366 lines
86 KiB
HTML
366 lines
86 KiB
HTML
|
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns=http://www.w3.org/1999/xhtml xml:lang=en style lang=en><!--
|
||
|
|
Page saved with SingleFile
|
||
|
|
url: http://arxiv.org/abs/quant-ph/0104066
|
||
|
|
saved date: Mon Jul 15 2024 02:56:46 GMT-0400 (EDT)
|
||
|
|
--><meta charset=utf-8>
|
||
|
|
<title>[quant-ph/0104066] Mechanical interpretation of the Klein-Gordon equation</title>
|
||
|
|
<meta name=viewport content="width=device-width, initial-scale=1">
|
||
|
|
<meta name=msapplication-TileColor content=#da532c>
|
||
|
|
<meta name=theme-color content=#ffffff>
|
||
|
|
<style media=screen>body{margin:0;padding:0;background-color:#fff;color:#000;font-family:"Lucida Grande",helvetica,arial,verdana,sans-serif}a:link,a:visited,a:active{text-decoration:none;font-weight:normal}a:hover{text-decoration:underline}img{border:0}em{font-weight:bold;font-style:normal}.primary-subject{font-weight:bold}#cu-identity{font-family:verdana,arial,helvetica,sans-serif;font-size:63.125%;color:#fff;background-color:#222;width:100%;display:flex;justify-content:space-between}#cu-logo{position:relative;left:10px;top:2px;width:300px;height:49px}#cu-logo a img{width:200px}#support-ack{top:12px;right:0%;margin:0 12px 0 0;padding:8px 0;text-align:right;font-size:120%;font-weight:normal;font-family:"Lucida Grande",helvetica,arial,verdana,sans-serif;color:#fff}#support-ack-url{max-width:400px;float:right;display:block}#support-ack-url a{color:#fff;border:none;text-decoration:underline}#support-ack-url a:hover{color:#1e8bc3}#header{background-color:#b31b1b;color:#fff;margin:0;padding:10px 0 10px 0;border-bottom:2px solid #ccc;position:relative;overflow:auto}#header .header-breadcrumbs{margin:0;font-size:1em;padding:10px 0 .2em 10px;font-style:normal;float:left;display:inline-flex;align-items:center}#header .header-breadcrumbs span{margin-right:5px;margin-left:5px}#header a,#header a:visited{color:#fff;text-decoration:none}#header a:hover{text-decoration:underline}#header form{margin:0 12px 0 0;padding:0;text-align:right;font-size:.8em;line-height:100%}#header form input,#header form select{margin:0;padding:0}@media screen and (max-width:768px){.search-block.level-right{clear:both!important}#header .header-breadcrumbs{float:none;text-align:center}}main{flex-grow:1}.flex-wrap-footer{display:flex;min-height:100vh;flex-direction:column}footer ul li{display:flex;align-items:center;font-size:14px}footer ul li a{font-size:13.5px}footer{background-color:hsl(0,0%,95%);color:#000;padding:1em 2em;font-size:0.9rem;-webkit-font-smoothing:antialiased;margin-top:6rem}footer a,footer a:visited{color:#000;text-decoration:none;border-bottom:1px solid transparent;line-height:1.75em}footer a:hover,footer a:active{color:#005e9d;border-bottom:1px dotted #005e9d;text-decoration:none}footer ul{padding:0;margin:0}footer .sorry-app-links .help{font-size:0.75rem;margin-bottom:0;line-height:1.75em}footer .sorry-app-links .help a,footer .sorry-app-links .help a:visited{border-bottom:1px dotted #000}footer .sorry-app-links .help a:hover,footer .sorry-app-links .help a:active{border-bottom:1px dotted #005e9d}footer .sorry-app-links svg.icon{margin-bottom:-2px!important}footer .sorry-app-links .icon.filter-black:hover,footer .sorry-app-links .icon.filter-black:active,footer .sorry-app-links a:hover .icon.filter-black,footer .sorry-app-links a:hover .icon.filter-black{fill:#005e9d!important}footer .sorry-app-links .a11y-main-link{font-size:110%;border-bottom:1px solid transparent!important;padding:0;margin:0}@media screen and (max-width:768px){footer .sorry-app-links.column{padding:0}}.endorsers .help{position:relative;top:4rem}@media screen and (min-width:990px){.endorsers .help{top:5rem}}@media screen and (min-width:769px){.columns{display:flex;flex-direction:row}}.icon{width:.9rem;margin-right:.45em;margin-top:-.15rem}.help{font-family:"Lucida Grande","Helvetica Neue",Helvetica,Arial,sans-serif;display:block;font-size:0.75rem;margin-top:0.25rem}#content,#content-inner{margin:.7em;font-size:90%}#abs-outer,#abs{margin:-0.7em}#abs-outer .leftcolumn{margin:0 0 1em 0;padding:0px;width:calc(100% - 18em);float:left}#abs-outer .extra-services{float:right;margin:0;width:18em}#abs-outer .extra-services span.bib-cite-button{color:rgb(0,0,238);font-weight:bold;padding:.35em;display:block;text-transform:capitalize}#abs-outer .extra-services span.bib-cite-button:hover,#abs-outer .extra-services span.bib-cite-button:focus{text-decoration:underline;cursor:pointer}#labstabs{clear:both;margin:1em 1.5em}#labstabs .labstabs{display:flex;flex-wrap:wrap;white-space:normal;justify-content:flex-start}#labstabs .labstabs>label{order:1;display:block;padding:.75em 1.5em;fon
|
||
|
|
<link rel=canonical href=http://arxiv.org/abs/quant-ph/0104066><meta property=og:type content=website>
|
||
|
|
<meta property=og:site_name content=arXiv.org>
|
||
|
|
<meta property=og:title content="Mechanical interpretation of the Klein-Gordon equation">
|
||
|
|
<meta property=og:url content=https://arxiv.org/abs/quant-ph/0104066v1>
|
||
|
|
<meta property=og:image content=/static/browse/0.3.4/images/arxiv-logo-fb.png>
|
||
|
|
<meta property=og:image:secure_url content=/static/browse/0.3.4/images/arxiv-logo-fb.png>
|
||
|
|
<meta property=og:image:width content=1200>
|
||
|
|
<meta property=og:image:height content=700>
|
||
|
|
<meta property=og:image:alt content="arXiv logo">
|
||
|
|
<meta property=og:description content="The substratum for physics can be seen microscopically as an ideal fluid pierced in all directions by the straight vortex filaments. Small disturbances of an isolated filament are considered. The Klein-Gordon equation without mass corresponds to elastic stretching of the filament. The wave function has the meaning of the curve's position vector. The mass part of the Klein-Gordon equation describes the rotation of the helical curve about the screw axis due to the hydrodynamic self-induction of the bent vortex filament.">
|
||
|
|
<meta name=twitter:site content=@arxiv>
|
||
|
|
<meta name=twitter:card content=summary>
|
||
|
|
<meta name=twitter:title content="Mechanical interpretation of the Klein-Gordon equation">
|
||
|
|
<meta name=twitter:description content="The substratum for physics can be seen microscopically as an ideal fluid pierced in all directions by the straight vortex filaments. Small disturbances of an isolated filament are considered. The...">
|
||
|
|
<meta name=twitter:image content=https://static.arxiv.org/icons/twitter/arxiv-logo-twitter-square.png>
|
||
|
|
<meta name=twitter:image:alt content="arXiv logo">
|
||
|
|
<style media=screen>.visually-hidden{clip-path:inset(100%);clip:rect(1px,1px,1px,1px);height:1px;overflow:hidden;position:absolute;white-space:nowrap;width:1px}.button-and-tooltip{position:relative;display:inline}.button-and-tooltip button{background:transparent;border:none;box-shadow:none;position:relative;padding:0 0 0 6px}td.tablecell.arxivdoi{display:inline-flex;align-items:center}.arrow{width:0;height:0;border-left:8px solid transparent;border-right:8px solid transparent}@-webkit-keyframes pulsate{0%{-webkit-transform:scale(.1);transform:scale(.1);opacity:0}30%{opacity:1}60%{-webkit-transform:scale(.8);transform:scale(.8);opacity:0}}@keyframes pulsate{0%{-webkit-transform:scale(.1);transform:scale(.1);opacity:0}30%{opacity:1}60%{-webkit-transform:scale(.8);transform:scale(.8);opacity:0}}</style>
|
||
|
|
<meta name=citation_title content="Mechanical interpretation of the Klein-Gordon equation"><meta name=citation_author content="Dmitriyev, V. P."><meta name=citation_date content=2001/04/12><meta name=citation_online_date content=2001/04/12><meta name=citation_pdf_url content=http://arxiv.org/pdf/quant-ph/0104066><meta name=citation_arxiv_id content=quant-ph/0104066><meta name=citation_abstract content=" The substratum for physics can be seen microscopically as an ideal fluid pierced in all directions by the straight vortex filaments. Small disturbances of an isolated filament are considered. The Klein-Gordon equation without mass corresponds to elastic stretching of the filament. The wave function has the meaning of the curve's position vector. The mass part of the Klein-Gordon equation describes the rotation of the helical curve about the screw axis due to the hydrodynamic self-induction of the bent vortex filament.">
|
||
|
|
<style>#MathJax_Message{position:fixed;left:1px;bottom:2px;background-color:#E6E6E6;border:1px solid #959595;margin:0px;padding:2px 8px;z-index:102;color:black;font-size:80%;width:auto;white-space:nowrap}</style><link rel=icon type=image/png sizes=32x32 href="data:image/png;base64,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"><style>.sf-hidden{display:none!important}</style><meta http-equiv=content-security-policy content="default-src 'none'; font-src 'self' data:; img-src 'self' data:; style-src 'unsafe-inline'; media-src 'self' data:; script-src 'unsafe-inline' data:; object-src 'self' data:;"><style>img[src="data:,"],source[src="data:,"]{display:none!important}</style></head>
|
||
|
|
<body class=with-cu-identity><div id=MathJax_Message style=display:none></div>
|
||
|
|
|
||
|
|
<div class=flex-wrap-footer>
|
||
|
|
<header>
|
||
|
|
<a href=#content class=is-sr-only>Skip to main content</a>
|
||
|
|
|
||
|
|
<div class="columns is-vcentered is-hidden-mobile" id=cu-identity>
|
||
|
|
<div class=column id=cu-logo>
|
||
|
|
<a href=https://www.cornell.edu/><img src=data:image/svg+xml;base64,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
|
||
|
|
</div><div class=column id=support-ack>
|
||
|
|
<span id=support-ack-url>We gratefully acknowledge support from the Simons Foundation, <a href=https://info.arxiv.org/about/ourmembers.html>member institutions</a>, and all contributors. <a href=https://info.arxiv.org/about/donate.html>Donate</a></span>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
<div id=header class=is-hidden-mobile>
|
||
|
|
<a aria-hidden=true href="http://arxiv.org/abs/quant-ph/%7Burl_path('ignore_me')%7D"></a>
|
||
|
|
<div class="header-breadcrumbs is-hidden-mobile">
|
||
|
|
<a href=http://arxiv.org/><img src=data:image/svg+xml;base64,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
|
||
|
|
</div>
|
||
|
|
<div class="search-block level-right">
|
||
|
|
<form class="level-item mini-search" method=GET action=https://arxiv.org/search>
|
||
|
|
<div class="field has-addons">
|
||
|
|
<div class=control>
|
||
|
|
<input class="input is-small" name=query placeholder=Search... aria-label="Search term or terms" value type=text>
|
||
|
|
<p class=help><a href=https://info.arxiv.org/help>Help</a> | <a href=https://arxiv.org/search/advanced>Advanced Search</a></p>
|
||
|
|
</div>
|
||
|
|
<div class=control>
|
||
|
|
<div class="select is-small">
|
||
|
|
<select name=searchtype aria-label="Field to search">
|
||
|
|
<option value=all selected>All fields</option>
|
||
|
|
<option value=title>Title</option>
|
||
|
|
<option value=author>Author</option>
|
||
|
|
<option value=abstract>Abstract</option>
|
||
|
|
<option value=comments>Comments</option>
|
||
|
|
<option value=journal_ref>Journal reference</option>
|
||
|
|
<option value=acm_class>ACM classification</option>
|
||
|
|
<option value=msc_class>MSC classification</option>
|
||
|
|
<option value=report_num>Report number</option>
|
||
|
|
<option value=paper_id>arXiv identifier</option>
|
||
|
|
<option value=doi>DOI</option>
|
||
|
|
<option value=orcid>ORCID</option>
|
||
|
|
<option value=author_id>arXiv author ID</option>
|
||
|
|
<option value=help>Help pages</option>
|
||
|
|
<option value=full_text>Full text</option>
|
||
|
|
</select>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<button class="button is-small is-cul-darker">Search</button>
|
||
|
|
</div>
|
||
|
|
</form>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
<div class="mobile-header sf-hidden">
|
||
|
|
<div class="columns is-mobile sf-hidden">
|
||
|
|
|
||
|
|
<div class="column logo-cornell sf-hidden"><a href=https://www.cornell.edu/ class=sf-hidden>
|
||
|
|
<picture class=sf-hidden>
|
||
|
|
<source media="(min-width: 501px)" srcset="data:image/svg+xml;base64,PD94bWwgdmVyc2lvbj0iMS4wIiBlbmNvZGluZz0idXRmLTgiPz4KPCEtLSBHZW5lcmF0b3I6IEFkb2JlIElsbHVzdHJhdG9yIDIyLjEuMCwgU1ZHIEV4cG9ydCBQbHVnLUluIC4gU1ZHIFZlcnNpb246IDYuMDAgQnVpbGQgMCkgIC0tPgo8c3ZnIHZlcnNpb249IjEuMSIgaWQ9IkxheWVyXzEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgeG1sbnM6eGxpbms9Imh0dHA6Ly93d3cudzMub3JnLzE5OTkveGxpbmsiIHg9IjBweCIgeT0iMHB4IgoJIHZpZXdCb3g9IjAgMCAyMDAuNyA0NSIgc3R5bGU9ImVuYWJsZS1iYWNrZ3JvdW5kOm5ldyAwIDAgMjAwLjcgNDU7IiB4bWw6c3BhY2U9InByZXNlcnZlIj4KPHN0eWxlIHR5cGU9InRleHQvY3NzIj4KCS5zdDB7ZmlsbDojRkZGRkZGO30KCS5zdDF7ZmlsbDojRkZGRkZGO3N0cm9rZTojMDAwMDAwO3N0cm9rZS13aWR0aDowLjE1NjE7fQoJLnN0MntmaWxsOiNGRkZGRkY7c3Ryb2tlOiMwMDAwMDA7fQo8L3N0eWxlPgo8ZyBpZD0iTGF5ZXJfMl8xXyI+CjwvZz4KPGc+Cgk8ZyBpZD0iTGF5ZXJfMV8xXyI+CgkJPHBhdGggY2xhc3M9InN0MCIgZD0iTTIyLjQsNDVDMTAsNDUsMCwzNC44LDAsMjIuNFMxMCwwLDIyLjQsMHMyMi40LDEwLDIyLjQsMjIuNEM0NC45LDM0LjgsMzQuOCw0NSwyMi40LDQ1eiBNMjIuNCwyLjUKCQkJYy0xMSwwLTIwLDktMjAsMjBzOSwyMCwyMCwyMHMyMC05LDIwLTIwQzQyLjQsMTEuNCwzMy41LDIuNSwyMi40LDIuNXoiLz4KCQk8cGF0aCBjbGFzcz0ic3QxIiBkPSJNMTcuMiwyNC45Ii8+CgkJPHBhdGggY2xhc3M9InN0MCIgZD0iTTIyLjQsNDIuM2wtMC40LTAuMWMtMC41LTAuMi0xMy4yLTUuOC0xMy4yLTE1LjlWOC4xaDI3LjJ2MTguNGMwLDkuNy0xMi42LDE1LjMtMTMuMiwxNS42TDIyLjQsNDIuM3oKCQkJIE0xMC44LDkuOXYxNi4zYzAsOC4xLDkuNywxMy4xLDExLjgsMTQuMWMyLTEsMTEuOC02LjEsMTEuOC0xMy43VjEwSDEwLjhDMTAuOCwxMCwxMC44LDkuOSwxMC44LDkuOXoiLz4KCQk8cGF0aCBjbGFzcz0ic3QwIiBkPSJNMTYuNywxOC44bC0wLjItMC4xYzAsMC0xLjUtMC45LTIuMy0xLjVjLTAuNy0wLjUtMS4xLTEuMS0xLjItMS42YzAtMC4xLDAtMS42LDAtNC41di0wLjZoNy43VjExCgkJCWMwLDIuOSwwLDQuNCwwLDQuNWMwLDAuNi0wLjQsMS4xLTEuMSwxLjZjLTEsMC42LTIuMywxLjUtMi40LDEuNUwxNi43LDE4Ljh6IE0xNCwxMS41YzAsMS42LDAsMy43LDAsMy45YzAsMC4xLDAuMiwwLjUsMC42LDAuNwoJCQljMC42LDAuNCwxLjUsMSwyLDEuMmMwLjUtMC4yLDEuNS0wLjksMi4xLTEuMmMwLjItMC4xLDAuNi0wLjQsMC42LTAuNmMwLTAuMiwwLTIuMiwwLTMuOUgxNEwxNCwxMS41TDE0LDExLjV6Ii8+CgkJPHBhdGggY2xhc3M9InN0MCIgZD0iTTI4LjcsMTguOGwtMC4yLTAuMWMwLDAtMS41LTAuOS0yLjMtMS41Yy0wLjctMC41LTEuMS0xLjEtMS4yLTEuNmMwLTAuMSwwLTEuNiwwLTQuNXYtMC42aDcuN1YxMQoJCQljMCwyLjksMCw0LjQsMCw0LjVjMCwwLjYtMC40LDEuMS0xLjEsMS42Yy0xLDAuNi0yLjMsMS41LTIuNCwxLjVMMjguNywxOC44eiBNMjYsMTEuNWMwLDEuNiwwLDMuNywwLDMuOWMwLDAuMSwwLjIsMC41LDAuNiwwLjcKCQkJYzAuNiwwLjQsMS41LDEsMiwxLjJjMC41LTAuMiwxLjUtMC45LDIuMS0xLjJjMC4yLTAuMSwwLjYtMC40LDAuNi0wLjZjMC0wLjIsMC0yLjIsMC0zLjlIMjZMMjYsMTEuNUwyNiwxMS41eiIvPgoJCTxyZWN0IHg9IjkuMyIgeT0iMTkuMSIgY2xhc3M9InN0MCIgd2lkdGg9IjI2LjUiIGhlaWdodD0iMS42Ii8+CgkJPGc+CgkJCTxnPgoJCQkJPHBhdGggY2xhc3M9InN0MCIgZD0iTTIyLjQsMzUuMmMtMC41LDAtMC43LTAuNC0wLjktMC41Yy0wLjEtMC4xLTAuMi0wLjItMC40LTAuMmMtMC43LDAtMS4yLDAtMS44LDAuMWMtMC42LDAtMS4yLDAuMS0yLjIsMC4xCgkJCQkJcy0xLjcsMC0xLjcsMGgtMC43VjIyLjNoMC43YzAuNSwwLDEuMSwwLDIuMSwwYzAuNSwwLDEtMC4xLDEuNi0wLjFjMC40LDAsMC43LTAuMSwxLjEtMC4xYzAuOS0wLjEsMS42LDAuMSwxLjcsMC4xCgkJCQkJYzAuMiwwLDAuNCwwLjEsMC42LDAuMmMwLjEtMC4xLDAuNC0wLjEsMC42LTAuMmMwLDAsMC45LTAuMSwxLjctMC4xYzAuNCwwLDAuNywwLjEsMS4xLDAuMWMwLjYsMC4xLDEuMSwwLjEsMS42LDAuMQoJCQkJCWMxLDAsMS42LDAsMi4xLDBoMC43djEyLjRoLTAuN2MwLDAtMC43LDAtMS43LDBjLTEsMC0xLjYtMC4xLTIuMi0wLjFjLTAuNiwwLTEuMS0wLjEtMS44LTAuMWMtMC4yLDAtMC4yLDAtMC40LDAuMgoJCQkJCUMyMy4yLDM1LDIyLjksMzUuMiwyMi40LDM1LjJ6IE0yMS4yLDMzLjFjMC42LDAsMS4xLDAuMiwxLjQsMC41YzAuMi0wLjIsMC43LTAuNSwxLjQtMC41YzAuNywwLDEuNCwwLDIsMC4xCgkJCQkJYzAuNiwwLDEuMiwwLjEsMi4xLDAuMWMwLjQsMCwwLjYsMCwwLjksMHYtOS41Yy0wLjQsMC0wLjksMC0xLjQsMGMtMC41LDAtMS4xLTAuMS0xLjctMC4xYy0wLjQsMC0wLjctMC4xLTEuMS0wLjEKCQkJCQljLTAuNi0wLjEtMS4yLDAtMS4yLDBjLTAuMSwwLTAuMiwwLjEtMC4yLDAuMXMwLDAsMC4xLTAuMWwtMC43LTAuMWwtMC43LDAuMWMwLDAuMSwwLDAuMSwwLjEsMC4xYzAsMCwwLDAtMC4yLTAuMWwwLDAKCQkJCQljMCwwLTAuNi0wLjEtMS4yLDBjLTAuNCwwLTAuNywwLjEtMS4xLDAuMWMtMC42LDAuMS0xLjIsMC4xLTEuNywwLjFjLTAuNiwwLTEsMC0xLjQsMHY5LjVjMC4yLDAsMC42LDAsMC45LDAKCQkJCQljMC45LDAsMS41LTAuMSwyLjEtMC4xQzE5LjksMzMuMSwyMC40LDMzLjEsMjEuMiwzMy4xeiIvPgoJCQk8L2c+CgkJPC9nPgoJCTxyZWN0IHg9IjEzLjQiIHk9IjEyLjgiIGNsYXNzPSJzdDAiIHdpZHRoPSI2LjQiIGhlaWdodD0iMS4xIi8+CgkJPHJlY3QgeD0iMjEuOCIgeT0iMTkuNSIgY2xhc3M9InN0MCIgd2lkdGg9IjEuNSIgaGVpZ2h0PSIyMS44Ii8+CgkJPHBvbHlnb24gY2xhc3M9InN0MCIgcG9pbnRzPSIzMS40LDE1LjIgMjguNiwxMy40IDI2LDE1LjIgMjUuMywxNC4zIDI4LjYsM
|
||
|
|
<source srcset="data:image/svg+xml;base64,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
|
||
|
|
|
||
|
|
</picture>
|
||
|
|
</a></div>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</header>
|
||
|
|
<main>
|
||
|
|
<div id=content>
|
||
|
|
<div id=abs-outer>
|
||
|
|
<div class=leftcolumn>
|
||
|
|
<div class=subheader>
|
||
|
|
<h1>Quantum Physics</h1>
|
||
|
|
</div>
|
||
|
|
<div class="header-breadcrumbs-mobile sf-hidden">
|
||
|
|
(quant-ph)
|
||
|
|
</div>
|
||
|
|
<style>#abs{font-family:"Lucida Grande",Helvetica,Arial,sans-serif!important}#abs h1.title{display:block;font-size:1.8em!important;font-weight:700;margin-block-end:12px;margin-block-start:12px;margin-bottom:12px;margin-inline-end:0px;margin-inline-start:20px;margin-left:20px;margin-right:0px;margin-top:12px}#abs div.authors{font-size:1.2em;line-height:24px;margin-bottom:8px;margin-left:20px;margin-right:0px;margin-top:8px}#abs div.dateline{font-size:0.9em;font-style:italic;margin-bottom:6.5px;margin-left:20px;margin-right:0px;margin-top:6.5px}#abs blockquote.abstract{font-size:1.05em;margin-block-end:21.6px;margin-block-start:14.4px;margin-bottom:21.6px;margin-inline-end:40px;margin-inline-start:40px;background-color:white;border-left:0px;padding:0px}#abs div.metatable{font-size:0.95em!important;margin-bottom:19px;margin-left:20px;margin-right:0px;margin-top:0px;border:0px;padding:0px}#abs div.metatable tbody{vertical-align:middle}#abs tr{margin-top:0px;margin-bottom:0px}#abs td.tablecell{padding-top:0px;padding-bottom:0px;padding-right:6.5px;padding-left:0px;vertical-align:top;font-size:0.95em!important;margin-top:0px;margin-bottom:0px;border:0px}#abs td.tablecell.label{font-weight:400!important}#abs span.primary-subject{font-weight:700}#abs span.arxivid{font-weight:700}</style>
|
||
|
|
<div id=content-inner>
|
||
|
|
<div id=abs>
|
||
|
|
<div class=dateline>
|
||
|
|
[Submitted on 12 Apr 2001]</div>
|
||
|
|
<h1 class="title mathjax"><span class="descriptor sf-hidden">Title:</span>Mechanical interpretation of the Klein-Gordon equation</h1>
|
||
|
|
<div class=authors><span class="descriptor sf-hidden">Authors:</span><a href="https://arxiv.org/search/quant-ph?searchtype=author&query=Dmitriyev,+V+P">V. P. Dmitriyev</a></div> <div id=download-button-info class=sf-hidden hidden>View a PDF of the paper titled Mechanical interpretation of the Klein-Gordon equation, by V. P. Dmitriyev</div>
|
||
|
|
<a class="mobile-submission-download sf-hidden" href=http://arxiv.org/pdf/quant-ph/0104066>View PDF</a>
|
||
|
|
<blockquote class="abstract mathjax">
|
||
|
|
<span class="descriptor sf-hidden">Abstract:</span> The substratum for physics can be seen microscopically as an ideal fluid pierced in all directions by the straight vortex filaments. Small disturbances of an isolated filament are considered. The Klein-Gordon equation without mass corresponds to elastic stretching of the filament. The wave function has the meaning of the curve's position vector. The mass part of the Klein-Gordon equation describes the rotation of the helical curve about the screw axis due to the hydrodynamic self-induction of the bent vortex filament.
|
||
|
|
</blockquote>
|
||
|
|
|
||
|
|
<div class=metatable>
|
||
|
|
<table summary="Additional metadata"> <tbody><tr>
|
||
|
|
<td class="tablecell label">Comments:</td>
|
||
|
|
<td class="tablecell comments mathjax">3 pages; see also <a href=http://xxx.lanl.gov/abs/quant-ph/0012008 rel="external noopener nofollow" class="link-external link-http">this http URL</a></td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td class="tablecell label">Subjects:</td>
|
||
|
|
<td class="tablecell subjects">
|
||
|
|
<span class=primary-subject>Quantum Physics (quant-ph)</span>; High Energy Physics - Theory (hep-th); Fluid Dynamics (physics.flu-dyn)</td>
|
||
|
|
<tr>
|
||
|
|
<td class="tablecell label">Cite as:</td>
|
||
|
|
<td class="tablecell arxivid"><span class=arxivid><a href=https://arxiv.org/abs/quant-ph/0104066>arXiv:quant-ph/0104066</a></span></td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td class="tablecell label"> </td>
|
||
|
|
<td class="tablecell arxividv">(or <span class=arxivid>
|
||
|
|
<a href=https://arxiv.org/abs/quant-ph/0104066v1>arXiv:quant-ph/0104066v1</a></span> for this version)
|
||
|
|
</td>
|
||
|
|
</tr> <tr>
|
||
|
|
<td class="tablecell label"> </td>
|
||
|
|
<td class="tablecell arxivdoi">
|
||
|
|
<a href=https://doi.org/10.48550/arXiv.quant-ph/0104066>https://doi.org/10.48550/arXiv.quant-ph/0104066</a>
|
||
|
|
<div class=button-and-tooltip>
|
||
|
|
<button class=more-info aria-describedby=more-info-desc-1>
|
||
|
|
<svg height=15 role=presentation xmlns=http://www.w3.org/2000/svg viewBox="0 0 512 512"><path fill=currentColor d="M256 8C119.043 8 8 119.083 8 256c0 136.997 111.043 248 248 248s248-111.003 248-248C504 119.083 392.957 8 256 8zm0 110c23.196 0 42 18.804 42 42s-18.804 42-42 42-42-18.804-42-42 18.804-42 42-42zm56 254c0 6.627-5.373 12-12 12h-88c-6.627 0-12-5.373-12-12v-24c0-6.627 5.373-12 12-12h12v-64h-12c-6.627 0-12-5.373-12-12v-24c0-6.627 5.373-12 12-12h64c6.627 0 12 5.373 12 12v100h12c6.627 0 12 5.373 12 12v24z"></path></svg>
|
||
|
|
<span class=visually-hidden>Focus to learn more</span>
|
||
|
|
</button>
|
||
|
|
|
||
|
|
<div role=tooltip id=more-info-desc-1 class=sf-hidden>
|
||
|
|
|
||
|
|
arXiv-issued DOI via DataCite
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</td>
|
||
|
|
</table>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
<div class=submission-history>
|
||
|
|
<h2>Submission history</h2> From: Valery P. Dmitriyev [<a href=http://arxiv.org/show-email/4244873d/quant-ph/0104066>view email</a>] <br> <strong>[v1]</strong>
|
||
|
|
Thu, 12 Apr 2001 20:38:28 UTC (34 KB)<br>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div class=extra-services> <div class=full-text>
|
||
|
|
<a name=other></a>
|
||
|
|
<span class="descriptor sf-hidden">Full-text links:</span>
|
||
|
|
<h2>Access Paper:</h2>
|
||
|
|
<ul>
|
||
|
|
<div id=download-button-info class=sf-hidden hidden>
|
||
|
|
View a PDF of the paper titled Mechanical interpretation of the Klein-Gordon equation, by V. P. Dmitriyev</div><li><a href=http://arxiv.org/pdf/quant-ph/0104066 aria-describedby=download-button-info accesskey=f class="abs-button download-pdf">View PDF</a><li><a href=http://arxiv.org/src/quant-ph/0104066 class="abs-button download-eprint">TeX Source</a><li><a href=http://arxiv.org/format/quant-ph/0104066 class="abs-button download-format">Other Formats</a></ul>
|
||
|
|
<div class=abs-license><a href=http://arxiv.org/licenses/assumed-1991-2003/ title="Rights to this article">view license</a></div>
|
||
|
|
</div>
|
||
|
|
<div class=browse>
|
||
|
|
Current browse context: <div class=current>quant-ph</div>
|
||
|
|
<div class=prevnext>
|
||
|
|
<span class=arrow>
|
||
|
|
<a class="abs-button prev-url" href="http://arxiv.org/prevnext?id=quant-ph/0104066&function=prev&context=quant-ph" accesskey=p title="previous in quant-ph (accesskey p)">< prev</a>
|
||
|
|
</span>
|
||
|
|
<span class=is-hidden-mobile> | </span> <span class=arrow>
|
||
|
|
<a class="abs-button next-url" href="http://arxiv.org/prevnext?id=quant-ph/0104066&function=next&context=quant-ph" accesskey=n title="next in quant-ph (accesskey n)">next ></a>
|
||
|
|
</span><br>
|
||
|
|
</div><div class=list>
|
||
|
|
<a class="abs-button abs-button-grey abs-button-small context-new" href=http://arxiv.org/list/quant-ph/new>new</a>
|
||
|
|
<span class=is-hidden-mobile> | </span>
|
||
|
|
<a class="abs-button abs-button-grey abs-button-small context-recent" href=http://arxiv.org/list/quant-ph/recent>recent</a>
|
||
|
|
<span class=is-hidden-mobile> | </span><a class="abs-button abs-button-grey abs-button-small context-id" href=http://arxiv.org/list/quant-ph/2001-04>2001-04</a>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
<div class=extra-ref-cite>
|
||
|
|
<h3>References & Citations</h3>
|
||
|
|
<ul>
|
||
|
|
<li>
|
||
|
|
<a class="abs-button abs-button-small cite-inspire" href=https://inspirehep.net/arxiv/quant-ph/0104066>INSPIRE HEP</a><br>
|
||
|
|
</li>
|
||
|
|
<li><a class="abs-button abs-button-small cite-ads" href=https://ui.adsabs.harvard.edu/abs/arXiv:quant-ph%2F0104066>NASA ADS</a><li><a class="abs-button abs-button-small cite-google-scholar" href="https://scholar.google.com/scholar_lookup?arxiv_id=quant-ph/0104066" target=_blank rel=noopener>Google Scholar</a></li>
|
||
|
|
<li><a class="abs-button abs-button-small cite-semantic-scholar" href=https://api.semanticscholar.org/arXiv:quant-ph/0104066 target=_blank rel=noopener>Semantic Scholar</a></li>
|
||
|
|
</ul>
|
||
|
|
<div style=clear:both></div>
|
||
|
|
</div>
|
||
|
|
<div class=extra-ref-cite>
|
||
|
|
<a id=bib-cite-css href=http://arxiv.org/static/browse/0.3.4/css/cite.css class=sf-hidden hidden>a</a>
|
||
|
|
<span id=bib-cite-trigger class="bib-cite-button abs-button">export BibTeX citation</span>
|
||
|
|
<span id=bib-cite-loading class=sf-hidden hidden>Loading...</span>
|
||
|
|
</div>
|
||
|
|
<div id=bib-cite-modal class="bib-modal sf-hidden" hidden>
|
||
|
|
|
||
|
|
</div><div class=bookmarks>
|
||
|
|
<div><h3>Bookmark</h3></div><a class="abs-button abs-button-grey abs-button-small" href="http://www.bibsonomy.org/BibtexHandler?requTask=upload&url=https://arxiv.org/abs/quant-ph/0104066&description=Mechanical%20interpretation%20of%20the%20Klein-Gordon%20equation" title="Bookmark on BibSonomy">
|
||
|
|
<img src=data:image/png;base64,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 alt="BibSonomy logo">
|
||
|
|
</a>
|
||
|
|
<a class="abs-button abs-button-grey abs-button-small" href="https://reddit.com/submit?url=https://arxiv.org/abs/quant-ph/0104066&title=Mechanical%20interpretation%20of%20the%20Klein-Gordon%20equation" title="Bookmark on Reddit">
|
||
|
|
<img src="data:image/png;base64,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" alt="Reddit logo">
|
||
|
|
</a>
|
||
|
|
</div> </div>
|
||
|
|
|
||
|
|
<div id=labstabs>
|
||
|
|
<div class=labstabs><input name=tabs id=tabone checked class=sf-hidden type=radio>
|
||
|
|
<label for=tabone>Bibliographic Tools</label>
|
||
|
|
<div class="tab labs-display-bib">
|
||
|
|
<h1>Bibliographic and Citation Tools</h1>
|
||
|
|
<div class=toggle>
|
||
|
|
<div class="columns is-mobile lab-row">
|
||
|
|
<div class="column lab-switch">
|
||
|
|
<label class=switch>
|
||
|
|
<input id=bibex-toggle class="lab-toggle sf-hidden" type=checkbox>
|
||
|
|
<span class=slider></span>
|
||
|
|
<span class=is-sr-only>Bibliographic Explorer Toggle</span>
|
||
|
|
</label>
|
||
|
|
</div>
|
||
|
|
<div class="column lab-name">
|
||
|
|
<span id=label-for-bibex>Bibliographic Explorer</span> <em>(<a href=https://info.arxiv.org/labs/showcase.html#arxiv-bibliographic-explorer>What is the Explorer?</a>)</em>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
<div class="columns is-mobile lab-row">
|
||
|
|
<div class="column lab-switch">
|
||
|
|
<label class=switch>
|
||
|
|
<input id=litmaps-toggle class="lab-toggle sf-hidden" data-script-url=/static/browse/0.3.4/js/litmaps.js?20210617 aria-labelledby=label-for-litmaps type=checkbox>
|
||
|
|
<span class=slider></span>
|
||
|
|
<span class=is-sr-only>Litmaps Toggle</span>
|
||
|
|
</label>
|
||
|
|
</div>
|
||
|
|
<div class="column lab-name">
|
||
|
|
<span id=label-for-litmaps>Litmaps</span> <em>(<a href=https://www.litmaps.co/ target=_blank>What is Litmaps?</a>)</em>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
<div class="columns is-mobile lab-row">
|
||
|
|
<div class="column lab-switch">
|
||
|
|
<label class=switch>
|
||
|
|
<input id=scite-toggle class="lab-toggle sf-hidden" data-script-url=/static/browse/0.3.4/js/scite.js?20210617 aria-labelledby=label-for-scite type=checkbox>
|
||
|
|
<span class=slider></span>
|
||
|
|
<span class=is-sr-only>scite.ai Toggle</span>
|
||
|
|
</label>
|
||
|
|
</div>
|
||
|
|
<div class="column lab-name">
|
||
|
|
<span id=label-for-scite>scite Smart Citations</span> <em>(<a href=https://www.scite.ai/ target=_blank>What are Smart Citations?</a>)</em>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
<div class="labs-content-placeholder labs-display" style=display:none></div>
|
||
|
|
<div style=min-height:15px id=litmaps-open-in></div>
|
||
|
|
<div style=min-height:15px id=scite-open-in></div>
|
||
|
|
</div>
|
||
|
|
<input name=tabs id=tabtwo class=sf-hidden type=radio>
|
||
|
|
<label for=tabtwo>Code, Data, Media</label>
|
||
|
|
<div class="tab sf-hidden">
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</div>
|
||
|
|
<input name=tabs id=labstabs-demos-input class=sf-hidden type=radio>
|
||
|
|
<label for=labstabs-demos-input id=labstabs-demos-label>Demos</label>
|
||
|
|
<div class="tab sf-hidden">
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</div>
|
||
|
|
<input name=tabs id=tabfour class=sf-hidden type=radio>
|
||
|
|
<label for=tabfour>Related Papers</label>
|
||
|
|
<div class="tab sf-hidden">
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</div>
|
||
|
|
<input name=tabs id=tabfive class=sf-hidden type=radio>
|
||
|
|
<label for=tabfive>
|
||
|
|
About arXivLabs
|
||
|
|
</label>
|
||
|
|
<div class="tab sf-hidden">
|
||
|
|
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
<div class=endorsers>
|
||
|
|
<a href=http://arxiv.org/auth/show-endorsers/quant-ph/0104066 class=endorser-who>Which authors of this paper are endorsers?</a> |
|
||
|
|
<a id=mathjax_toggle>Disable MathJax</a> (<a href=https://info.arxiv.org/help/mathjax.html>What is MathJax?</a>)
|
||
|
|
<span class=help style=font-style:normal;float:right;margin-top:0;margin-right:1em></span>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</main>
|
||
|
|
<footer style=clear:both>
|
||
|
|
<div class="columns is-desktop" role=navigation aria-label=Secondary style="margin:-0.75em -0.75em 0.75em -0.75em">
|
||
|
|
|
||
|
|
<div class=column style=padding:0>
|
||
|
|
<div class=columns>
|
||
|
|
<div class=column>
|
||
|
|
<ul style=list-style:none;line-height:2>
|
||
|
|
<li><a href=https://info.arxiv.org/about>About</a></li>
|
||
|
|
<li><a href=https://info.arxiv.org/help>Help</a></li>
|
||
|
|
</ul>
|
||
|
|
</div>
|
||
|
|
<div class=column>
|
||
|
|
<ul style=list-style:none;line-height:2>
|
||
|
|
<li>
|
||
|
|
<svg xmlns=http://www.w3.org/2000/svg viewBox="0 0 512 512" class="icon filter-black" role=presentation><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"></path></svg>
|
||
|
|
<a href=https://info.arxiv.org/help/contact.html> Contact</a>
|
||
|
|
</li>
|
||
|
|
<li>
|
||
|
|
<svg xmlns=http://www.w3.org/2000/svg viewBox="0 0 512 512" class="icon filter-black" role=presentation><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"></path></svg>
|
||
|
|
<a href=https://info.arxiv.org/help/subscribe> Subscribe</a>
|
||
|
|
</li>
|
||
|
|
</ul>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
|
||
|
|
<div class=column style=padding:0>
|
||
|
|
<div class=columns>
|
||
|
|
<div class=column>
|
||
|
|
<ul style=list-style:none;line-height:2>
|
||
|
|
<li><a href=https://info.arxiv.org/help/license/index.html>Copyright</a></li>
|
||
|
|
<li><a href=https://info.arxiv.org/help/policies/privacy_policy.html>Privacy Policy</a></li>
|
||
|
|
</ul>
|
||
|
|
</div>
|
||
|
|
<div class="column sorry-app-links">
|
||
|
|
<ul style=list-style:none;line-height:2>
|
||
|
|
<li><a href=https://info.arxiv.org/help/web_accessibility.html>Web Accessibility Assistance</a></li>
|
||
|
|
<li>
|
||
|
|
<p class=help>
|
||
|
|
<a class=a11y-main-link href=https://status.arxiv.org/ target=_blank>arXiv Operational Status <svg xmlns=http://www.w3.org/2000/svg viewBox="0 0 256 512" class="icon filter-dark_grey" role=presentation><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"></path></svg></a><br>
|
||
|
|
Get status notifications via
|
||
|
|
<a class=is-link href=https://subscribe.sorryapp.com/24846f03/email/new target=_blank><svg xmlns=http://www.w3.org/2000/svg viewBox="0 0 512 512" class="icon filter-black" role=presentation><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"></path></svg>email</a>
|
||
|
|
or <a class=is-link href=https://subscribe.sorryapp.com/24846f03/slack/new target=_blank><svg xmlns=http://www.w3.org/2000/svg viewBox="0 0 448 512" class="icon filter-black" role=presentation><path d="M94.12 315.1c0 25.9-21.16 47.06-47.06 47.06S0 341 0 315.1c0-25.9 21.16-47.06 47.06-47.06h47.06v47.06zm23.72 0c0-25.9 21.16-47.06 47.06-47.06s47.06 21.16 47.06 47.06v117.84c0 25.9-21.16 47.06-47.06 47.06s-47.06-21.16-47.06-47.06V315.1zm47.06-188.98c-25.9 0-47.06-21.16-47.06-47.06S139 32 164.9 32s47.06 21.16 47.06 47.06v47.06H164.9zm0 23.72c25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06H47.06C21.16 243.96 0 222.8 0 196.9s21.16-47.06 47.06-47.06H164.9zm188.98 47.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06h-47.06V196.9zm-23.72 0c0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06V79.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06V196.9zM283.1 385.88c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06v-47.06h47.06zm0-23.72c-25.9 0-47.06-21.16-47.06-47.06 0-25.9 21.16-47.06 47.06-47.06h117.84c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06H283.1z"></path></svg>slack</a>
|
||
|
|
</p>
|
||
|
|
</li>
|
||
|
|
</ul>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
</footer>
|
||
|
|
</div>
|
||
|
|
|