meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"><meta charset="UTF-8" /> <script async src="https://www.googletagmanager.com/gtag/js?id=UA-2209856-4"></script> <script>window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-2209856-4');</script> <script data-optimized="1" src="https://www.physicsforums.com/insights/wp-content/litespeed/js/2592eef92248026c6738059400d0d827.js?ver=0d827" defer type="text/javascript"></script> <meta name="viewport" content="width=device-width, initial-scale=1"><meta name='robots' content='index, follow, max-image-preview:large, max-snippet:-1, max-video-preview:-1' /><style>img:is([sizes="auto" i], [sizes^="auto," i]) { contain-intrinsic-size: 3000px 1500px }</style> <script type="text/javascript" id="wpp-js" src="https://www.physicsforums.com/insights/wp-content/plugins/wordpress-popular-posts/assets/js/wpp.js?ver=7.1.0" data-sampling="0" data-sampling-rate="100" data-api-url="https://www.physicsforums.com/insights/wp-json/wordpress-popular-posts" data-post-id="21404" data-token="ac9d65413d" data-lang="0" data-debug="1"></script> <title>About Physics Forums | Our Mission, Values, Goals and History</title><meta name="description" content="Learn about Physics Forums. We provide a community for people to learn and discuss science as it is currently generally understood and practiced." /><link rel="canonical" href="https://www.physicsforums.com/insights/about-physics-forums/" /><meta property="og:locale" content="en_US" /><meta property="og:type" content="article" /><meta property="og:title" content="About Physics Forums | Our Mission, Values, Goals and History" /><meta property="og:description" content="Learn about Physics Forums. We provide a community for people to learn and discuss science as it is currently generally understood and practiced." /><meta property="og:url" content="https://www.physicsforums.com/insights/about-physics-forums/" /><meta property="og:site_name" content="Physics Forums Insights" /><meta property="article:publisher" content="https://www.facebook.com/physicsforums" /><meta property="article:modified_time" content="2024-11-01T12:53:12+00:00" /><meta property="og:image" content="https://www.physicsforums.com/styles/default/xenforo/clear.png" /><meta name="twitter:card" content="summary_large_image" /><meta name="twitter:site" content="@physicsforums" /><meta name="twitter:label1" content="Est. reading time" /><meta name="twitter:data1" content="10 minutes" /> <script type="application/ld+json" class="yoast-schema-graph">{"@context":"https://schema.org","@graph":[{"@type":["WebPage","AboutPage"],"@id":"https://www.physicsforums.com/insights/about-physics-forums/","url":"https://www.physicsforums.com/insights/about-physics-forums/","name":"About Physics Forums | Our Mission, Values, Goals and History","isPartOf":{"@id":"https://www.physicsforums.com/insights/#website"},"primaryImageOfPage":{"@id":"https://www.physicsforums.com/insights/about-physics-forums/#primaryimage"},"image":{"@id":"https://www.physicsforums.com/insights/about-physics-forums/#primaryimage"},"thumbnailUrl":"https://www.physicsforums.com/styles/default/xenforo/clear.png","datePublished":"2018-08-16T01:58:19+00:00","dateModified":"2024-11-01T12:53:12+00:00","description":"Learn about Physics Forums. We provide a community for people to learn and discuss science as it is currently generally understood and practiced.","breadcrumb":{"@id":"https://www.physicsforums.com/insights/about-physics-forums/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https://www.physicsforums.com/insights/about-physics-forums/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https://www.physicsforums.com/insights/about-physics-forums/#primaryimage","url":"https://www.physicsforums.com/styles/default/xenforo/clear.png","contentUrl":"https://www.physicsforums.com/styles/default/xenforo/clear.png"},{"@type":"BreadcrumbList","@id":"https://www.physicsforums.com/insights/about-physics-forums/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https://www.physicsforums.com/insights/"},{"@type":"ListItem","position":2,"name":"About Physics Forums"}]},{"@type":"WebSite","@id":"https://www.physicsforums.com/insights/#website","url":"https://www.physicsforums.com/insights/","name":"Physics Forums Insights","description":"Science and Math Articles, Tutorials and Guides","publisher":{"@id":"https://www.physicsforums.com/insights/#organization"},"alternateName":"PF Insights","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://www.physicsforums.com/insights/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https://www.physicsforums.com/insights/#organization","name":"Physics Forums","url":"https://www.physicsforums.com/insights/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https://www.physicsforums.com/insights/#/schema/logo/image/","url":"https://www.physicsforums.com/insights/wp-content/uploads/2018/05/facebook_image-1.png","contentUrl":"https://www.physicsforums.com/insights/wp-content/uploads/2018/05/facebook_image-1.png","width":205,"height":200,"caption":"Physics Forums"},"image":{"@id":"https://www.physicsforums.com/insights/#/schema/logo/image/"},"sameAs":["https://www.facebook.com/physicsforums","https://x.com/physicsforums","https://www.linkedin.com/company/physics-forums","https://www.pinterest.com/physicsforums"]}]}</script> <link rel="alternate" type="application/rss+xml" title="Physics Forums Insights » Feed" href="https://www.physicsforums.com/insights/feed/" /><link data-optimized="1" rel='stylesheet' id='xpress_wp_admin_style-css' href='https://www.physicsforums.com/insights/wp-content/litespeed/css/9294efc37b077c18f8cbd596b1da1840.css?ver=a1840' type='text/css' media='all' /><link data-optimized="1" rel='stylesheet' id='wp-block-library-css' href='https://www.physicsforums.com/insights/wp-content/litespeed/css/ad10b27e06583ae315af8368433fa1f7.css?ver=6d365' type='text/css' media='all' /><style id='global-styles-inline-css' type='text/css'>:root{--wp--preset--aspect-ratio--square: 1;--wp--preset--aspect-ratio--4-3: 4/3;--wp--preset--aspect-ratio--3-4: 3/4;--wp--preset--aspect-ratio--3-2: 3/2;--wp--preset--aspect-ratio--2-3: 2/3;--wp--preset--aspect-ratio--16-9: 16/9;--wp--preset--aspect-ratio--9-16: 9/16;--wp--preset--color--black: #000000;--wp--preset--color--cyan-bluish-gray: #abb8c3;--wp--preset--color--white: #ffffff;--wp--preset--color--pale-pink: #f78da7;--wp--preset--color--vivid-red: #cf2e2e;--wp--preset--color--luminous-vivid-orange: #ff6900;--wp--preset--color--luminous-vivid-amber: #fcb900;--wp--preset--color--light-green-cyan: #7bdcb5;--wp--preset--color--vivid-green-cyan: #00d084;--wp--preset--color--pale-cyan-blue: #8ed1fc;--wp--preset--color--vivid-cyan-blue: #0693e3;--wp--preset--color--vivid-purple: #9b51e0;--wp--preset--color--metallic-red: #b02b2c;--wp--preset--color--maximum-yellow-red: #edae44;--wp--preset--color--yellow-sun: #eeee22;--wp--preset--color--palm-leaf: #83a846;--wp--preset--color--aero: #7bb0e7;--wp--preset--color--old-lavender: #745f7e;--wp--preset--color--steel-teal: #5f8789;--wp--preset--color--raspberry-pink: #d65799;--wp--preset--color--medium-turquoise: #4ecac2;--wp--preset--gradient--vivid-cyan-blue-to-vivid-purple: linear-gradient(135deg,rgba(6,147,227,1) 0%,rgb(155,81,224) 100%);--wp--preset--gradient--light-green-cyan-to-vivid-green-cyan: linear-gradient(135deg,rgb(122,220,180) 0%,rgb(0,208,130) 100%);--wp--preset--gradient--luminous-vivid-amber-to-luminous-vivid-orange: linear-gradient(135deg,rgba(252,185,0,1) 0%,rgba(255,105,0,1) 100%);--wp--preset--gradient--luminous-vivid-orange-to-vivid-red: linear-gradient(135deg,rgba(255,105,0,1) 0%,rgb(207,46,46) 100%);--wp--preset--gradient--very-light-gray-to-cyan-bluish-gray: linear-gradient(135deg,rgb(238,238,238) 0%,rgb(169,184,195) 100%);--wp--preset--gradient--cool-to-warm-spectrum: linear-gradient(135deg,rgb(74,234,220) 0%,rgb(151,120,209) 20%,rgb(207,42,186) 40%,rgb(238,44,130) 60%,rgb(251,105,98) 80%,rgb(254,248,76) 100%);--wp--preset--gradient--blush-light-purple: linear-gradient(135deg,rgb(255,206,236) 0%,rgb(152,150,240) 100%);--wp--preset--gradient--blush-bordeaux: linear-gradient(135deg,rgb(254,205,165) 0%,rgb(254,45,45) 50%,rgb(107,0,62) 100%);--wp--preset--gradient--luminous-dusk: linear-gradient(135deg,rgb(255,203,112) 0%,rgb(199,81,192) 50%,rgb(65,88,208) 100%);--wp--preset--gradient--pale-ocean: linear-gradient(135deg,rgb(255,245,203) 0%,rgb(182,227,212) 50%,rgb(51,167,181) 100%);--wp--preset--gradient--electric-grass: linear-gradient(135deg,rgb(202,248,128) 0%,rgb(113,206,126) 100%);--wp--preset--gradient--midnight: linear-gradient(135deg,rgb(2,3,129) 0%,rgb(40,116,252) 100%);--wp--preset--font-size--small: 1rem;--wp--preset--font-size--medium: 1.125rem;--wp--preset--font-size--large: 1.75rem;--wp--preset--font-size--x-large: clamp(1.75rem, 3vw, 2.25rem);--wp--preset--spacing--20: 0.44rem;--wp--preset--spacing--30: 0.67rem;--wp--preset--spacing--40: 1rem;--wp--preset--spacing--50: 1.5rem;--wp--preset--spacing--60: 2.25rem;--wp--preset--spacing--70: 3.38rem;--wp--preset--spacing--80: 5.06rem;--wp--preset--shadow--natural: 6px 6px 9px rgba(0, 0, 0, 0.2);--wp--preset--shadow--deep: 12px 12px 50px rgba(0, 0, 0, 0.4);--wp--preset--shadow--sharp: 6px 6px 0px rgba(0, 0, 0, 0.2);--wp--preset--shadow--outlined: 6px 6px 0px -3px rgba(255, 255, 255, 1), 6px 6px rgba(0, 0, 0, 1);--wp--preset--shadow--crisp: 6px 6px 0px rgba(0, 0, 0, 1);}:root { --wp--style--global--content-size: 800px;--wp--style--global--wide-size: 1130px; }:where(body) { margin: 0; }.wp-site-blocks > .alignleft { float: left; margin-right: 2em; }.wp-site-blocks > .alignright { float: right; margin-left: 2em; }.wp-site-blocks > .aligncenter { justify-content: center; margin-left: auto; margin-right: auto; }:where(.is-layout-flex){gap: 0.5em;}:where(.is-layout-grid){gap: 0.5em;}.is-layout-flow > .alignleft{float: left;margin-inline-start: 0;margin-inline-end: 2em;}.is-layout-flow > .alignright{float: right;margin-inline-start: 2em;margin-inline-end: 0;}.is-layout-flow > .aligncenter{margin-left: auto !important;margin-right: auto !important;}.is-layout-constrained > .alignleft{float: left;margin-inline-start: 0;margin-inline-end: 2em;}.is-layout-constrained > .alignright{float: right;margin-inline-start: 2em;margin-inline-end: 0;}.is-layout-constrained > .aligncenter{margin-left: auto !important;margin-right: auto !important;}.is-layout-constrained > :where(:not(.alignleft):not(.alignright):not(.alignfull)){max-width: var(--wp--style--global--content-size);margin-left: auto !important;margin-right: auto !important;}.is-layout-constrained > .alignwide{max-width: var(--wp--style--global--wide-size);}body .is-layout-flex{display: flex;}.is-layout-flex{flex-wrap: wrap;align-items: center;}.is-layout-flex > :is(*, div){margin: 0;}body .is-layout-grid{display: grid;}.is-layout-grid > :is(*, div){margin: 0;}body{padding-top: 0px;padding-right: 0px;padding-bottom: 0px;padding-left: 0px;}a:where(:not(.wp-element-button)){text-decoration: underline;}:root :where(.wp-element-button, .wp-block-button__link){background-color: #32373c;border-width: 0;color: #fff;font-family: inherit;font-size: inherit;line-height: inherit;padding: calc(0.667em + 2px) calc(1.333em + 2px);text-decoration: none;}.has-black-color{color: var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-color{color: var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-color{color: var(--wp--preset--color--white) !important;}.has-pale-pink-color{color: var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-color{color: var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-color{color: var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-color{color: var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-color{color: var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-color{color: var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-color{color: var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-color{color: var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-color{color: var(--wp--preset--color--vivid-purple) !important;}.has-metallic-red-color{color: var(--wp--preset--color--metallic-red) !important;}.has-maximum-yellow-red-color{color: var(--wp--preset--color--maximum-yellow-red) !important;}.has-yellow-sun-color{color: var(--wp--preset--color--yellow-sun) !important;}.has-palm-leaf-color{color: var(--wp--preset--color--palm-leaf) !important;}.has-aero-color{color: var(--wp--preset--color--aero) !important;}.has-old-lavender-color{color: var(--wp--preset--color--old-lavender) !important;}.has-steel-teal-color{color: var(--wp--preset--color--steel-teal) !important;}.has-raspberry-pink-color{color: var(--wp--preset--color--raspberry-pink) !important;}.has-medium-turquoise-color{color: var(--wp--preset--color--medium-turquoise) !important;}.has-black-background-color{background-color: var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-background-color{background-color: var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-background-color{background-color: var(--wp--preset--color--white) !important;}.has-pale-pink-background-color{background-color: var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-background-color{background-color: var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-background-color{background-color: var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-background-color{background-color: var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-background-color{background-color: var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-background-color{background-color: var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-background-color{background-color: var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-background-color{background-color: var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-background-color{background-color: var(--wp--preset--color--vivid-purple) !important;}.has-metallic-red-background-color{background-color: var(--wp--preset--color--metallic-red) !important;}.has-maximum-yellow-red-background-color{background-color: var(--wp--preset--color--maximum-yellow-red) !important;}.has-yellow-sun-background-color{background-color: var(--wp--preset--color--yellow-sun) !important;}.has-palm-leaf-background-color{background-color: var(--wp--preset--color--palm-leaf) !important;}.has-aero-background-color{background-color: var(--wp--preset--color--aero) !important;}.has-old-lavender-background-color{background-color: var(--wp--preset--color--old-lavender) !important;}.has-steel-teal-background-color{background-color: var(--wp--preset--color--steel-teal) !important;}.has-raspberry-pink-background-color{background-color: var(--wp--preset--color--raspberry-pink) !important;}.has-medium-turquoise-background-color{background-color: var(--wp--preset--color--medium-turquoise) !important;}.has-black-border-color{border-color: var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-border-color{border-color: var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-border-color{border-color: var(--wp--preset--color--white) !important;}.has-pale-pink-border-color{border-color: var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-border-color{border-color: var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-border-color{border-color: var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-border-color{border-color: var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-border-color{border-color: var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-border-color{border-color: var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-border-color{border-color: var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-border-color{border-color: var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-border-color{border-color: var(--wp--preset--color--vivid-purple) !important;}.has-metallic-red-border-color{border-color: var(--wp--preset--color--metallic-red) !important;}.has-maximum-yellow-red-border-color{border-color: var(--wp--preset--color--maximum-yellow-red) !important;}.has-yellow-sun-border-color{border-color: var(--wp--preset--color--yellow-sun) !important;}.has-palm-leaf-border-color{border-color: var(--wp--preset--color--palm-leaf) !important;}.has-aero-border-color{border-color: var(--wp--preset--color--aero) !important;}.has-old-lavender-border-color{border-color: var(--wp--preset--color--old-lavender) !important;}.has-steel-teal-border-color{border-color: var(--wp--preset--color--steel-teal) !important;}.has-raspberry-pink-border-color{border-color: var(--wp--preset--color--raspberry-pink) !important;}.has-medium-turquoise-border-color{border-color: var(--wp--preset--color--medium-turquoise) !important;}.has-vivid-cyan-blue-to-vivid-purple-gradient-background{background: var(--wp--preset--gradient--vivid-cyan-blue-to-vivid-purple) !important;}.has-light-green-cyan-to-vivid-green-cyan-gradient-background{background: var(--wp--preset--gradient--light-green-cyan-to-vivid-green-cyan) !important;}.has-luminous-vivid-amber-to-luminous-vivid-orange-gradient-background{background: var(--wp--preset--gradient--luminous-vivid-amber-to-luminous-vivid-orange) !important;}.has-luminous-vivid-orange-to-vivid-red-gradient-background{background: var(--wp--preset--gradient--luminous-vivid-orange-to-vivid-red) !important;}.has-very-light-gray-to-cyan-bluish-gray-gradient-background{background: var(--wp--preset--gradient--very-light-gray-to-cyan-bluish-gray) !important;}.has-cool-to-warm-spectrum-gradient-background{background: var(--wp--preset--gradient--cool-to-warm-spectrum) !important;}.has-blush-light-purple-gradient-background{background: var(--wp--preset--gradient--blush-light-purple) !important;}.has-blush-bordeaux-gradient-background{background: var(--wp--preset--gradient--blush-bordeaux) !important;}.has-luminous-dusk-gradient-background{background: var(--wp--preset--gradient--luminous-dusk) !important;}.has-pale-ocean-gradient-background{background: var(--wp--preset--gradient--pale-ocean) !important;}.has-electric-grass-gradient-background{background: var(--wp--preset--gradient--electric-grass) !important;}.has-midnight-gradient-background{background: var(--wp--preset--gradient--midnight) !important;}.has-small-font-size{font-size: var(--wp--preset--font-size--small) !important;}.has-medium-font-size{font-size: var(--wp--preset--font-size--medium) !important;}.has-large-font-size{font-size: var(--wp--preset--font-size--large) !important;}.has-x-large-font-size{font-size: var(--wp--preset--font-size--x-large) !important;} :where(.wp-block-post-template.is-layout-flex){gap: 1.25em;}:where(.wp-block-post-template.is-layout-grid){gap: 1.25em;} :where(.wp-block-columns.is-layout-flex){gap: 2em;}:where(.wp-block-columns.is-layout-grid){gap: 2em;} :root :where(.wp-block-pullquote){font-size: 1.5em;line-height: 1.6;}</style><link data-optimized="1" rel='stylesheet' id='ez-toc-css' href='https://www.physicsforums.com/insights/wp-content/litespeed/css/008d509d4fec340652d0312244582360.css?ver=ec21b' type='text/css' media='all' /><style id='ez-toc-inline-css' type='text/css'>div#ez-toc-container .ez-toc-title {font-size: 120%;}div#ez-toc-container .ez-toc-title {font-weight: 500;}div#ez-toc-container ul li {font-size: 95%;}div#ez-toc-container ul li {font-weight: 500;}div#ez-toc-container nav ul ul li {font-size: 90%;}div#ez-toc-container {background: #fff;border: 1px solid #ddd;}div#ez-toc-container p.ez-toc-title , #ez-toc-container .ez_toc_custom_title_icon , #ez-toc-container .ez_toc_custom_toc_icon {color: #4c4c4c;}div#ez-toc-container ul.ez-toc-list a {color: #066fac;}div#ez-toc-container ul.ez-toc-list a:hover {color: #235887;}div#ez-toc-container ul.ez-toc-list a:visited {color: #4594d1;} .ez-toc-container-direction {direction: ltr;}.ez-toc-counter ul{counter-reset: item ;}.ez-toc-counter nav ul li a::before {content: counters(item, '.', decimal) '. ';display: inline-block;counter-increment: item;flex-grow: 0;flex-shrink: 0;margin-right: .2em; float: left; }.ez-toc-widget-direction {direction: ltr;}.ez-toc-widget-container ul{counter-reset: item ;}.ez-toc-widget-container nav ul li a::before {content: counters(item, '.', decimal) '. ';display: inline-block;counter-increment: item;flex-grow: 0;flex-shrink: 0;margin-right: .2em; float: left; }</style><link data-optimized="1" rel='stylesheet' id='wordpress-popular-posts-css-css' href='https://www.physicsforums.com/insights/wp-content/litespeed/css/f37de7c74c7905b881abee3714c59450.css?ver=e678c' type='text/css' media='all' /><link data-optimized="1" rel='stylesheet' id='avia-merged-styles-css' href='https://www.physicsforums.com/insights/wp-content/litespeed/css/cfb9c80d41094e4ad473a1e04dc00f70.css?ver=00f70' type='text/css' media='all' /> <script data-optimized="1" type="text/javascript" async='async' src="https://www.physicsforums.com/insights/wp-content/litespeed/js/22e6cada7a5696283f0dcecdd91a44c9.js?ver=a44c9" id="avia-head-scripts-js"></script> <style id="wpp-loading-animation-styles">@-webkit-keyframes bgslide{from{background-position-x:0}to{background-position-x:-200%}}@keyframes bgslide{from{background-position-x:0}to{background-position-x:-200%}}.wpp-widget-block-placeholder,.wpp-shortcode-placeholder{margin:0 auto;width:60px;height:3px;background:#dd3737;background:linear-gradient(90deg,#dd3737 0%,#571313 10%,#dd3737 100%);background-size:200% auto;border-radius:3px;-webkit-animation:bgslide 1s infinite linear;animation:bgslide 1s infinite linear}</style><link rel="profile" href="https://gmpg.org/xfn/11" /><link rel="alternate" type="application/rss+xml" title="Physics Forums Insights RSS2 Feed" href="https://www.physicsforums.com/insights/feed/" /><link rel="pingback" href="https://www.physicsforums.com/insights/xmlrpc.php" /><style type='text/css' media='screen'>#top #header_main > .container, #top #header_main > .container .main_menu .av-main-nav > li > a, #top #header_main #menu-item-shop .cart_dropdown_link{ height:70px; line-height: 70px; } .html_top_nav_header .av-logo-container{ height:70px; } .html_header_top.html_header_sticky #top #wrap_all #main{ padding-top:70px; }</style><link rel="icon" href="https://www.physicsforums.com/insights/wp-content/uploads/2016/08/favicon.ico" type="image/x-icon"><style type="text/css">.saboxplugin-wrap{-webkit-box-sizing:border-box;-moz-box-sizing:border-box;-ms-box-sizing:border-box;box-sizing:border-box;border:1px solid #eee;width:100%;clear:both;display:block;overflow:hidden;word-wrap:break-word;position:relative}.saboxplugin-wrap .saboxplugin-gravatar{float:left;padding:0 20px 20px 20px}.saboxplugin-wrap .saboxplugin-gravatar img{max-width:100px;height:auto;border-radius:0;}.saboxplugin-wrap .saboxplugin-authorname{font-size:18px;line-height:1;margin:20px 0 0 20px;display:block}.saboxplugin-wrap .saboxplugin-authorname a{text-decoration:none}.saboxplugin-wrap .saboxplugin-authorname a:focus{outline:0}.saboxplugin-wrap .saboxplugin-desc{display:block;margin:5px 20px}.saboxplugin-wrap .saboxplugin-desc a{text-decoration:underline}.saboxplugin-wrap .saboxplugin-desc p{margin:5px 0 12px}.saboxplugin-wrap .saboxplugin-web{margin:0 20px 15px;text-align:left}.saboxplugin-wrap .sab-web-position{text-align:right}.saboxplugin-wrap .saboxplugin-web a{color:#ccc;text-decoration:none}.saboxplugin-wrap .saboxplugin-socials{position:relative;display:block;background:#fcfcfc;padding:5px;border-top:1px solid #eee}.saboxplugin-wrap .saboxplugin-socials a svg{width:20px;height:20px}.saboxplugin-wrap .saboxplugin-socials a svg .st2{fill:#fff; transform-origin:center center;}.saboxplugin-wrap .saboxplugin-socials a svg .st1{fill:rgba(0,0,0,.3)}.saboxplugin-wrap .saboxplugin-socials a:hover{opacity:.8;-webkit-transition:opacity .4s;-moz-transition:opacity .4s;-o-transition:opacity .4s;transition:opacity .4s;box-shadow:none!important;-webkit-box-shadow:none!important}.saboxplugin-wrap .saboxplugin-socials .saboxplugin-icon-color{box-shadow:none;padding:0;border:0;-webkit-transition:opacity .4s;-moz-transition:opacity .4s;-o-transition:opacity .4s;transition:opacity .4s;display:inline-block;color:#fff;font-size:0;text-decoration:inherit;margin:5px;-webkit-border-radius:0;-moz-border-radius:0;-ms-border-radius:0;-o-border-radius:0;border-radius:0;overflow:hidden}.saboxplugin-wrap .saboxplugin-socials .saboxplugin-icon-grey{text-decoration:inherit;box-shadow:none;position:relative;display:-moz-inline-stack;display:inline-block;vertical-align:middle;zoom:1;margin:10px 5px;color:#444;fill:#444}.clearfix:after,.clearfix:before{content:' ';display:table;line-height:0;clear:both}.ie7 .clearfix{zoom:1}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-twitch{border-color:#38245c}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-addthis{border-color:#e91c00}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-behance{border-color:#003eb0}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-delicious{border-color:#06c}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-deviantart{border-color:#036824}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-digg{border-color:#00327c}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-dribbble{border-color:#ba1655}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-facebook{border-color:#1e2e4f}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-flickr{border-color:#003576}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-github{border-color:#264874}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-google{border-color:#0b51c5}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-googleplus{border-color:#96271a}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-html5{border-color:#902e13}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-instagram{border-color:#1630aa}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-linkedin{border-color:#00344f}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-pinterest{border-color:#5b040e}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-reddit{border-color:#992900}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-rss{border-color:#a43b0a}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-sharethis{border-color:#5d8420}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-skype{border-color:#00658a}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-soundcloud{border-color:#995200}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-spotify{border-color:#0f612c}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-stackoverflow{border-color:#a95009}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-steam{border-color:#006388}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-user_email{border-color:#b84e05}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-stumbleUpon{border-color:#9b280e}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-tumblr{border-color:#10151b}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-twitter{border-color:#0967a0}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-vimeo{border-color:#0d7091}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-windows{border-color:#003f71}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-whatsapp{border-color:#003f71}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-wordpress{border-color:#0f3647}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-yahoo{border-color:#14002d}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-youtube{border-color:#900}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-xing{border-color:#000202}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-mixcloud{border-color:#2475a0}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-vk{border-color:#243549}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-medium{border-color:#00452c}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-quora{border-color:#420e00}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-meetup{border-color:#9b181c}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-goodreads{border-color:#000}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-snapchat{border-color:#999700}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-500px{border-color:#00557f}.saboxplugin-socials.sabox-colored .saboxplugin-icon-color .sab-mastodont{border-color:#185886}.sabox-plus-item{margin-bottom:20px}@media screen and (max-width:480px){.saboxplugin-wrap{text-align:center}.saboxplugin-wrap .saboxplugin-gravatar{float:none;padding:20px 0;text-align:center;margin:0 auto;display:block}.saboxplugin-wrap .saboxplugin-gravatar img{float:none;display:inline-block;display:-moz-inline-stack;vertical-align:middle;zoom:1}.saboxplugin-wrap .saboxplugin-desc{margin:0 10px 20px;text-align:center}.saboxplugin-wrap .saboxplugin-authorname{text-align:center;margin:10px 0 20px}}body .saboxplugin-authorname a,body .saboxplugin-authorname a:hover{box-shadow:none;-webkit-box-shadow:none}a.sab-profile-edit{font-size:16px!important;line-height:1!important}.sab-edit-settings a,a.sab-profile-edit{color:#0073aa!important;box-shadow:none!important;-webkit-box-shadow:none!important}.sab-edit-settings{margin-right:15px;position:absolute;right:0;z-index:2;bottom:10px;line-height:20px}.sab-edit-settings i{margin-left:5px}.saboxplugin-socials{line-height:1!important}.rtl .saboxplugin-wrap .saboxplugin-gravatar{float:right}.rtl .saboxplugin-wrap .saboxplugin-authorname{display:flex;align-items:center}.rtl .saboxplugin-wrap .saboxplugin-authorname .sab-profile-edit{margin-right:10px}.rtl .sab-edit-settings{right:auto;left:0}img.sab-custom-avatar{max-width:75px;}.saboxplugin-wrap .saboxplugin-gravatar img {-webkit-border-radius:50%;-moz-border-radius:50%;-ms-border-radius:50%;-o-border-radius:50%;border-radius:50%;}.saboxplugin-wrap .saboxplugin-gravatar img {-webkit-border-radius:50%;-moz-border-radius:50%;-ms-border-radius:50%;-o-border-radius:50%;border-radius:50%;}.saboxplugin-wrap .saboxplugin-gravatar img {-webkit-transition:all .5s ease;-moz-transition:all .5s ease;-o-transition:all .5s ease;transition:all .5s ease;}.saboxplugin-wrap .saboxplugin-gravatar img:hover {-webkit-transform:rotate(45deg);-moz-transform:rotate(45deg);-o-transform:rotate(45deg);-ms-transform:rotate(45deg);transform:rotate(45deg);}.saboxplugin-wrap {margin-top:0px; margin-bottom:0px; padding: 0px 0px }.saboxplugin-wrap .saboxplugin-authorname {font-size:18px; line-height:25px;}.saboxplugin-wrap .saboxplugin-desc p, .saboxplugin-wrap .saboxplugin-desc {font-size:14px !important; line-height:21px !important;}.saboxplugin-wrap .saboxplugin-web {font-size:14px;}.saboxplugin-wrap .saboxplugin-socials a svg {width:18px;height:18px;}</style> <script type="text/javascript">'use strict';var avia_is_mobile=!1;if(/Android|webOS|iPhone|iPad|iPod|BlackBerry|IEMobile|Opera Mini/i.test(navigator.userAgent)&&'ontouchstart' in document.documentElement){avia_is_mobile=!0;document.documentElement.className+=' avia_mobile '} else{document.documentElement.className+=' avia_desktop '};document.documentElement.className+=' js_active ';(function(){var e=['-webkit-','-moz-','-ms-',''],n='',o=!1,a=!1;for(var t in e){if(e[t]+'transform' in document.documentElement.style){o=!0;n=e[t]+'transform'};if(e[t]+'perspective' in document.documentElement.style){a=!0}};if(o){document.documentElement.className+=' avia_transform '};if(a){document.documentElement.className+=' avia_transform3d '};if(typeof document.getElementsByClassName=='function'&&typeof document.documentElement.getBoundingClientRect=='function'&&avia_is_mobile==!1){if(n&&window.innerHeight>0){setTimeout(function(){var e=0,o={},a=0,t=document.getElementsByClassName('av-parallax'),i=window.pageYOffset||document.documentElement.scrollTop;for(e=0;e<t.length;e++){t[e].style.top='0px';o=t[e].getBoundingClientRect();a=Math.ceil((window.innerHeight+i-o.top)*0.3);t[e].style[n]='translate(0px, '+a+'px)';t[e].style.top='auto';t[e].className+=' enabled-parallax '}},50)}}})();</script><style type="text/css">@font-face {font-family: 'entypo-fontello'; font-weight: normal; font-style: normal; font-display: swap; src: url('https://www.physicsforums.com/insights/wp-content/themes/enfold/config-templatebuilder/avia-template-builder/assets/fonts/entypo-fontello.woff2') format('woff2'), url('https://www.physicsforums.com/insights/wp-content/themes/enfold/config-templatebuilder/avia-template-builder/assets/fonts/entypo-fontello.woff') format('woff'), url('https://www.physicsforums.com/insights/wp-content/themes/enfold/config-templatebuilder/avia-template-builder/assets/fonts/entypo-fontello.ttf') format('truetype'), url('https://www.physicsforums.com/insights/wp-content/themes/enfold/config-templatebuilder/avia-template-builder/assets/fonts/entypo-fontello.svg#entypo-fontello') format('svg'), url('https://www.physicsforums.com/insights/wp-content/themes/enfold/config-templatebuilder/avia-template-builder/assets/fonts/entypo-fontello.eot'), url('https://www.physicsforums.com/insights/wp-content/themes/enfold/config-templatebuilder/avia-template-builder/assets/fonts/entypo-fontello.eot?#iefix') format('embedded-opentype'); } #top .avia-font-entypo-fontello, body .avia-font-entypo-fontello, html body [data-av_iconfont='entypo-fontello']:before{ font-family: 'entypo-fontello'; }</style></head><body id="top" class="page-template-default page page-id-21404 boxed avia-mobile-no-animations rtl_columns av-curtain-numeric arial-websave arial avia-responsive-images-support" itemscope="itemscope" itemtype="https://schema.org/WebPage" ><div id='wrap_all'><header id='header' class='all_colors header_color light_bg_color av_header_top av_logo_left av_main_nav_header av_menu_right av_custom av_header_sticky av_header_shrinking_disabled av_header_stretch_disabled av_mobile_menu_phone av_header_searchicon av_header_unstick_top_disabled av_bottom_nav_disabled av_header_border_disabled' aria-label="Header" data-av_shrink_factor='50' role="banner" itemscope="itemscope" itemtype="https://schema.org/WPHeader" ><div id='header_main' class='container_wrap container_wrap_logo'><div class='container av-logo-container'><div class='inner-container'><span class='logo avia-standard-logo'><a href='https://www.physicsforums.com/insights/' class='' aria-label='Physics_Forums_Insights_logo' title='Physics_Forums_Insights_logo'><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIzMDAiIGhlaWdodD0iMTAwIiB2aWV3Qm94PSIwIDAgMzAwIDEwMCI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png" height="100" width="300" alt='Physics Forums Insights' title='Physics_Forums_Insights_logo' /><noscript><img src="https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png" height="100" width="300" alt='Physics Forums Insights' title='Physics_Forums_Insights_logo' /></noscript></a></span><nav class='main_menu' data-selectname='Select a page' role="navigation" itemscope="itemscope" itemtype="https://schema.org/SiteNavigationElement" ><div class="avia-menu av-main-nav-wrap"><ul role="menu" class="menu av-main-nav" id="avia-menu"><li role="menuitem" id="menu-item-27276" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-top-level menu-item-top-level-1"><a href="https://www.physicsforums.com/insights/trending-physics-articles/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Physics</span><span class="avia-menu-fx"><span class="avia-arrow-wrap"><span class="avia-arrow"></span></span></span></a><ul class="sub-menu"><li role="menuitem" id="menu-item-26559" class="menu-item menu-item-type-taxonomy menu-item-object-category"><a href="https://www.physicsforums.com/insights/science-math-articles/physics-articles/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Physics Articles</span></a></li><li role="menuitem" id="menu-item-26568" class="menu-item menu-item-type-taxonomy menu-item-object-category"><a href="https://www.physicsforums.com/insights/science-math-tutorials/physics-tutorials/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Physics Tutorials</span></a></li><li role="menuitem" id="menu-item-26564" class="menu-item menu-item-type-taxonomy menu-item-object-category"><a href="https://www.physicsforums.com/insights/science-math-guides/physics-guides/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Physics Guides</span></a></li><li role="menuitem" id="menu-item-26561" class="menu-item menu-item-type-taxonomy menu-item-object-category"><a href="https://www.physicsforums.com/insights/science-math-faqs/physics-faqs/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Physics FAQs</span></a></li></ul></li><li role="menuitem" id="menu-item-27288" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-top-level menu-item-top-level-2"><a href="https://www.physicsforums.com/insights/trending-math-articles/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Math</span><span class="avia-menu-fx"><span class="avia-arrow-wrap"><span class="avia-arrow"></span></span></span></a><ul class="sub-menu"><li role="menuitem" id="menu-item-26558" class="menu-item menu-item-type-taxonomy menu-item-object-category"><a href="https://www.physicsforums.com/insights/science-math-articles/math-articles/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Math Articles</span></a></li><li role="menuitem" id="menu-item-26567" class="menu-item menu-item-type-taxonomy menu-item-object-category"><a href="https://www.physicsforums.com/insights/science-math-tutorials/math-tutorials/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Math Tutorials</span></a></li><li role="menuitem" id="menu-item-26563" class="menu-item menu-item-type-taxonomy menu-item-object-category"><a href="https://www.physicsforums.com/insights/science-math-guides/math-guides/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Math Guides</span></a></li><li role="menuitem" id="menu-item-26560" class="menu-item menu-item-type-taxonomy menu-item-object-category"><a href="https://www.physicsforums.com/insights/science-math-faqs/math-faqs/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Math FAQs</span></a></li></ul></li><li role="menuitem" id="menu-item-27287" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-top-level menu-item-top-level-3"><a href="https://www.physicsforums.com/insights/trending-bio-chem-tech-articles/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Bio/Chem/Tech</span><span class="avia-menu-fx"><span class="avia-arrow-wrap"><span class="avia-arrow"></span></span></span></a><ul class="sub-menu"><li role="menuitem" id="menu-item-26556" class="menu-item menu-item-type-taxonomy menu-item-object-category"><a href="https://www.physicsforums.com/insights/science-math-articles/biology-chemistry-articles/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Bio/Chem Articles</span></a></li><li role="menuitem" id="menu-item-26566" class="menu-item menu-item-type-taxonomy menu-item-object-category"><a href="https://www.physicsforums.com/insights/science-math-tutorials/computer-science-tutorials/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Computer Science Tutorials</span></a></li><li role="menuitem" id="menu-item-26565" class="menu-item menu-item-type-taxonomy menu-item-object-category"><a href="https://www.physicsforums.com/insights/science-math-guides/technology-guides/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Technology Guides</span></a></li></ul></li><li role="menuitem" id="menu-item-27286" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-top-level menu-item-top-level-4"><a href="https://www.physicsforums.com/insights/trending-education-articles/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Education</span><span class="avia-menu-fx"><span class="avia-arrow-wrap"><span class="avia-arrow"></span></span></span></a><ul class="sub-menu"><li role="menuitem" id="menu-item-26557" class="menu-item menu-item-type-taxonomy menu-item-object-category"><a href="https://www.physicsforums.com/insights/science-math-articles/education-articles/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Education Articles</span></a></li><li role="menuitem" id="menu-item-26562" class="menu-item menu-item-type-taxonomy menu-item-object-category"><a href="https://www.physicsforums.com/insights/science-math-guides/education-guides/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Education Guides</span></a></li></ul></li><li role="menuitem" id="menu-item-26569" class="menu-item menu-item-type-taxonomy menu-item-object-category menu-item-top-level menu-item-top-level-5"><a href="https://www.physicsforums.com/insights/scientist-interviews/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Interviews</span><span class="avia-menu-fx"><span class="avia-arrow-wrap"><span class="avia-arrow"></span></span></span></a></li><li role="menuitem" id="menu-item-26570" class="menu-item menu-item-type-taxonomy menu-item-object-category menu-item-top-level menu-item-top-level-6"><a href="https://www.physicsforums.com/insights/science-math-quizzes/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Quizzes</span><span class="avia-menu-fx"><span class="avia-arrow-wrap"><span class="avia-arrow"></span></span></span></a></li><li role="menuitem" id="menu-item-26571" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-top-level menu-item-top-level-7"><a href="https://www.physicsforums.com/" itemprop="url" tabindex="0"><span class="avia-bullet"></span><span class="avia-menu-text">Forums</span><span class="avia-menu-fx"><span class="avia-arrow-wrap"><span class="avia-arrow"></span></span></span></a></li><li id="menu-item-search" class="noMobile menu-item menu-item-search-dropdown menu-item-avia-special" role="menuitem"><a aria-label="Search" href="?s=" rel="nofollow" data-avia-search-tooltip=" <search> <form role="search" action="https://www.physicsforums.com/insights/" id="searchform" method="get" class=""> <div> <input type="submit" value="" id="searchsubmit" class="button avia-font-entypo-fontello" title="Enter at least 3 characters to show search results in a dropdown or click to route to search result page to show all results" /> <input type="search" id="s" name="s" value="" aria-label='Search' placeholder='Search' required /> </div> </form> </search> " aria-hidden='false' data-av_icon='' data-av_iconfont='entypo-fontello'><span class="avia_hidden_link_text">Search</span></a></li><li class="av-burger-menu-main menu-item-avia-special " role="menuitem"> <a href="#" aria-label="Menu" aria-hidden="false"> <span class="av-hamburger av-hamburger--spin av-js-hamburger"> <span class="av-hamburger-box"> <span class="av-hamburger-inner"></span> <strong>Menu</strong> </span> </span> <span class="avia_hidden_link_text">Menu</span> </a></li></ul></div></nav></div></div></div><div class="header_bg"></div></header><div id='main' class='all_colors' data-scroll-offset='70'><div class='container_wrap container_wrap_first main_color sidebar_right'><div class='container'><main class='template-page content av-content-small alpha units av-main-page' role="main" itemprop="mainContentOfPage" ><article class='post-entry post-entry-type-page post-entry-21404' itemscope="itemscope" itemtype="https://schema.org/CreativeWork" ><div class="entry-content-wrapper clearfix"><header class="entry-content-header" aria-label="Page Content for: About Physics Forums"></header><div class="entry-content" itemprop="text" ><p><script type="application/ld+json">{ "@context" : "http://schema.org", "@type" : "Organization", "name" : "Physics Forums", "url" : "https://www.physicsforums.com", "logo" : "https://www.physicsforums.com/misc/apple-touch-icon.png", "sameAs" : [ "https://www.facebook.com/physicsforums", "https://www.youtube.com/@physicsforum", "https://twitter.com/physicsforums", "https://www.linkedin.com/company/physics-forums", "https://plus.google.com/+physicsforum", "https://www.pinterest.com/physicsforums", "https://www.youtube.com/@physicsforum"] }</script></p><h1><span class="ez-toc-section" id="About-Physics-Forums"></span>About Physics Forums<span class="ez-toc-section-end"></span></h1><div id="ez-toc-container" class="ez-toc-v2_0_69_1 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction"><p class="ez-toc-title" style="cursor:inherit">Table of Contents</p> <label for="ez-toc-cssicon-toggle-item-67436b787e6bc" class="ez-toc-cssicon-toggle-label"><span class="ez-toc-cssicon"><span class="eztoc-hide" style="display:none;">Toggle</span><span class="ez-toc-icon-toggle-span"><svg style="fill: #4c4c4c;color:#4c4c4c" xmlns="http://www.w3.org/2000/svg" class="list-377408" width="20px" height="20px" viewBox="0 0 24 24" fill="none"><path d="M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z" fill="currentColor"></path></svg><svg style="fill: #4c4c4c;color:#4c4c4c" class="arrow-unsorted-368013" xmlns="http://www.w3.org/2000/svg" width="10px" height="10px" viewBox="0 0 24 24" version="1.2" baseProfile="tiny"><path d="M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z"/></svg></span></span></label><input type="checkbox" id="ez-toc-cssicon-toggle-item-67436b787e6bc" aria-label="Toggle" /><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class="ez-toc-link ez-toc-heading-1" href="#About-Physics-Forums" title="About Physics Forums">About Physics Forums</a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class="ez-toc-link ez-toc-heading-2" href="#Values-and-Mission" title="Values and Mission">Values and Mission</a></li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class="ez-toc-link ez-toc-heading-3" href="#Summary" title="Summary">Summary</a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-4" href="#Boardroom-Stats" title="Boardroom Stats:">Boardroom Stats:</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-5" href="#Community-Stats" title="Community Stats:">Community Stats:</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-6" href="#Follow-Us-On" title="Follow Us On:">Follow Us On:</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-7" href="#Common-Support-Pages" title="Common Support Pages:">Common Support Pages:</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-8" href="#Support-Email" title="Support Email:">Support Email:</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-9" href="#Demographics" title="Demographics:">Demographics:</a></li></ul></li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class="ez-toc-link ez-toc-heading-10" href="#FAQ" title="FAQ">FAQ</a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-11" href="#What-is-Physics-Forums" title="What is Physics Forums?">What is Physics Forums?</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-12" href="#Is-Physics-Forums-free-to-use" title="Is Physics Forums free to use?">Is Physics Forums free to use?</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-13" href="#How-can-I-join-Physics-Forums" title="How can I join Physics Forums?">How can I join Physics Forums?</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-14" href="#Can-I-ask-questions-on-Physics-Forums" title="Can I ask questions on Physics Forums?">Can I ask questions on Physics Forums?</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-15" href="#Are-there-experts-or-professionals-on-the-forum" title="Are there experts or professionals on the forum?">Are there experts or professionals on the forum?</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-16" href="#How-do-I-search-for-existing-discussions-or-topics" title="How do I search for existing discussions or topics?">How do I search for existing discussions or topics?</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-17" href="#Can-I-contribute-to-ongoing-discussions" title="Can I contribute to ongoing discussions?">Can I contribute to ongoing discussions?</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-18" href="#Are-there-rules-and-guidelines-for-posting-on-Physics-Forums" title="Are there rules and guidelines for posting on Physics Forums?">Are there rules and guidelines for posting on Physics Forums?</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-19" href="#How-do-I-report-inappropriate-content-or-behavior" title="How do I report inappropriate content or behavior?">How do I report inappropriate content or behavior?</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-20" href="#Can-I-share-my-own-research-or-projects-on-Physics-Forums" title="Can I share my own research or projects on Physics Forums?">Can I share my own research or projects on Physics Forums?</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-21" href="#Is-Physics-Forums-only-for-professionals-or-academics" title="Is Physics Forums only for professionals or academics?">Is Physics Forums only for professionals or academics?</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-22" href="#How-can-I-contact-the-administrators-or-moderators" title="How can I contact the administrators or moderators?">How can I contact the administrators or moderators?</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-23" href="#Is-Physics-Forums-associated-with-any-educational-institution-or-organization" title="Is Physics Forums associated with any educational institution or organization?">Is Physics Forums associated with any educational institution or organization?</a></li></ul></li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class="ez-toc-link ez-toc-heading-24" href="#History-of-Physics-Forums" title="History of Physics Forums">History of Physics Forums</a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-25" href="#The-Beginning-Spring-2001" title="The Beginning (Spring 2001)">The Beginning (Spring 2001)</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-26" href="#Early-Years-2001-2003" title="Early Years (2001-2003)">Early Years (2001-2003)</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-27" href="#The-Middle-Ages-2003-2005" title="The Middle Ages (2003-2005)">The Middle Ages (2003-2005)</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-28" href="#The-%E2%80%9CGolden%E2%80%9D-Years-2005-Present" title="The “Golden” Years (2005-Present)">The “Golden” Years (2005-Present)</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-29" href="#Reform-2006-2014" title="Reform (2006-2014)">Reform (2006-2014)</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-30" href="#Modernization-2014-2016" title="Modernization (2014-2016)">Modernization (2014-2016)</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-31" href="#Refinement-2016-2018" title="Refinement (2016-2018)">Refinement (2016-2018)</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-32" href="#Refinement-2019" title="Refinement (2019+)">Refinement (2019+)</a></li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-33" href="#MHB-Merger-2022" title="MHB Merger (2022)">MHB Merger (2022)</a></li></ul></li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class="ez-toc-link ez-toc-heading-34" href="#List-of-mentors" title="List of mentors">List of mentors</a></li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class="ez-toc-link ez-toc-heading-35" href="#Testimonials" title="Testimonials">Testimonials</a></li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class="ez-toc-link ez-toc-heading-36" href="#Visual-History" title="Visual History">Visual History</a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class="ez-toc-link ez-toc-heading-37" href="#More-Related-Articles" title="More Related Articles">More Related Articles</a></li></ul></li></ul></li></ul></nav></div><h2><span class="ez-toc-section" id="Values-and-Mission"></span>Values and Mission<span class="ez-toc-section-end"></span></h2><p>Our goal is to provide a community for people (whether students, professional scientists, or hobbyists) to learn and discuss science as it is currently generally understood and practiced by the professional scientific community. As our name suggests, our main focus is on physics, but we also have forums for most other academic areas including engineering, chemistry, biology, social sciences, etc. Physics and math homework help is available for students.</p><p><b>PF values quality</b><br /> • Topics based on science published in real scientific journals or textbooks<br /> • Proper English grammar and correct spelling</p><p><b>PF values civility</b><br /> • Positive and compassionate attitudes<br /> • Patience and diplomacy while debating</p><p><b>PF values productivity</b><br /> • Disciplined to remain on-topic<br /> • Honest recognition of own weaknesses<br /> • Solo and cooperative problem-solving</p><h2><span class="ez-toc-section" id="Summary"></span>Summary<span class="ez-toc-section-end"></span></h2><p>Owner <a href="https://gregbernhardt.com/" target="_blank">Greg Bernhardt</a> started Physics Forums as a high school extra credit project for a physics class in 2001. Since then with the help of dozens of staff and hundreds of advisors, it has developed to become the #1 community for high-quality science and math discussion. <a href="https://www.physicsforums.com/insights/about-pf-insights/">Find information on our Insights Blog</a>.</p><h3><span class="ez-toc-section" id="Boardroom-Stats"></span>Boardroom Stats:<span class="ez-toc-section-end"></span></h3><p>Founder/Owner: Greg Bernhardt (<a href="https://twitter.com/GregBernhardt4" target="_blank">Twitter</a>, <a href="https://www.linkedin.com/in/gregbernhardt/" target="_blank">LinkedIn</a>, <a href="https://importsem.com/about-greg-bernhardt/" target="_blank">ImportSEM</a>)<br /> Founded: 2001<br /> Location: Milwaukee, Wisconsin<br /> Revenue: Adsense, Gold Memberships<br /> Software: Customized Xenforo</p><p><script type="application/ld+json">{ "@context": "http://schema.org/", "@type": "Person", "name": "Greg Bernhardt", "url": "", "image": "https://physicsforums-bernhardtmediall.netdna-ssl.com/data/avatars/l/0/1.jpg?1534652475", "sameAs": [ "https://www.facebook.com/ballerbernhardt", "https://twitter.com/GregBernhardt4", "https://www.linkedin.com/in/gregbernhardt/" ], "jobTitle": "Founder", "worksFor": { "@type": "Organization", "name": "Physics Forums" } }</script></p><h3><span class="ez-toc-section" id="Community-Stats"></span>Community Stats:<span class="ez-toc-section-end"></span></h3><ul><li>200,000 members</li><li>6.5M posts</li><li>20 Staff Members</li><li>265 Science and Education Advisors</li><li>142 Homework Helpers</li><li>700 Blog Insights Articles</li><li>68 Insights Authors</li></ul><h3><span class="ez-toc-section" id="Follow-Us-On"></span><strong>Follow Us On:</strong><span class="ez-toc-section-end"></span></h3><p><a href="https://www.facebook.com/physicsforums/" rel="nofollow" target="_blank">Facebook</a> | <a href="https://twitter.com/physicsforums" rel="nofollow" target="_blank">Twitter</a> | <a href="https://www.linkedin.com/company/physics-forums/" rel="nofollow" target="_blank">LinkedIn</a> | <a href="https://en.wikipedia.org/wiki/Physics_Forums" target="_blank">Wiki</a></p><h3><span class="ez-toc-section" id="Common-Support-Pages"></span>Common Support Pages:<span class="ez-toc-section-end"></span></h3><p><a href="https://www.physicsforums.com/insights/about-physics-forums/">About Us</a> | <a href="https://www.physicsforums.com/help/terms-of-service/">Terms and Rules</a> | <a href="https://www.physicsforums.com/help/member-privacy-policy/">Privacy Policy</a> | <a href="https://www.physicsforums.com/help/">Help Pages</a></p><h3><span class="ez-toc-section" id="Support-Email"></span>Support Email:<span class="ez-toc-section-end"></span></h3><p><a href="mailto:admin@physicsforums.com">admin@physicsforums.com</a></p><h3><span class="ez-toc-section" id="Demographics"></span><strong>Demographics:</strong><span class="ez-toc-section-end"></span></h3><p>PF averages 100,000+ visitors, 50+ new members, and 500+ posts per day.<br /> 80% search engines, 10% referral sites, 10% direct traffic<br /> 80% of our visitors are from North America. 10% Europe, 5% Asia and 5% other.<br /> 65% use Chrome. 20% use Firefox. 10% IE, 5% Opera/Safari<br /> 90% on high-speed internet, 10% dialup<br /> 85% on Windows, 10% Mac, 5% Linux<br /> 55% on Desktop and 45% on Mobile</p><h2><span class="ez-toc-section" id="FAQ"></span>FAQ<span class="ez-toc-section-end"></span></h2><h3><span class="ez-toc-section" id="What-is-Physics-Forums"></span><strong>What is Physics Forums?</strong><span class="ez-toc-section-end"></span></h3><p>Physicsforums.com is an online platform dedicated to physics enthusiasts and learners. It serves as a community where individuals can discuss, ask questions, and share knowledge related to physics and related topics.</p><h3><span class="ez-toc-section" id="Is-Physics-Forums-free-to-use"></span><strong>Is Physics Forums free to use?</strong><span class="ez-toc-section-end"></span></h3><p>Yes, Physicsforums.com is completely free to use. You can register an account and participate in discussions without any cost.</p><h3><span class="ez-toc-section" id="How-can-I-join-Physics-Forums"></span><strong>How can I join Physics Forums?</strong><span class="ez-toc-section-end"></span></h3><p>To join Physicsforums.com, simply visit the website and click on the “Register” or “Sign Up” button. You’ll need to provide some basic information and create a username and password to get started.</p><h3><span class="ez-toc-section" id="Can-I-ask-questions-on-Physics-Forums"></span><strong>Can I ask questions on Physics Forums?</strong><span class="ez-toc-section-end"></span></h3><p>Yes, you can ask questions related to physics or related fields. There are specific sub-forums for different topics within physics where you can post your questions.</p><h3><span class="ez-toc-section" id="Are-there-experts-or-professionals-on-the-forum"></span><strong>Are there experts or professionals on the forum?</strong><span class="ez-toc-section-end"></span></h3><p>Yes, Physicsforums.com has a diverse user base, including experts, educators, and enthusiasts in the field of physics. You can benefit from their knowledge and expertise by engaging in discussions and asking questions.</p><h3><span class="ez-toc-section" id="How-do-I-search-for-existing-discussions-or-topics"></span><strong>How do I search for existing discussions or topics?</strong><span class="ez-toc-section-end"></span></h3><p>You can use the search bar located on the forum’s homepage to search for specific topics or keywords. This will help you find relevant discussions that have already taken place.</p><h3><span class="ez-toc-section" id="Can-I-contribute-to-ongoing-discussions"></span><strong>Can I contribute to ongoing discussions?</strong><span class="ez-toc-section-end"></span></h3><p>Absolutely! You can participate in existing discussions by posting replies or comments. Just make sure your contribution is relevant to the topic and follows the forum’s guidelines.</p><h3><span class="ez-toc-section" id="Are-there-rules-and-guidelines-for-posting-on-Physics-Forums"></span><strong>Are there rules and guidelines for posting on Physics Forums?</strong><span class="ez-toc-section-end"></span></h3><p>Yes, Physicsforums.com has rules and guidelines in place to maintain a respectful and informative community. Be sure to review these guidelines before posting to ensure your contributions align with the forum’s standards.</p><h3><span class="ez-toc-section" id="How-do-I-report-inappropriate-content-or-behavior"></span><strong>How do I report inappropriate content or behavior?</strong><span class="ez-toc-section-end"></span></h3><p>If you come across any inappropriate content or behavior on the forum, you can use the “Report” feature to notify the forum moderators. They will review the report and take appropriate action if necessary.</p><h3><span class="ez-toc-section" id="Can-I-share-my-own-research-or-projects-on-Physics-Forums"></span><strong>Can I share my own research or projects on Physics Forums?</strong><span class="ez-toc-section-end"></span></h3><p>Yes, you can share your research or projects related to physics, as long as they adhere to the forum’s guidelines. Sharing your work can lead to valuable feedback and discussions within the community.</p><h3><span class="ez-toc-section" id="Is-Physics-Forums-only-for-professionals-or-academics"></span><strong>Is Physics Forums only for professionals or academics?</strong><span class="ez-toc-section-end"></span></h3><p>No, Physicsforums.com is open to everyone, regardless of their level of expertise. Whether you’re a student, educator, enthusiast, or professional, you’re welcome to join and participate in discussions.</p><h3><span class="ez-toc-section" id="How-can-I-contact-the-administrators-or-moderators"></span><strong>How can I contact the administrators or moderators?</strong><span class="ez-toc-section-end"></span></h3><p>You can usually find a “Contact Us” or “Moderator” link on the forum where you can reach out to the administrators or moderators if you have specific questions or concerns not addressed in the FAQ or guidelines.</p><h3><span class="ez-toc-section" id="Is-Physics-Forums-associated-with-any-educational-institution-or-organization"></span><strong> Is Physics Forums associated with any educational institution or organization?</strong><span class="ez-toc-section-end"></span></h3><p>Physicsforums.com is an independent online community and is not directly affiliated with any specific educational institution or organization. It is a platform created for physics enthusiasts, students, educators, and professionals to share knowledge.</p><h2><span class="ez-toc-section" id="History-of-Physics-Forums"></span>History of Physics Forums<span class="ez-toc-section-end"></span></h2><div class="bbCodeBlock bbCodeQuote"><aside><blockquote class="quoteContainer"><div class="quote">PF is a beautiful example of people coming together to create something with the purpose to help, to learn, and to create a sense of community among people that share a love of science and not for monetary gain. – Evo</div></blockquote></aside></div><h3><span class="ez-toc-section" id="The-Beginning-Spring-2001"></span>The Beginning (Spring 2001)<span class="ez-toc-section-end"></span></h3><p>It comes to many people’s surprise to find I am actually not very good at math and physics. PF started in the spring of 2001. I was taking Physics II in high school my senior year. The semester was ending and I found myself getting a “D” in the class. I badly needed at least a “C” to minimize the impact on my overall GPA.</p><p>Through the year I gained mass interest in the Internet, web designing, and community building. My interest in physics was also sparked by popular physics books by Michio Kaku, Brian Greene, Stephen Hawking, and Paul Davies.</p><p>So I thought of proposing the idea of creating a useful physics community on the web as an extra credit project to my physics teacher. The teacher bought it and away I went. In the end, it took me just a month to get enough done and promote it for the thing to look halfway decent. I found a “C” on my report card end of the semester <img data-lazyloaded="1" src="data:image/gif;base64,R0lGODdhAQABAPAAAMPDwwAAACwAAAAAAQABAAACAkQBADs=" decoding="async" class="mceSmilieSprite mceSmilie1" title="Smile :)" data-src="https://www.physicsforums.com/styles/default/xenforo/clear.png" alt=":)" /><noscript><img decoding="async" class="mceSmilieSprite mceSmilie1" title="Smile :)" src="https://www.physicsforums.com/styles/default/xenforo/clear.png" alt=":)" /></noscript></p><h3><span class="ez-toc-section" id="Early-Years-2001-2003"></span>Early Years (2001-2003)<span class="ez-toc-section-end"></span></h3><p>PF started out on the ASP-driven software of Snitz. I believe we also started on the web host “DreamHost”. Unfortunately, two years later in 2003, we grew too big and too fast. We ended up having to ditch the software and the host. This resulted in starting completely from scratch. The database had about 200,000 posts in it. It still hurts to lose all that data to this day. But it has proven to be a turning point marker for PF’s history. We moved to a dedicated server and professional software to last us for many years. During this time I also admit to hiring some non-qualified staff members. Once we got Integral, Tom Mattson, and Chroot, things started to change.</p><h3><span class="ez-toc-section" id="The-Middle-Ages-2003-2005"></span>The Middle Ages (2003-2005)<span class="ez-toc-section-end"></span></h3><p>Before the “beginning from scratch”, PF was becoming quite popular, but our forum management and organization were severely lacking. Over the next couple of years, PF would prove itself a giant in the science web community. Early 2004 we even hosted Michio Kaku’s official forums.</p><p>In these years PF would:<br /> 1. Develop an organized forum structure<br /> 2. Start creating a strict but fair policy<br /> 3. Hire competent staff with similar visions<br /> 4. Start member award days<br /> 5. Install LaTeX for equations<br /> 6. Start the Homework Helper and Science Advisor programs</p><h3><span class="ez-toc-section" id="The-%E2%80%9CGolden%E2%80%9D-Years-2005-Present"></span>The “Golden” Years (2005-Present)<span class="ez-toc-section-end"></span></h3><p>Physics Forums is now finally working like a well-oiled high-performance machine. The standard has been set. We’re pretty much coasting now that we have a complete system in place that has proven to be successful. Crackpots and spam are almost non-existent. Along with what seemed like a new design a year ago, we found one that works and will stick with it for a long time now.</p><p>A few highlights of these past couple of years include:<br /> 1. Partnership with Scientific American<br /> 2. Partnership with Ph.D. Comics<br /> 3. PF Library</p><h3><span class="ez-toc-section" id="Reform-2006-2014"></span>Reform (2006-2014)<span class="ez-toc-section-end"></span></h3><p>Over the next 8 years, Physics Forums would solidify themselves as the dominant resource and destination for science discussion. In 2010 PF won the physics.org Best FAQ Site Popular Vote award. PF would continue to refine its policies to encourage a healthy and productive environment. Features like chat were added to provide a respite from forum life. Partnerships with educator.com and phys.org would be established. PF would go through three style changes. Each is a little more modern, clean, and readable. In 2007 dear member selfAdjoint passed away.</p><p>In 2010 Physics Forums won the “People’s Choice” award for best online physics community by <a href="https://www.iop.org/explore-physics" target="_blank">physics.org</a>. Results <a href="https://boingboing.net/2010/11/15/the-best-physics-web.html" target="_blank">here</a>.</p><h3><span class="ez-toc-section" id="Modernization-2014-2016"></span>Modernization (2014-2016)<span class="ez-toc-section-end"></span></h3><p>The decision to move from vBulletin to Xenforo was made. A new style and new features gave us the jump into the modern web. Physics Forums Insights was opened. PF Insights is a science and math variety blog written by experts in our community. More on this era in a bit. Our dear members marcus and arildno passed away in 2016.</p><h3><span class="ez-toc-section" id="Refinement-2016-2018"></span>Refinement (2016-2018)<span class="ez-toc-section-end"></span></h3><p><strong><br /> </strong>Much of this time was spent refining our mission, policies, and style. Many changes were made from suggestions and concerns from several member surveys. PF pushes for higher and higher quality each year while remaining friendly and welcoming. A curated video section was added and links to now over 1000 math and science videos. Big things are planned for winter 2018…</p><h3><span class="ez-toc-section" id="Refinement-2019"></span>Refinement (2019+)<span class="ez-toc-section-end"></span></h3><p><strong><br /> </strong>PF5 was released in March 2019 and brought a polished style and a host of new community features like expanded reactions, push notifications, and an enhanced editor. The PF mobile app was also ended. More dear members have passed away, such as turbo and jimhardy.</p><h3><span class="ez-toc-section" id="MHB-Merger-2022"></span>MHB Merger (2022)<span class="ez-toc-section-end"></span></h3><p><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2NDAiIGhlaWdodD0iMTU5IiB2aWV3Qm94PSIwIDAgNjQwIDE1OSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" decoding="async" class="alignnone size-full wp-image-41876" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2022/08/mathhelpboard.png" alt="math help board logo" width="640" height="159" data-srcset="https://www.physicsforums.com/insights/wp-content/uploads/2022/08/mathhelpboard.png 640w, https://www.physicsforums.com/insights/wp-content/uploads/2022/08/mathhelpboard-768x191.png 768w, https://www.physicsforums.com/insights/wp-content/uploads/2022/08/mathhelpboard-705x175.png 705w" data-sizes="(max-width: 640px) 100vw, 640px" /><noscript><img decoding="async" class="alignnone size-full wp-image-41876" src="https://www.physicsforums.com/insights/wp-content/uploads/2022/08/mathhelpboard.png" alt="math help board logo" width="640" height="159" srcset="https://www.physicsforums.com/insights/wp-content/uploads/2022/08/mathhelpboard.png 640w, https://www.physicsforums.com/insights/wp-content/uploads/2022/08/mathhelpboard-768x191.png 768w, https://www.physicsforums.com/insights/wp-content/uploads/2022/08/mathhelpboard-705x175.png 705w" sizes="(max-width: 640px) 100vw, 640px" /></noscript></p><p>August of 2022 saw the merger of Mathhelpboards.com founded and managed by <a href="https://www.physicsforums.com/members/jameson1.703381/">Jameson</a>. Threads and members were merged into Physics Forums with the prefix MHB and members are given a special badge. MHB was a wonderful math community with a dedicated member base. They had innovative features like Desmos and TikZ integration.</p><h2><span class="ez-toc-section" id="List-of-mentors"></span><b>List of mentors</b><span class="ez-toc-section-end"></span></h2><p>Let’s use this section to list Mentors. Oldest to Newest. (Bold means they are still on staff)</p><p>1. Monique (Niqqie,theOwl)<br /> 2. JordanW<br /> 3. Silverquest<br /> 4. Phobos<br /> 5. Grady<br /> 6. dav2008<br /> 7. MacCoder<br /> 8. joaoninhio<br /> 9. Beatle42<br /> 10. SCOTT2004<br /> 11. Sting1983 (Sting)<br /> 12. Stephen<br /> 13. Integral<br /> 14. Zero<br /> 15. Kerrie (skorpiano)<br /> 16. BryanGmyrek<br /> 15. Tom Mattson (Tom)<br /> 16. Janus<br /> 17. ahrkron<br /> 18. damgo (alis)<br /> 19. selfAdjoint<br /> 20. chroot<br /> 21. Hurkyl<br /> 22. <b>Russ Watters</b><br /> 23. Engima<br /> 24. Another God<br /> 25. HallsofIvy<br /> 26. Ivan Seeking<br /> 27. dduardo<br /> 28. <b>Doc Al</b><br /> 29. Iansmith<br /> 30. hypnagogue<br /> 31. <b>Evo</b><br /> 32. Gokul43201<br /> 33. ZapperZ<br /> 34. loseyourname<br /> 35. Moonbear<br /> 36. SpaceTiger<br /> 37. <b>Berkeman</b><br /> 38. <b>jtbell</b><br /> 39. vanesch<br /> 40. Pervect<br /> 41. Math is Hard<br /> 42. Astronuc<br /> 43. cristo<br /> 44. George Jones<br /> 45. Hootenanny<br /> 46. Kurdt<br /> 47. Redbelly98<br /> 48. Vanadium_50<br /> 49. D H<br /> 50. <b>Borek</b><br /> 51. bcrowell<br /> 52. <b>Mark44</b><br /> 53. Ryan_m_b<br /> 54. micromass<br /> 55. vela<br /> 56. lisab<br /> 57. cepheid<br /> 58. <b>Dale</b><br /> 59. Fredrik<br /> 60. SammyS<br /> 61. <b>mfb</b><br /> 62. Office_Shredder<br /> 63. <b>gneill</b><br /> 64. SteamKing<br /> 65. Drakkith<br /> 66. <b>Chestermiller</b><br /> 67. <b>Nugatory</b><br /> 68. <b>PeterDonis</b><br /> 69. <b>Orodruin</b><br /> 70. NascentOxygen<br /> 71. <b>jedishrfu</b><br /> 72. <b>DrClaude</b><br /> 73. <b>Stevedaryl<br /> </b>74.<b> jim mcnamara<br /> </b>75. <b>bhobba<br /> </b>76. <b>anorlunda</b></p><h2><span class="ez-toc-section" id="Testimonials"></span>Testimonials<span class="ez-toc-section-end"></span></h2><blockquote><div class="bbCodeBlock-content"><div class="bbCodeBlock-expandContent ">“This is probably my favorite website on the web. To be able to engage world class physicists and interact with interested people on an international scale is invaluable. I believe this is the best use of the internet, to disseminate knowledge in a cooperative, voluntary way. The administrators are some of the best people I have interacted with online and they do an excellent job running the site. Highly recommended. All contributions are appreciated and help to create a rich environment of learning.”</div></div></blockquote><div><div class="bbWrapper"><blockquote class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote"><div class="bbCodeBlock-content"><div class="bbCodeBlock-expandContent ">“The most helpful forum site. The guys, the editors, administrators and all those people who handle the site + the members of the forum is very helpful when I bring one of my doubts on a subject or lesson to them. They help me a lot. Awesome I’d like to say the most awesome STEM community is the Physics forums community. I love browsing in the site, looking for tutorials and tips. I love everything about it. If not for the guys in it, I would have lost a hell of a lot of marks for the previous tests I took. I learn many things from this site. Long live PF community.”</div></div></blockquote></div><blockquote><div>“I just wanted to say a big thanks to the members of Physics Forums for their help and support especially while I was doing my physics degree and for help with some of the other strange (and dumb) questions I’ve asked whilst on my PhD!”</div></blockquote><div><div class="bbWrapper"><blockquote class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote"><div class="bbCodeBlock-content"><div class="bbCodeBlock-expandContent ">“One of the best scientific forums ever! It helped me a lot, and still, through my education and with my research.”</div></div></blockquote></div></div></div><div><div class="bbWrapper"><blockquote class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote"><div class="bbCodeBlock-content"><div class="bbCodeBlock-expandContent ">“Well the other day I just realized what valuable and integral part of my life and daily activities the forum has become and it made no sense for me not to support you and the others for what you contribute and for all of the things you do to keep the forum running smoothly.”</div></div></blockquote><h2><span class="ez-toc-section" id="Visual-History"></span>Visual History<span class="ez-toc-section-end"></span></h2><p><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2NDAiIGhlaWdodD0iNDUxIiB2aWV3Qm94PSIwIDAgNjQwIDQ1MSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" decoding="async" class="alignnone wp-image-26982 size-full" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2002.png" alt="Physics Forums Homepage in 2001" width="640" height="451" data-srcset="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2002.png 640w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2002-450x317.png 450w" data-sizes="(max-width: 640px) 100vw, 640px" /><noscript><img decoding="async" class="alignnone wp-image-26982 size-full" src="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2002.png" alt="Physics Forums Homepage in 2001" width="640" height="451" srcset="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2002.png 640w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2002-450x317.png 450w" sizes="(max-width: 640px) 100vw, 640px" /></noscript> <img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2MTkiIGhlaWdodD0iNDgwIiB2aWV3Qm94PSIwIDAgNjE5IDQ4MCI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" decoding="async" class="alignnone wp-image-26983 size-full" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2004.png" alt="Physics Forums Homepage in 2003" width="619" height="480" data-srcset="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2004.png 619w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2004-450x349.png 450w" data-sizes="(max-width: 619px) 100vw, 619px" /><noscript><img decoding="async" class="alignnone wp-image-26983 size-full" src="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2004.png" alt="Physics Forums Homepage in 2003" width="619" height="480" srcset="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2004.png 619w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2004-450x349.png 450w" sizes="(max-width: 619px) 100vw, 619px" /></noscript></p><p><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2NDAiIGhlaWdodD0iNDUwIiB2aWV3Qm94PSIwIDAgNjQwIDQ1MCI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" decoding="async" class="alignnone wp-image-26984 size-full" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2006.png" alt="Physics Forums Homepage in 2005" width="640" height="450" data-srcset="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2006.png 640w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2006-450x316.png 450w" data-sizes="(max-width: 640px) 100vw, 640px" /><noscript><img decoding="async" class="alignnone wp-image-26984 size-full" src="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2006.png" alt="Physics Forums Homepage in 2005" width="640" height="450" srcset="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2006.png 640w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2006-450x316.png 450w" sizes="(max-width: 640px) 100vw, 640px" /></noscript> <img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2NDAiIGhlaWdodD0iNDU3IiB2aWV3Qm94PSIwIDAgNjQwIDQ1NyI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" decoding="async" class="alignnone wp-image-26985 size-full" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2008.png" alt="Physics Forums Homepage in 2007" width="640" height="457" data-srcset="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2008.png 640w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2008-260x185.png 260w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2008-450x321.png 450w" data-sizes="(max-width: 640px) 100vw, 640px" /><noscript><img decoding="async" class="alignnone wp-image-26985 size-full" src="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2008.png" alt="Physics Forums Homepage in 2007" width="640" height="457" srcset="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2008.png 640w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2008-260x185.png 260w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2008-450x321.png 450w" sizes="(max-width: 640px) 100vw, 640px" /></noscript></p><p><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2NDAiIGhlaWdodD0iNDQ3IiB2aWV3Qm94PSIwIDAgNjQwIDQ0NyI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" decoding="async" class="alignnone wp-image-26986 size-full" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2013.png" alt="Physics Forums Homepage in 2009" width="640" height="447" data-srcset="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2013.png 640w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2013-450x314.png 450w" data-sizes="(max-width: 640px) 100vw, 640px" /><noscript><img decoding="async" class="alignnone wp-image-26986 size-full" src="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2013.png" alt="Physics Forums Homepage in 2009" width="640" height="447" srcset="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2013.png 640w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2013-450x314.png 450w" sizes="(max-width: 640px) 100vw, 640px" /></noscript> <img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2NDAiIGhlaWdodD0iNDUwIiB2aWV3Qm94PSIwIDAgNjQwIDQ1MCI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" decoding="async" class="alignnone wp-image-26987 size-full" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2014.png" alt="Physics Forums Homepage in 2012" width="640" height="450" data-srcset="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2014.png 640w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2014-450x316.png 450w" data-sizes="(max-width: 640px) 100vw, 640px" /><noscript><img decoding="async" class="alignnone wp-image-26987 size-full" src="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2014.png" alt="Physics Forums Homepage in 2012" width="640" height="450" srcset="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2014.png 640w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/PF_in_2014-450x316.png 450w" sizes="(max-width: 640px) 100vw, 640px" /></noscript></p><p><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2NDAiIGhlaWdodD0iNDY2IiB2aWV3Qm94PSIwIDAgNjQwIDQ2NiI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" decoding="async" class="alignnone wp-image-26979 size-full" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2018.png" alt="Physics Forums Homepage in 2018" width="640" height="466" data-srcset="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2018.png 640w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2018-768x559.png 768w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2018-1030x749.png 1030w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2018-705x513.png 705w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2018-450x327.png 450w" data-sizes="(max-width: 640px) 100vw, 640px" /><noscript><img decoding="async" class="alignnone wp-image-26979 size-full" src="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2018.png" alt="Physics Forums Homepage in 2018" width="640" height="466" srcset="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2018.png 640w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2018-768x559.png 768w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2018-1030x749.png 1030w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2018-705x513.png 705w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2018-450x327.png 450w" sizes="(max-width: 640px) 100vw, 640px" /></noscript> <img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2NDAiIGhlaWdodD0iNDY2IiB2aWV3Qm94PSIwIDAgNjQwIDQ2NiI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==" decoding="async" class="alignnone wp-image-26980 size-full" data-src="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2019.png" alt="Physics Forums Homepage in 2019" width="640" height="466" data-srcset="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2019.png 640w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2019-768x559.png 768w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2019-1030x749.png 1030w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2019-705x513.png 705w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2019-450x327.png 450w" data-sizes="(max-width: 640px) 100vw, 640px" /><noscript><img decoding="async" class="alignnone wp-image-26980 size-full" src="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2019.png" alt="Physics Forums Homepage in 2019" width="640" height="466" srcset="https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2019.png 640w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2019-768x559.png 768w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2019-1030x749.png 1030w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2019-705x513.png 705w, https://www.physicsforums.com/insights/wp-content/uploads/2019/12/2019-450x327.png 450w" sizes="(max-width: 640px) 100vw, 640px" /></noscript></p></div></div><p><script type="application/ld+json">{ "@context": "https://schema.org", "@type": "WebPage", "headline": "About Physics Forums | Our Mission, Values, Goals and History", "about": [ {"@type": "Thing","name": "Physics","sameAs": "https://en.wikipedia.org/wiki/Physics"}, {"@type": "Thing","name": "Forums","sameAs": "https://en.wikipedia.org/wiki/Internet_forum"} ], "mentions": [ {"@type": "Thing","name": "Learn","sameAs": "https://en.wikipedia.org/wiki/Learning"}, {"@type": "Thing","name": "community","sameAs": "https://en.wikipedia.org/wiki/Community"}, {"@type": "Thing","name": "discuss","sameAs": "https://en.wikipedia.org/wiki/Conversation"}, {"@type": "Thing","name": "science","sameAs": "https://en.wikipedia.org/wiki/Science"}, {"@type": "Thing","name": "guidelines","sameAs": "https://en.wikipedia.org/wiki/Tutorial"}, {"@type": "Thing","name": "behavior","sameAs": "https://en.wikipedia.org/wiki/Consumer_behaviour"}, {"@type": "Thing","name": "research","sameAs": "https://en.wikipedia.org/wiki/Research"} ] }</script></p><style>.lwrp.link-whisper-related-posts{ margin-top: 25px; margin-bottom: 25px; } .lwrp .lwrp-title{ }.lwrp .lwrp-description{ } .lwrp .lwrp-list-container{ } .lwrp .lwrp-list-multi-container{ display: flex; } .lwrp .lwrp-list-double{ width: 48%; } .lwrp .lwrp-list-triple{ width: 32%; } .lwrp .lwrp-list-row-container{ display: flex; justify-content: space-between; } .lwrp .lwrp-list-row-container .lwrp-list-item{ width: calc(33% - 20px); } .lwrp .lwrp-list-item:not(.lwrp-no-posts-message-item){ margin-bottom: 25px; } .lwrp .lwrp-list-item img{ max-width: 100%; height: auto; object-fit: cover; aspect-ratio: 1 / 1; } .lwrp .lwrp-list-item.lwrp-empty-list-item{ background: initial !important; } .lwrp .lwrp-list-item .lwrp-list-link .lwrp-list-link-title-text, .lwrp .lwrp-list-item .lwrp-list-no-posts-message{ }@media screen and (max-width: 480px) { .lwrp.link-whisper-related-posts{ } .lwrp .lwrp-title{ }.lwrp .lwrp-description{ } .lwrp .lwrp-list-multi-container{ flex-direction: column; } .lwrp .lwrp-list-multi-container ul.lwrp-list{ margin-top: 0px; margin-bottom: 0px; padding-top: 0px; padding-bottom: 0px; } .lwrp .lwrp-list-double, .lwrp .lwrp-list-triple{ width: 100%; } .lwrp .lwrp-list-row-container{ justify-content: initial; flex-direction: column; } .lwrp .lwrp-list-row-container .lwrp-list-item{ width: 100%; } .lwrp .lwrp-list-item:not(.lwrp-no-posts-message-item){ } .lwrp .lwrp-list-item .lwrp-list-link .lwrp-list-link-title-text, .lwrp .lwrp-list-item .lwrp-list-no-posts-message{ }; }</style><div id="link-whisper-related-posts-widget" class="link-whisper-related-posts lwrp"><h3 class="lwrp-title">More Related Articles</h3><div class="lwrp-list-container"><div class="lwrp-list-multi-container"><ul class="lwrp-list lwrp-list-double lwrp-list-left"><li class="lwrp-list-item"><a href="https://www.physicsforums.com/insights/interview-mathematician-fresh_42/" class="lwrp-list-link"><span class="lwrp-list-link-title-text">Interview with Mathematician Fresh_42</span></a></li><li class="lwrp-list-item"><a href="https://www.physicsforums.com/insights/postindex/" class="lwrp-list-link"><span class="lwrp-list-link-title-text">Table of Contents</span></a></li><li class="lwrp-list-item"><a href="https://www.physicsforums.com/insights/about-pf-insights/" class="lwrp-list-link"><span class="lwrp-list-link-title-text">About Physics Forums Insights</span></a></li></ul><ul class="lwrp-list lwrp-list-double lwrp-list-right"><li class="lwrp-list-item"><a href="https://www.physicsforums.com/insights/why-we-dont-discuss-perpetual-motion-machines-pmm/" class="lwrp-list-link"><span class="lwrp-list-link-title-text">Why We Don’t Discuss Perpetual Motion Machines (PMM)</span></a></li><li class="lwrp-list-item"><a href="https://www.physicsforums.com/insights/the-most-important-thing-you-can-learn-from-physics-forums/" class="lwrp-list-link"><span class="lwrp-list-link-title-text">The Most Important Thing You Can Learn from Physics Forums</span></a></li><li class="lwrp-list-item"><a href="https://www.physicsforums.com/insights/how-to-avoid-breaking-physics-with-your-what-if-question/" class="lwrp-list-link"><span class="lwrp-list-link-title-text">How to Avoid Breaking Physics With Your “What If” Question</span></a></li></ul></div></div></div></div><footer class="entry-footer"></footer></div></article></main><aside class='sidebar sidebar_right smartphones_sidebar_active alpha units' aria-label="Sidebar" role="complementary" itemscope="itemscope" itemtype="https://schema.org/WPSideBar" ><div class="inner_sidebar extralight-border"><section id="custom_html-2" class="widget_text widget clearfix widget_custom_html"><div class="textwidget custom-html-widget"><h2 class="widgettitle">Trending Articles</h2><ul class="wpp-list wpp-sunset"><li class="" style="--item-position: 1;--total-items: 10"><div class="item-position"></div><div class="item-data"><a href="https://www.physicsforums.com/insights/can-see-atom/" class="wpp-post-title" target="_self">Can We See an Atom?</a></div></li><li class="" style="--item-position: 2;--total-items: 10"><div class="item-position"></div><div class="item-data"><a href="https://www.physicsforums.com/insights/hand-wavy-discussion-planck-length/" class="wpp-post-title" target="_self">What Planck Length Is and It’s Common Misconceptions</a></div></li><li class="" style="--item-position: 3;--total-items: 10"><div class="item-position"></div><div class="item-data"><a href="https://www.physicsforums.com/insights/self-study-algebra-part-ii-abstract-algebra/" class="wpp-post-title" target="_self">How to Self Study Abstract Algebra</a></div></li><li class="" style="--item-position: 4;--total-items: 10"><div class="item-position"></div><div class="item-data"><a href="https://www.physicsforums.com/insights/self-study-basic-high-school-mathematics/" class="wpp-post-title" target="_self">How to Self-Study Basic High School Mathematics</a></div></li><li class="" style="--item-position: 5;--total-items: 10"><div class="item-position"></div><div class="item-data"><a href="https://www.physicsforums.com/insights/the-7-basic-rules-of-quantum-mechanics/" class="wpp-post-title" target="_self">The 7 Basic Rules of Quantum Mechanics</a></div></li><li class="" style="--item-position: 6;--total-items: 10"><div class="item-position"></div><div class="item-data"><a href="https://www.physicsforums.com/insights/visualizing-2-d-particle-box/" class="wpp-post-title" target="_self">How to Visualize the 2-D Particle in a Box</a></div></li><li class="" style="--item-position: 7;--total-items: 10"><div class="item-position"></div><div class="item-data"><a href="https://www.physicsforums.com/insights/what-is-a-tensor/" class="wpp-post-title" target="_self">What Is a Tensor? The mathematical point of view.</a></div></li><li class="" style="--item-position: 8;--total-items: 10"><div class="item-position"></div><div class="item-data"><a href="https://www.physicsforums.com/insights/parallel-programming-on-an-nvidia-gpu/" class="wpp-post-title" target="_self">Parallel Programming on an NVIDIA GPU</a></div></li><li class="" style="--item-position: 9;--total-items: 10"><div class="item-position"></div><div class="item-data"><a href="https://www.physicsforums.com/insights/relativity-using-bondi-k-calculus/" class="wpp-post-title" target="_self">Learn Relativity Using the Bondi K-calculus</a></div></li><li class="" style="--item-position: 10;--total-items: 10"><div class="item-position"></div><div class="item-data"><a href="https://www.physicsforums.com/insights/schrodingers-cat-and-the-qbit/" class="wpp-post-title" target="_self">Schrödinger’s Cat and the Qbit</a></div></li></ul></div><span class="seperator extralight-border"></span></section><section id="nav_menu-3" class="widget clearfix widget_nav_menu"><h3 class="widgettitle">Physics Forums</h3><div class="menu-sidebar-forums-container"><ul id="menu-sidebar-forums" class="menu"><li id="menu-item-26724" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-26724"><a href="https://www.physicsforums.com/forums/classical-physics.61/">Classical Physics</a></li><li id="menu-item-26725" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-26725"><a href="https://www.physicsforums.com/forums/atomic-and-condensed-matter.64/">Atomic and Condensed Matter</a></li><li id="menu-item-26726" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-26726"><a href="https://www.physicsforums.com/forums/quantum-physics.62/">Quantum Physics</a></li><li id="menu-item-26727" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-26727"><a href="https://www.physicsforums.com/forums/special-and-general-relativity.70/">Special and General Relativity</a></li><li id="menu-item-26728" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-26728"><a href="https://www.physicsforums.com/forums/beyond-the-standard-model.66/">Beyond the Standard Model</a></li><li id="menu-item-26729" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-26729"><a href="https://www.physicsforums.com/forums/high-energy-nuclear-particle-physics.65/">High Energy, Nuclear, Particle Physics</a></li><li id="menu-item-26731" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-26731"><a href="https://www.physicsforums.com/forums/astronomy-and-astrophysics.71/">Astronomy and Astrophysics</a></li><li id="menu-item-26732" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-26732"><a href="https://www.physicsforums.com/forums/cosmology.69/">Cosmology</a></li><li id="menu-item-26730" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-26730"><a href="https://www.physicsforums.com/forums/other-physics-topics.111/">Other Physics Topics</a></li></ul></div><span class="seperator extralight-border"></span></section><section id="text-4" class="widget clearfix widget_text"><h3 class="widgettitle">Receive Insights Articles to Your Inbox</h3><div class="textwidget"><form style="border:0px solid #ccc;text-align:left;" action="https://feedburner.google.com/fb/a/mailverify" method="post" target="popupwindow" onsubmit="window.open('https://feedburner.google.com/fb/a/mailverify?uri=PhysicsForumsInsights', 'popupwindow', 'scrollbars=yes,width=550,height=520');return true"><p>Enter your email address:</p><p><input type="text" style="width:200px;border:2px solid #ccc;" name="email"/></p><input type="hidden" value="PhysicsForumsInsights" name="uri"/><input type="hidden" name="loc" value="en_US"/><input type="submit" value="Subscribe" /></p></form></div> <span class="seperator extralight-border"></span></section><section id="nav_menu-2" class="widget clearfix widget_nav_menu"><h3 class="widgettitle">Blog Information</h3><div class="menu-sidebar-container"><ul id="menu-sidebar" class="menu"><li id="menu-item-14015" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-14015"><a href="https://www.physicsforums.com/register">Become a Member!</a></li><li id="menu-item-14012" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-14012"><a href="https://www.physicsforums.com/insights/application/">Write for Us!</a></li><li id="menu-item-18348" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-18348"><a href="https://www.physicsforums.com/insights/postindex/">Table of Contents</a></li><li id="menu-item-18353" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-18353"><a href="https://www.physicsforums.com/insights/authors/">Blog Author List</a></li></ul></div><span class="seperator extralight-border"></span></section><section id="tag_cloud-3" class="widget clearfix widget_tag_cloud"><h3 class="widgettitle">Popular Topics</h3><div class="tagcloud"><a href="https://www.physicsforums.com/insights/tag/astronomy/" class="tag-cloud-link tag-link-307 tag-link-position-1" style="font-size: 9.1666666666667pt;" aria-label="astronomy (17 items)">astronomy<span class="tag-link-count"> (17)</span></a> <a href="https://www.physicsforums.com/insights/tag/black-holes/" class="tag-cloud-link tag-link-28 tag-link-position-2" style="font-size: 9.1666666666667pt;" aria-label="black holes (17 items)">black holes<span class="tag-link-count"> (17)</span></a> <a href="https://www.physicsforums.com/insights/tag/classical-physics/" class="tag-cloud-link tag-link-852 tag-link-position-3" style="font-size: 20.833333333333pt;" aria-label="classical physics (35 items)">classical physics<span class="tag-link-count"> (35)</span></a> <a href="https://www.physicsforums.com/insights/tag/cosmology/" class="tag-cloud-link tag-link-224 tag-link-position-4" style="font-size: 8pt;" aria-label="cosmology (16 items)">cosmology<span class="tag-link-count"> (16)</span></a> <a href="https://www.physicsforums.com/insights/tag/education/" class="tag-cloud-link tag-link-104 tag-link-position-5" style="font-size: 13.833333333333pt;" aria-label="education (23 items)">education<span class="tag-link-count"> (23)</span></a> <a href="https://www.physicsforums.com/insights/tag/electromagnetism/" class="tag-cloud-link tag-link-21 tag-link-position-6" style="font-size: 10.722222222222pt;" aria-label="electromagnetism (19 items)">electromagnetism<span class="tag-link-count"> (19)</span></a> <a href="https://www.physicsforums.com/insights/tag/general-relativity/" class="tag-cloud-link tag-link-333 tag-link-position-7" style="font-size: 10.722222222222pt;" aria-label="general relativity (19 items)">general relativity<span class="tag-link-count"> (19)</span></a> <a href="https://www.physicsforums.com/insights/tag/gravity/" class="tag-cloud-link tag-link-40 tag-link-position-8" style="font-size: 14.611111111111pt;" aria-label="gravity (24 items)">gravity<span class="tag-link-count"> (24)</span></a> <a href="https://www.physicsforums.com/insights/tag/interview/" class="tag-cloud-link tag-link-858 tag-link-position-9" style="font-size: 13.055555555556pt;" aria-label="interview (22 items)">interview<span class="tag-link-count"> (22)</span></a> <a href="https://www.physicsforums.com/insights/tag/mathematics/" class="tag-cloud-link tag-link-69 tag-link-position-10" style="font-size: 22pt;" aria-label="mathematics (38 items)">mathematics<span class="tag-link-count"> (38)</span></a> <a href="https://www.physicsforums.com/insights/tag/mathematics-self-study/" class="tag-cloud-link tag-link-484 tag-link-position-11" style="font-size: 9.9444444444444pt;" aria-label="mathematics self-study (18 items)">mathematics self-study<span class="tag-link-count"> (18)</span></a> <a href="https://www.physicsforums.com/insights/tag/physicist/" class="tag-cloud-link tag-link-11 tag-link-position-12" style="font-size: 15.777777777778pt;" aria-label="Physicist (26 items)">Physicist<span class="tag-link-count"> (26)</span></a> <a href="https://www.physicsforums.com/insights/tag/programming/" class="tag-cloud-link tag-link-42 tag-link-position-13" style="font-size: 9.9444444444444pt;" aria-label="programming (18 items)">programming<span class="tag-link-count"> (18)</span></a> <a href="https://www.physicsforums.com/insights/tag/quantum-field-theory/" class="tag-cloud-link tag-link-87 tag-link-position-14" style="font-size: 18.888888888889pt;" aria-label="Quantum Field Theory (31 items)">Quantum Field Theory<span class="tag-link-count"> (31)</span></a> <a href="https://www.physicsforums.com/insights/tag/quantum-mechanics/" class="tag-cloud-link tag-link-62 tag-link-position-15" style="font-size: 21.222222222222pt;" aria-label="quantum mechanics (36 items)">quantum mechanics<span class="tag-link-count"> (36)</span></a> <a href="https://www.physicsforums.com/insights/tag/quantum-physics/" class="tag-cloud-link tag-link-314 tag-link-position-16" style="font-size: 13.055555555556pt;" aria-label="quantum physics (22 items)">quantum physics<span class="tag-link-count"> (22)</span></a> <a href="https://www.physicsforums.com/insights/tag/relativity/" class="tag-cloud-link tag-link-114 tag-link-position-17" style="font-size: 21.611111111111pt;" aria-label="relativity (37 items)">relativity<span class="tag-link-count"> (37)</span></a> <a href="https://www.physicsforums.com/insights/tag/special-relativity/" class="tag-cloud-link tag-link-89 tag-link-position-18" style="font-size: 8pt;" aria-label="Special Relativity (16 items)">Special Relativity<span class="tag-link-count"> (16)</span></a> <a href="https://www.physicsforums.com/insights/tag/technology/" class="tag-cloud-link tag-link-861 tag-link-position-19" style="font-size: 10.722222222222pt;" aria-label="technology (19 items)">technology<span class="tag-link-count"> (19)</span></a> <a href="https://www.physicsforums.com/insights/tag/universe/" class="tag-cloud-link tag-link-265 tag-link-position-20" style="font-size: 12.277777777778pt;" aria-label="universe (21 items)">universe<span class="tag-link-count"> (21)</span></a></div> <span class="seperator extralight-border"></span></section></div></aside></div></div><footer class='container_wrap socket_color' id='socket' role="contentinfo" itemscope="itemscope" itemtype="https://schema.org/WPFooter" aria-label="Copyright and company info" ><div class='container'><span class='copyright'> 2024 © PHYSICS FORUMS, ALL RIGHTS RESERVED - <a href="https://www.physicsforums.com/misc/contact">Contact Us</a> - <a href="https://www.physicsforums.com/threads/physics-forums-privacy-policy.797829/">Privacy Policy</a> - <a href="https://www.physicsforums.com/insights/about-pf-insights/">About PF Insights</a></span><ul class='noLightbox social_bookmarks icon_count_4'><li class='social_bookmarks_twitter av-social-link-twitter social_icon_1'><a target="_blank" aria-label="Link to X" href="https://twitter.com/physicsforums" aria-hidden='false' data-av_icon='' data-av_iconfont='entypo-fontello' title='X' rel="noopener"><span class='avia_hidden_link_text'>X</span></a></li><li class='social_bookmarks_facebook av-social-link-facebook social_icon_2'><a target="_blank" aria-label="Link to Facebook" href='https://www.facebook.com/physicsforums' aria-hidden='false' data-av_icon='' data-av_iconfont='entypo-fontello' title='Facebook' rel="noopener"><span class='avia_hidden_link_text'>Facebook</span></a></li><li class='social_bookmarks_linkedin av-social-link-linkedin social_icon_3'><a target="_blank" aria-label="Link to LinkedIn" href='https://www.linkedin.com/company/physics-forums/' aria-hidden='false' data-av_icon='' data-av_iconfont='entypo-fontello' title='LinkedIn' rel="noopener"><span class='avia_hidden_link_text'>LinkedIn</span></a></li><li class='social_bookmarks_youtube av-social-link-youtube social_icon_4'><a target="_blank" aria-label="Link to Youtube" href='https://www.youtube.com/@physicsforum' aria-hidden='false' data-av_icon='' data-av_iconfont='entypo-fontello' title='Youtube' rel="noopener"><span class='avia_hidden_link_text'>Youtube</span></a></li></ul></div></footer></div></div><a href='#top' title='Scroll to top' id='scroll-top-link' aria-hidden='true' data-av_icon='' data-av_iconfont='entypo-fontello' tabindex='-1'><span class="avia_hidden_link_text">Scroll to top</span></a><div id="fb-root"></div> <script data-optimized="1" type="text/javascript" src="https://www.physicsforums.com/insights/wp-content/litespeed/js/ffe2445567cebbe851874e864ab606aa.js?ver=606aa" defer></script> <script type='text/javascript'>/* */ var avia_framework_globals = avia_framework_globals || {}; avia_framework_globals.frameworkUrl = 'https://www.physicsforums.com/insights/wp-content/themes/enfold/framework/'; avia_framework_globals.installedAt = 'https://www.physicsforums.com/insights/wp-content/themes/enfold/'; avia_framework_globals.ajaxurl = 'https://www.physicsforums.com/insights/wp-admin/admin-ajax.php'; /* */</script> <script type="text/javascript" async='async' src="https://www.physicsforums.com/insights/wp-includes/js/jquery/jquery.min.js?ver=3.7.1" id="jquery-core-js"></script> <script type="text/javascript" id="wpil-frontend-script-js-extra">/* */ var wpilFrontend = {"ajaxUrl":"\/insights\/wp-admin\/admin-ajax.php","postId":"21404","postType":"post","openInternalInNewTab":"0","openExternalInNewTab":"1","disableClicks":"0","openLinksWithJS":"0","trackAllElementClicks":"0","clicksI18n":{"imageNoText":"Image in link: No Text","imageText":"Image Title: ","noText":"No Anchor Text Found"}}; /* */</script> <script data-optimized="1" type="text/javascript" async='async' src="https://www.physicsforums.com/insights/wp-content/litespeed/js/32fbbb44e22394d8c0f1ada21cfadab5.js?ver=e0bd3" id="wpil-frontend-script-js"></script> <script data-optimized="1" type="text/javascript" async='async' src="https://www.physicsforums.com/insights/wp-content/litespeed/js/7433b54a869d4261e4332aa625ab7215.js?ver=b7215" id="avia-footer-scripts-js"></script> <script data-no-optimize="1">!function(t,e){"object"==typeof exports&&"undefined"!=typeof module?module.exports=e():"function"==typeof define&&define.amd?define(e):(t="undefined"!=typeof globalThis?globalThis:t||self).LazyLoad=e()}(this,function(){"use strict";function e(){return(e=Object.assign||function(t){for(var e=1;e<arguments.length;e++){var n,a=arguments[e];for(n in a)Object.prototype.hasOwnProperty.call(a,n)&&(t[n]=a[n])}return t}).apply(this,arguments)}function i(t){return e({},it,t)}function o(t,e){var n,a="LazyLoad::Initialized",i=new t(e);try{n=new CustomEvent(a,{detail:{instance:i}})}catch(t){(n=document.createEvent("CustomEvent")).initCustomEvent(a,!1,!1,{instance:i})}window.dispatchEvent(n)}function l(t,e){return t.getAttribute(gt+e)}function c(t){return l(t,bt)}function s(t,e){return function(t,e,n){e=gt+e;null!==n?t.setAttribute(e,n):t.removeAttribute(e)}(t,bt,e)}function r(t){return s(t,null),0}function u(t){return null===c(t)}function d(t){return c(t)===vt}function f(t,e,n,a){t&&(void 0===a?void 0===n?t(e):t(e,n):t(e,n,a))}function _(t,e){nt?t.classList.add(e):t.className+=(t.className?" ":"")+e}function v(t,e){nt?t.classList.remove(e):t.className=t.className.replace(new RegExp("(^|\\s+)"+e+"(\\s+|$)")," ").replace(/^\s+/,"").replace(/\s+$/,"")}function g(t){return t.llTempImage}function b(t,e){!e||(e=e._observer)&&e.unobserve(t)}function p(t,e){t&&(t.loadingCount+=e)}function h(t,e){t&&(t.toLoadCount=e)}function n(t){for(var e,n=[],a=0;e=t.children[a];a+=1)"SOURCE"===e.tagName&&n.push(e);return n}function m(t,e){(t=t.parentNode)&&"PICTURE"===t.tagName&&n(t).forEach(e)}function a(t,e){n(t).forEach(e)}function E(t){return!!t[st]}function I(t){return t[st]}function y(t){return delete t[st]}function A(e,t){var n;E(e)||(n={},t.forEach(function(t){n[t]=e.getAttribute(t)}),e[st]=n)}function k(a,t){var i;E(a)&&(i=I(a),t.forEach(function(t){var e,n;e=a,(t=i[n=t])?e.setAttribute(n,t):e.removeAttribute(n)}))}function L(t,e,n){_(t,e.class_loading),s(t,ut),n&&(p(n,1),f(e.callback_loading,t,n))}function w(t,e,n){n&&t.setAttribute(e,n)}function x(t,e){w(t,ct,l(t,e.data_sizes)),w(t,rt,l(t,e.data_srcset)),w(t,ot,l(t,e.data_src))}function O(t,e,n){var a=l(t,e.data_bg_multi),i=l(t,e.data_bg_multi_hidpi);(a=at&&i?i:a)&&(t.style.backgroundImage=a,n=n,_(t=t,(e=e).class_applied),s(t,ft),n&&(e.unobserve_completed&&b(t,e),f(e.callback_applied,t,n)))}function N(t,e){!e||0<e.loadingCount||0<e.toLoadCount||f(t.callback_finish,e)}function C(t,e,n){t.addEventListener(e,n),t.llEvLisnrs[e]=n}function M(t){return!!t.llEvLisnrs}function z(t){if(M(t)){var e,n,a=t.llEvLisnrs;for(e in a){var i=a[e];n=e,i=i,t.removeEventListener(n,i)}delete t.llEvLisnrs}}function R(t,e,n){var a;delete t.llTempImage,p(n,-1),(a=n)&&--a.toLoadCount,v(t,e.class_loading),e.unobserve_completed&&b(t,n)}function T(o,r,c){var l=g(o)||o;M(l)||function(t,e,n){M(t)||(t.llEvLisnrs={});var a="VIDEO"===t.tagName?"loadeddata":"load";C(t,a,e),C(t,"error",n)}(l,function(t){var e,n,a,i;n=r,a=c,i=d(e=o),R(e,n,a),_(e,n.class_loaded),s(e,dt),f(n.callback_loaded,e,a),i||N(n,a),z(l)},function(t){var e,n,a,i;n=r,a=c,i=d(e=o),R(e,n,a),_(e,n.class_error),s(e,_t),f(n.callback_error,e,a),i||N(n,a),z(l)})}function G(t,e,n){var a,i,o,r,c;t.llTempImage=document.createElement("IMG"),T(t,e,n),E(c=t)||(c[st]={backgroundImage:c.style.backgroundImage}),o=n,r=l(a=t,(i=e).data_bg),c=l(a,i.data_bg_hidpi),(r=at&&c?c:r)&&(a.style.backgroundImage='url("'.concat(r,'")'),g(a).setAttribute(ot,r),L(a,i,o)),O(t,e,n)}function D(t,e,n){var a;T(t,e,n),a=e,e=n,(t=It[(n=t).tagName])&&(t(n,a),L(n,a,e))}function V(t,e,n){var a;a=t,(-1<yt.indexOf(a.tagName)?D:G)(t,e,n)}function F(t,e,n){var a;t.setAttribute("loading","lazy"),T(t,e,n),a=e,(e=It[(n=t).tagName])&&e(n,a),s(t,vt)}function j(t){t.removeAttribute(ot),t.removeAttribute(rt),t.removeAttribute(ct)}function P(t){m(t,function(t){k(t,Et)}),k(t,Et)}function S(t){var e;(e=At[t.tagName])?e(t):E(e=t)&&(t=I(e),e.style.backgroundImage=t.backgroundImage)}function U(t,e){var n;S(t),n=e,u(e=t)||d(e)||(v(e,n.class_entered),v(e,n.class_exited),v(e,n.class_applied),v(e,n.class_loading),v(e,n.class_loaded),v(e,n.class_error)),r(t),y(t)}function $(t,e,n,a){var i;n.cancel_on_exit&&(c(t)!==ut||"IMG"===t.tagName&&(z(t),m(i=t,function(t){j(t)}),j(i),P(t),v(t,n.class_loading),p(a,-1),r(t),f(n.callback_cancel,t,e,a)))}function q(t,e,n,a){var i,o,r=(o=t,0<=pt.indexOf(c(o)));s(t,"entered"),_(t,n.class_entered),v(t,n.class_exited),i=t,o=a,n.unobserve_entered&&b(i,o),f(n.callback_enter,t,e,a),r||V(t,n,a)}function H(t){return t.use_native&&"loading"in HTMLImageElement.prototype}function B(t,i,o){t.forEach(function(t){return(a=t).isIntersecting||0<a.intersectionRatio?q(t.target,t,i,o):(e=t.target,n=t,a=i,t=o,void(u(e)||(_(e,a.class_exited),$(e,n,a,t),f(a.callback_exit,e,n,t))));var e,n,a})}function J(e,n){var t;et&&!H(e)&&(n._observer=new IntersectionObserver(function(t){B(t,e,n)},{root:(t=e).container===document?null:t.container,rootMargin:t.thresholds||t.threshold+"px"}))}function K(t){return Array.prototype.slice.call(t)}function Q(t){return t.container.querySelectorAll(t.elements_selector)}function W(t){return c(t)===_t}function X(t,e){return e=t||Q(e),K(e).filter(u)}function Y(e,t){var n;(n=Q(e),K(n).filter(W)).forEach(function(t){v(t,e.class_error),r(t)}),t.update()}function t(t,e){var n,a,t=i(t);this._settings=t,this.loadingCount=0,J(t,this),n=t,a=this,Z&&window.addEventListener("online",function(){Y(n,a)}),this.update(e)}var Z="undefined"!=typeof window,tt=Z&&!("onscroll"in window)||"undefined"!=typeof navigator&&/(gle|ing|ro)bot|crawl|spider/i.test(navigator.userAgent),et=Z&&"IntersectionObserver"in window,nt=Z&&"classList"in document.createElement("p"),at=Z&&1<window.devicePixelRatio,it={elements_selector:".lazy",container:tt||Z?document:null,threshold:300,thresholds:null,data_src:"src",data_srcset:"srcset",data_sizes:"sizes",data_bg:"bg",data_bg_hidpi:"bg-hidpi",data_bg_multi:"bg-multi",data_bg_multi_hidpi:"bg-multi-hidpi",data_poster:"poster",class_applied:"applied",class_loading:"litespeed-loading",class_loaded:"litespeed-loaded",class_error:"error",class_entered:"entered",class_exited:"exited",unobserve_completed:!0,unobserve_entered:!1,cancel_on_exit:!0,callback_enter:null,callback_exit:null,callback_applied:null,callback_loading:null,callback_loaded:null,callback_error:null,callback_finish:null,callback_cancel:null,use_native:!1},ot="src",rt="srcset",ct="sizes",lt="poster",st="llOriginalAttrs",ut="loading",dt="loaded",ft="applied",_t="error",vt="native",gt="data-",bt="ll-status",pt=[ut,dt,ft,_t],ht=[ot],mt=[ot,lt],Et=[ot,rt,ct],It={IMG:function(t,e){m(t,function(t){A(t,Et),x(t,e)}),A(t,Et),x(t,e)},IFRAME:function(t,e){A(t,ht),w(t,ot,l(t,e.data_src))},VIDEO:function(t,e){a(t,function(t){A(t,ht),w(t,ot,l(t,e.data_src))}),A(t,mt),w(t,lt,l(t,e.data_poster)),w(t,ot,l(t,e.data_src)),t.load()}},yt=["IMG","IFRAME","VIDEO"],At={IMG:P,IFRAME:function(t){k(t,ht)},VIDEO:function(t){a(t,function(t){k(t,ht)}),k(t,mt),t.load()}},kt=["IMG","IFRAME","VIDEO"];return t.prototype={update:function(t){var e,n,a,i=this._settings,o=X(t,i);{if(h(this,o.length),!tt&&et)return H(i)?(e=i,n=this,o.forEach(function(t){-1!==kt.indexOf(t.tagName)&&F(t,e,n)}),void h(n,0)):(t=this._observer,i=o,t.disconnect(),a=t,void i.forEach(function(t){a.observe(t)}));this.loadAll(o)}},destroy:function(){this._observer&&this._observer.disconnect(),Q(this._settings).forEach(function(t){y(t)}),delete this._observer,delete this._settings,delete this.loadingCount,delete this.toLoadCount},loadAll:function(t){var e=this,n=this._settings;X(t,n).forEach(function(t){b(t,e),V(t,n,e)})},restoreAll:function(){var e=this._settings;Q(e).forEach(function(t){U(t,e)})}},t.load=function(t,e){e=i(e);V(t,e)},t.resetStatus=function(t){r(t)},Z&&function(t,e){if(e)if(e.length)for(var n,a=0;n=e[a];a+=1)o(t,n);else o(t,e)}(t,window.lazyLoadOptions),t});!function(e,t){"use strict";function a(){t.body.classList.add("litespeed_lazyloaded")}function n(){console.log("[LiteSpeed] Start Lazy Load Images"),d=new LazyLoad({elements_selector:"[data-lazyloaded]",callback_finish:a}),o=function(){d.update()},e.MutationObserver&&new MutationObserver(o).observe(t.documentElement,{childList:!0,subtree:!0,attributes:!0})}var d,o;e.addEventListener?e.addEventListener("load",n,!1):e.attachEvent("onload",n)}(window,document);</script></body></html>