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special relativity in nLab |
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</title> |
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|
background-color:#707; |
|
|
color:#FFF; |
|
|
} |
|
|
.web_protected a:hover.existingWikiWord[title], .web_normal a:hover.existingWikiWord[title] { |
|
|
background-color:#000; |
|
|
color:#FFF; |
|
|
} |
|
|
|
|
|
div.errorExplanation p,div.errorExplanation li { |
|
|
border:none; |
|
|
margin:0; |
|
|
padding:0; |
|
|
} |
|
|
|
|
|
textarea#content { |
|
|
font-size: 1em; |
|
|
line-height: 1.125; |
|
|
} |
|
|
|
|
|
ul#sortable_pages { |
|
|
list-style-type:none; |
|
|
padding-left:0; |
|
|
} |
|
|
ul#sortable_pages li { |
|
|
border: 1px solid #FFF; |
|
|
} |
|
|
ul#sortable_pages li:hover, ul#sortable_pages li:focus { |
|
|
border: 1px solid blue; |
|
|
} |
|
|
|
|
|
merror {display:inline;font-size:1em;} |
|
|
math[display=block] {overflow:auto;overflow-y:hidden} |
|
|
math { white-space: nowrap } |
|
|
.maruku-eq-number {float:right} |
|
|
.maruku-equation {text-align:center} |
|
|
.blockquotesource {margin-left:1em;} |
|
|
fieldset.search {display:inline; border:none;padding:0;margin:0;top:5px;position:relative;} |
|
|
span.keyboard { |
|
|
background: #CCC; |
|
|
color: #000; |
|
|
border: outset 2px; |
|
|
font-family:"Noto Sans", Roboto, "Lucida Grande", "San Francisco", sans-serif; |
|
|
font-size: .7em; |
|
|
margin-left:5px; |
|
|
padding:1px 2px; |
|
|
} |
|
|
.centeredfigure { |
|
|
position:relative; |
|
|
margin:auto; |
|
|
text-align:center; |
|
|
} |
|
|
|
|
|
body {counter-reset: theorem} |
|
|
.un_theorem, .num_theorem, |
|
|
.un_lemma, .num_lemma, |
|
|
.un_prop, .num_prop, |
|
|
.un_cor, .num_cor {font-style: italic} |
|
|
span.theorem_label {font-style:normal; font-weight:bold;} |
|
|
.proof span.theorem_label {font-style:italic;} |
|
|
.tombstone {text-align:right;} |
|
|
|
|
|
|
|
|
[mathvariant="bold"] * { |
|
|
font-style: normal; |
|
|
font-variant: normal; |
|
|
font-weight: bold; |
|
|
} |
|
|
[mathvariant="italic"] * { |
|
|
font-style: italic; |
|
|
font-variant: normal; |
|
|
font-weight: normal; |
|
|
} |
|
|
[mathvariant="bold-italic"] * { |
|
|
font-style: italic; |
|
|
font-variant: normal; |
|
|
font-weight: bold; |
|
|
} |
|
|
[mathvariant="sans-serif"] * { |
|
|
font-style: normal; |
|
|
font-variant: normal; |
|
|
font-weight: normal; |
|
|
} |
|
|
[mathvariant="bold-sans-serif"] * { |
|
|
font-style: normal; |
|
|
font-variant: normal; |
|
|
font-weight: bold; |
|
|
} |
|
|
[mathvariant="sans-serif-italic"] * { |
|
|
font-style: italic; |
|
|
font-variant: normal; |
|
|
font-weight: normal; |
|
|
} |
|
|
[mathvariant="sans-serif-bold-italic"] * { |
|
|
font-style: italic; |
|
|
font-variant: normal; |
|
|
font-weight: bold; |
|
|
} |
|
|
[actiontype="toggle"]:hover {text-shadow: #ccc 2px 2px 5px;} |
|
|
.maruku_toc ul { list-style: none; } |
|
|
[actiontype="toggle"]:hover {text-shadow: #ccc 2px 2px 5px;} |
|
|
.nlab_toc ul { list-style: none; } |
|
|
|
|
|
|
|
|
math {font-family: STIX Two Math;} |
|
|
mtext {font-family: STIX Two Text;} |
|
|
.mathscript { |
|
|
font-variant-alternates: styleset(ss01); |
|
|
font-feature-settings: "ss01" on; |
|
|
} |
|
|
|
|
|
@font-face { |
|
|
font-family: STIX Two Text; |
|
|
src: local('STIX Two Text'), local('STIX2Text-Regular'), |
|
|
url('../fonts/STIX2Text-Regular.woff2'), url('../fonts/STIX2Text-Regular.woff'); |
|
|
} |
|
|
@font-face { |
|
|
font-family: STIX Two Text; |
|
|
src: local('STIX Two Text Bold'), local('STIX2Text-Bold'), |
|
|
url('../fonts/STIX2Text-Bold.woff2'), url('../fonts/STIX2Text-Bold.woff'); |
|
|
font-weight: bold; |
|
|
} |
|
|
@font-face { |
|
|
font-family: STIX Two Text; |
|
|
src: local('STIX Two Text Italic'), local('STIX2Text-Italic'), |
|
|
url('../fonts/STIX2Text-Italic.woff2'), url('../fonts/STIX2Text-Italic.woff'); |
|
|
font-style: italic; |
|
|
} |
|
|
@font-face { |
|
|
font-family: STIX Two Text; |
|
|
src: local('STIX Two Text Bold Italic'), local('STIX2Text-BoldItalic'), |
|
|
url('../fonts/STIX2Text-BoldItalic.woff2'), url('../fonts/STIX2Text-BoldItalic.woff'); |
|
|
font-weight: bold; |
|
|
font-style: italic; |
|
|
} |
|
|
@font-face { |
|
|
font-family: STIX Two Math; |
|
|
src: local('STIX Two Math'), local('STIX2Math'), |
|
|
url('../fonts/STIX2Math.woff2'), url('../fonts/STIX2Math.woff'); |
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
@font-face { |
|
|
font-family: Stix Mathematics; |
|
|
src: url("/fonts/STIXMath-Regular.otf") format("opentype"); |
|
|
} |
|
|
|
|
|
span.mathematics { |
|
|
|
|
|
|
|
|
font-style: italic; |
|
|
font-family: DejaVu Math TeX Gyre; sans-serif; Stix Mathematics; |
|
|
} |
|
|
|
|
|
|
|
|
|
|
|
pre.ansic .normal {} |
|
|
pre.ansic .comment { color: #00F; } |
|
|
pre.ansic .keyword { color: #A00; } |
|
|
pre.ansic .predefined_types { color: #D00; } |
|
|
pre.ansic .char { color: #F07; } |
|
|
pre.ansic .ident { color: #004; } |
|
|
pre.ansic .hex { color: #F99; } |
|
|
pre.ansic .oct { color: #F99; } |
|
|
pre.ansic .integer { color: #F99; } |
|
|
pre.ansic .float { color: #F99; } |
|
|
pre.ansic .string { color: #494; } |
|
|
pre.ansic .preprocessor { color: #D0D; } |
|
|
pre.ansic .other { color: black; } |
|
|
|
|
|
pre.fortran .normal {} |
|
|
pre.fortran .string { color: #494; } |
|
|
pre.fortran .number { color: #D0D; } |
|
|
pre.fortran .comment { color: #00F; } |
|
|
pre.fortran .keyword { color: #A00; } |
|
|
pre.fortran .type { color: #D00; } |
|
|
pre.fortran .symbol { color: #008B8B; } |
|
|
pre.fortran .function { color: #F07; } |
|
|
|
|
|
pre.css21 .normal {} |
|
|
pre.css21 .comment { color: #888; } |
|
|
pre.css21 .cdo { color: #666; } |
|
|
pre.css21 .cdc { color: #666; } |
|
|
pre.css21 .string { color: #494; } |
|
|
pre.css21 .invalid { color: #FF0000; } |
|
|
pre.css21 .keyword { color: #BB0000; } |
|
|
pre.css21 .property {font-size: 1em; color: #ff4500; } |
|
|
pre.css21 .ident { color: #000080; } |
|
|
pre.css21 .id { color: #0000FF; } |
|
|
pre.css21 .important { color: #EE0000; background: #ffd700;} |
|
|
|
|
|
pre.css21 .import { color: #A0A; } |
|
|
pre.css21 .page { color: #A0A; } |
|
|
pre.css21 .media { color: #A0A; } |
|
|
pre.css21 .charset { color: #A0A; } |
|
|
pre.css21 .uri { color: #7BB; } |
|
|
pre.css21 .function { color: #077; } |
|
|
|
|
|
pre.css21 .hash { color: #07F; } |
|
|
pre.css21 .ems { color: #07F; } |
|
|
pre.css21 .exs { color: #07F; } |
|
|
pre.css21 .length { color: #07F; } |
|
|
pre.css21 .angle { color: #07F; } |
|
|
pre.css21 .time { color: #07F; } |
|
|
pre.css21 .freq { color: #07F; } |
|
|
pre.css21 .dimension { color: #07F; } |
|
|
pre.css21 .percentage { color: #07F; } |
|
|
pre.css21 .number { color: #07F; } |
|
|
|
|
|
pre.css21 .tag { color: #008000; } |
|
|
|
|
|
pre.javascript .normal {} |
|
|
pre.javascript .comment { color: #00A; } |
|
|
pre.javascript .keyword { color: #A00; } |
|
|
pre.javascript .predefined_types { color: #DD0000; } |
|
|
pre.javascript .char { color: #F07; } |
|
|
pre.javascript .ident { color: #004; } |
|
|
pre.javascript .hex { color: #F99; } |
|
|
pre.javascript .oct { color: #F99; } |
|
|
pre.javascript .integer { color: #F99; } |
|
|
pre.javascript .float { color: #F99; } |
|
|
pre.javascript .unicode { color: #F99; } |
|
|
pre.javascript .string { color: #494;} |
|
|
pre.javascript .other { color: #808; } |
|
|
|
|
|
pre.sqlite .normal {} |
|
|
pre.sqlite .comment { color: #33F; } |
|
|
pre.sqlite .function { color: #077; } |
|
|
pre.sqlite .keyword { color: #A00; } |
|
|
pre.sqlite .operator { color: #0A0; } |
|
|
pre.sqlite .datatype { color: #DD0000; } |
|
|
pre.sqlite .ident { color: #004; } |
|
|
pre.sqlite .string { color: #A4A; } |
|
|
pre.sqlite .other { color: black; } |
|
|
|
|
|
pre.yaml .normal {} |
|
|
pre.yaml .document { font-weight: bold; color: #07F; } |
|
|
pre.yaml .type { font-weight: bold; color: #05C; } |
|
|
pre.yaml .key { color: #F88; } |
|
|
pre.yaml .comment { color: #005; font-style: italic; } |
|
|
pre.yaml .punct { color: #447; font-weight: bold; } |
|
|
pre.yaml .string { color: #944; } |
|
|
pre.yaml .number { color: #F99; } |
|
|
pre.yaml .time { color: #F99; } |
|
|
pre.yaml .date { color: #F99; } |
|
|
pre.yaml .ref { color: #944; } |
|
|
pre.yaml .anchor { color: #944; } |
|
|
|
|
|
pre.ruby .normal {} |
|
|
pre.ruby span.attribute { color: #090; } |
|
|
pre.ruby span.char { color: #F00; } |
|
|
pre.ruby span.class { color: #A020F0; font-weight: bold; } |
|
|
pre.ruby span.comment { color: #00F; } |
|
|
pre.ruby span.constant { color: #008B8B; } |
|
|
pre.ruby span.escape { color: #6A5ACD; } |
|
|
pre.ruby span.expr { color: #22C; } |
|
|
pre.ruby span.global { color: #1A4; } |
|
|
pre.ruby span.ident { color: #004; } |
|
|
pre.ruby span.keyword { color: #A52A2A; font-weight: bold; } |
|
|
pre.ruby span.method { color: #008B8B; } |
|
|
pre.ruby span.module { color: #A020F0; font-weight: bold; } |
|
|
pre.ruby span.number { color: #D0D; } |
|
|
pre.ruby span.punct { color: #6A5ACD; } |
|
|
pre.ruby span.regex { color: #D0D; } |
|
|
pre.ruby span.string { color: #D0D; } |
|
|
pre.ruby span.symbol { color: #008B8B; } |
|
|
|
|
|
pre.xml .normal {} |
|
|
pre.xml .namespace { color: #D66; font-weight: bold; } |
|
|
pre.xml .tag { color: #F55; } |
|
|
pre.xml .comment { color: #070; font-style: italic; } |
|
|
pre.xml .punct { color: #449; font-weight: bold; } |
|
|
pre.xml .string { color: #949; } |
|
|
pre.xml .number { color: #F99; } |
|
|
pre.xml .attribute { color: #771; } |
|
|
|
|
|
|
|
|
|
|
|
body { |
|
|
font-family: "DejaVu Serif", "Cambria", Serif !important; |
|
|
font-size: 18px; |
|
|
text-align: justify; |
|
|
} |
|
|
h1, h2, h3, h4, h5, h6 { |
|
|
font-family: "DejaVu Serif", "Cambria", Serif !important; |
|
|
font-weight: normal; |
|
|
margin-top: 0.8em; |
|
|
margin-bottom: 0.8em; |
|
|
} |
|
|
h1 { |
|
|
font-size: 1.6em; |
|
|
margin-bottom: 0.6em; |
|
|
} |
|
|
h2 { |
|
|
font-size: 1.6em; |
|
|
margin-bottom: 0.6em; |
|
|
} |
|
|
h3 { |
|
|
font-weight: bold; |
|
|
font-style: italic; |
|
|
font-size: 1.25em; |
|
|
} |
|
|
h4 { |
|
|
font-weight: bold; |
|
|
font-size: 1.2em; |
|
|
} |
|
|
h5 { |
|
|
font-weight: bold; |
|
|
font-size: 1.1em; |
|
|
} |
|
|
h6 { |
|
|
font-weight: bold; |
|
|
font-size: 1.05em; |
|
|
} |
|
|
li p { |
|
|
margin-top: 0em; |
|
|
margin-bottom: 0em; |
|
|
} |
|
|
.query { |
|
|
border-radius: 3px; |
|
|
padding: 0 40px; |
|
|
border-width: 1px; |
|
|
margin: 40px 0; |
|
|
} |
|
|
strong { |
|
|
font-style: italic; |
|
|
} |
|
|
span.theorem_label { |
|
|
font-style: italic; |
|
|
} |
|
|
a { |
|
|
text-decoration: underline; |
|
|
color: #2222AA; |
|
|
} |
|
|
a:hover { |
|
|
color: #2c66d8; |
|
|
background: none; |
|
|
text-decoration: underline; |
|
|
} |
|
|
a:hover.existingWikiWord { |
|
|
color: #2c66d8; |
|
|
background: none; |
|
|
} |
|
|
a:visited:hover.existingWikiWord { |
|
|
color: #2c66d8; |
|
|
background: none; |
|
|
} |
|
|
|
|
|
img, svg { |
|
|
margin: 40px auto 10px; |
|
|
display: block; |
|
|
} |
|
|
h1#pageName { |
|
|
font-size: 2.5em; |
|
|
margin-top: 1.0em; |
|
|
margin-bottom: 0.4em; |
|
|
color: #000; |
|
|
} |
|
|
.maruku-equation { |
|
|
font-size: 1.05em; |
|
|
margin: 1.05em auto 1.05em auto; |
|
|
} |
|
|
.navigation:not(.navfoot) { |
|
|
position: absolute; |
|
|
top: 10px; |
|
|
right: 20px; |
|
|
padding: 15px; |
|
|
color: #888; |
|
|
font-size: 0; |
|
|
} |
|
|
.navigation a { |
|
|
color: #888!important; |
|
|
font-size: 13px; |
|
|
margin: 0 20px 0 0; |
|
|
font-family: Sans-Serif; |
|
|
font-weight: lighter; |
|
|
} |
|
|
.navigation a:hover { |
|
|
color: #555!important; |
|
|
background:none; |
|
|
} |
|
|
.navigation.navfoot { |
|
|
margin: 20px 0px; |
|
|
} |
|
|
a.navlinkbackintime { |
|
|
margin: 0 0 0 0; |
|
|
} |
|
|
span.backintime { |
|
|
color: #888!important; |
|
|
font-size: 13px; |
|
|
font-family: Sans-Serif; |
|
|
margin: 0 20px 0 0; |
|
|
} |
|
|
#pageName > span { |
|
|
position: absolute; |
|
|
font-size: .45em; |
|
|
top: 10px; |
|
|
left: 20px; |
|
|
} |
|
|
#pageName > span > svg { |
|
|
margin: 0; |
|
|
} |
|
|
#pageName > span.webName { |
|
|
left: 70px; |
|
|
top: 22px; |
|
|
color: #555; |
|
|
font-family: Sans-Serif; |
|
|
font-weight: lighter; |
|
|
} |
|
|
|
|
|
.maruku_toc li{ |
|
|
font-size: 19px; |
|
|
} |
|
|
.maruku_toc li a{ |
|
|
color: #226622; |
|
|
} |
|
|
.maruku_toc li a:hover { |
|
|
color: #2c66d8; |
|
|
} |
|
|
.maruku_toc li a:visited{ |
|
|
color: #164416; |
|
|
} |
|
|
|
|
|
.maruku_toc li a:visited:hover{ |
|
|
color: #2c66d8; |
|
|
} |
|
|
|
|
|
div.rightHandSide { |
|
|
border-radius: 3px; |
|
|
border: 1px solid rgba(0, 0, 0, 0.1); |
|
|
border-right: 0; |
|
|
border-top: 0; |
|
|
font-size: 14px; |
|
|
} |
|
|
.rightHandSide p { |
|
|
font-size: 14px; |
|
|
} |
|
|
.rightHandSide li { |
|
|
font-size: 14px; |
|
|
} |
|
|
.rightHandSide h3 { |
|
|
margin-top: 20px; |
|
|
font-size: 16px; |
|
|
} |
|
|
.rightHandSide h4 { |
|
|
font-size: 15px; |
|
|
} |
|
|
.rightHandSide h2 { |
|
|
font-size: 15px !important; |
|
|
margin-top: 15px; |
|
|
margin-bottom: 10px; |
|
|
} |
|
|
|
|
|
h1#contents { |
|
|
font-size: 1.8em; |
|
|
} |
|
|
input[type=text]#searchField { |
|
|
width: 100%; |
|
|
padding: 5px 10px; |
|
|
display: inline-block; |
|
|
border: 1px solid #ccc; |
|
|
border-radius: 4px; |
|
|
box-sizing: border-box; |
|
|
font-size: 13px; |
|
|
margin-bottom: -5px; |
|
|
margin-left: 10px; |
|
|
color: #555; |
|
|
} |
|
|
table { |
|
|
border: 0; |
|
|
margin: auto; |
|
|
} |
|
|
td, th { |
|
|
border: 1px solid #dddddd; |
|
|
text-align: left; |
|
|
padding: 8px; |
|
|
} |
|
|
|
|
|
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Context |
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Physics |
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physics |
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, |
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mathematical physics |
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philosophy of physics |
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Surveys, textbooks and lecture notes |
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(higher) category theory and physics |
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<a class="existingWikiWord"> |
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geometry of physics |
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books and reviews |
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, |
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physics resources |
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theory (physics) |
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, |
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model (physics) |
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experiment |
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measurement |
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computable physics |
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mechanics |
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mass |
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, |
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charge |
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, |
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momentum |
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, |
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angular momentum |
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moment of inertia |
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dynamics on Lie groups |
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<a class="existingWikiWord"> |
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rigid body dynamics |
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field (physics) |
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Lagrangian mechanics |
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<a class="existingWikiWord"> |
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configuration space |
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, |
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state |
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action functional |
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<a class="existingWikiWord"> |
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Lagrangian |
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covariant phase space |
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Euler-Lagrange equations |
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Hamiltonian mechanics |
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phase space |
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<a class="existingWikiWord"> |
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symplectic geometry |
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<a class="existingWikiWord"> |
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Poisson manifold |
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</li> |
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<p> |
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<a class="existingWikiWord"> |
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symplectic manifold |
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</li> |
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<p> |
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<a class="existingWikiWord"> |
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symplectic groupoid |
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</p> |
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</li> |
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</li> |
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<a class="existingWikiWord"> |
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multisymplectic geometry |
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<a class="existingWikiWord"> |
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n-symplectic manifold |
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</a> |
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</ul> |
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</ul> |
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spacetime |
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<li> |
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<p> |
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<a class="existingWikiWord"> |
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smooth Lorentzian manifold |
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</a> |
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</p> |
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</li> |
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<li> |
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<p> |
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<a class="existingWikiWord"> |
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special relativity |
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</li> |
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<a class="existingWikiWord"> |
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general relativity |
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gravity |
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supergravity |
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, |
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<a class="existingWikiWord"> |
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dilaton gravity |
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</a> |
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</li> |
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black hole |
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</li> |
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</ul> |
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</li> |
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</ul> |
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<strong> |
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Classical field theory |
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<ul> |
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<li> |
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<a class="existingWikiWord"> |
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classical physics |
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</p> |
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<ul> |
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<li> |
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<a class="existingWikiWord"> |
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classical mechanics |
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<a class="existingWikiWord"> |
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waves |
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and |
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optics |
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</a> |
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thermodynamics |
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</ul> |
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<li> |
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<p> |
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<strong> |
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<a class="existingWikiWord"> |
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Quantum Mechanics |
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</a> |
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</strong> |
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<ul> |
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<li> |
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<p> |
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<a class="existingWikiWord"> |
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in terms of ∞-compact categories |
|
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</a> |
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</p> |
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</li> |
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<li> |
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<p> |
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quantum information |
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</li> |
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<p> |
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<a class="existingWikiWord"> |
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Hamiltonian operator |
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</a> |
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</p> |
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</li> |
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<li> |
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<p> |
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<a class="existingWikiWord"> |
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density matrix |
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</a> |
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</p> |
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</li> |
|
|
</ul> |
|
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</li> |
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</ul> |
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<div> |
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<p> |
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<a> |
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Edit this sidebar |
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</a> |
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</p> |
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</div> |
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</div> |
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</div> |
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</div> |
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</div> |
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<h1 id="contents"> |
|
|
Contents |
|
|
</h1> |
|
|
<div class="maruku_toc"> |
|
|
<ul> |
|
|
<li> |
|
|
<a> |
|
|
1. Idea |
|
|
</a> |
|
|
</li> |
|
|
<li> |
|
|
<a> |
|
|
2. Related concepts |
|
|
</a> |
|
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</li> |
|
|
<li> |
|
|
<a> |
|
|
3. References |
|
|
</a> |
|
|
</li> |
|
|
</ul> |
|
|
</div> |
|
|
<h2 id="idea"> |
|
|
1. Idea |
|
|
</h2> |
|
|
<p> |
|
|
In |
|
|
<a class="existingWikiWord"> |
|
|
physics |
|
|
</a> |
|
|
the |
|
|
<a class="existingWikiWord"> |
|
|
theory |
|
|
</a> |
|
|
of |
|
|
<em> |
|
|
special relativity |
|
|
</em> |
|
|
describes dynamics in |
|
|
<a class="existingWikiWord"> |
|
|
physical |
|
|
</a> |
|
|
<a class="existingWikiWord"> |
|
|
spacetime |
|
|
</a> |
|
|
in absence of a field of |
|
|
<a class="existingWikiWord"> |
|
|
gravity |
|
|
</a> |
|
|
. |
|
|
</p> |
|
|
<p> |
|
|
Specifically, it models |
|
|
</p> |
|
|
<ul> |
|
|
<li> |
|
|
<p> |
|
|
<a class="existingWikiWord"> |
|
|
spacetime |
|
|
</a> |
|
|
as a flat time-oriented |
|
|
<a class="existingWikiWord"> |
|
|
pseudo-Riemannian manifold |
|
|
</a> |
|
|
: |
|
|
</p> |
|
|
<p> |
|
|
<a class="existingWikiWord"> |
|
|
Minkowski space |
|
|
</a> |
|
|
; |
|
|
</p> |
|
|
</li> |
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<li> |
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<p> |
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<a class="existingWikiWord"> |
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trajectories |
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</a> |
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of point |
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<a class="existingWikiWord"> |
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particles |
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</a> |
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as timelike |
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<a class="existingWikiWord"> |
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curves |
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</a> |
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in Minkowski space. |
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</p> |
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</li> |
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<li> |
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<p> |
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the |
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<a class="existingWikiWord"> |
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electromagnetic field |
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</a> |
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as a closed 2- |
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<a class="existingWikiWord"> |
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form |
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</a> |
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on Minkowski space. |
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</p> |
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</li> |
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<li> |
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<p> |
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the |
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<a class="existingWikiWord"> |
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Lorentz force |
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</a> |
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exerted by the electromagnetic field on a charged particle as the contraction of that 2-form with the tangent vector of the trajectory of the particle. |
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</p> |
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</li> |
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</ul> |
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<p> |
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If instead of restricting to Minkowski space, spacetime is allowed to be an arbitrary |
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<a class="existingWikiWord"> |
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pseudo-Riemannian manifold |
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</a> |
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one speaks of the resulting framework as the theory of |
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<em> |
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<a class="existingWikiWord"> |
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general relativity |
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</a> |
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</em> |
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. |
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</p> |
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<p> |
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Mathematically, special relativity is essentially the theory of |
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<a class="existingWikiWord"> |
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Minkowski space |
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</a> |
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as a |
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<a class="existingWikiWord"> |
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pseudo-Riemannian manifold |
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</a> |
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, hence equipped with the constant |
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<a class="existingWikiWord"> |
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metric |
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</a> |
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<a class="existingWikiWord"> |
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tensor |
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</a> |
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which at each point is the |
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<a class="existingWikiWord"> |
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bilinear form |
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</a> |
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with |
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<a class="existingWikiWord"> |
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signature |
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</a> |
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<math class="maruku-mathml" display="inline" xmlns=""> |
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<semantics> |
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<mrow> |
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<mo stretchy="false"> |
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( |
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</mo> |
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<mo lspace="verythinmathspace" rspace="0em"> |
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− |
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</mo> |
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<mo> |
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, |
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</mo> |
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<mo lspace="verythinmathspace" rspace="0em"> |
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+ |
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</mo> |
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<mo> |
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, |
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</mo> |
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<mi> |
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⋯ |
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</mi> |
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<mo> |
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, |
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</mo> |
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<mo lspace="verythinmathspace" rspace="0em"> |
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+ |
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</mo> |
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<mo stretchy="false"> |
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) |
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</mo> |
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</mrow> |
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|
<annotation encoding="application/x-tex"> |
|
|
(-,+, \cdots, +) |
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</annotation> |
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</semantics> |
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</math> |
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|
or else |
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|
<math class="maruku-mathml" display="inline" xmlns=""> |
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<semantics> |
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|
<mrow> |
|
|
<mo stretchy="false"> |
|
|
( |
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</mo> |
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|
<mo lspace="verythinmathspace" rspace="0em"> |
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+ |
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</mo> |
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<mo> |
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, |
|
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</mo> |
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<mo lspace="verythinmathspace" rspace="0em"> |
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− |
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</mo> |
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<mo> |
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, |
|
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</mo> |
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<mi> |
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|
⋯ |
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</mi> |
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<mo> |
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, |
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</mo> |
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<mo lspace="verythinmathspace" rspace="0em"> |
|
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− |
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|
</mo> |
|
|
<mo stretchy="false"> |
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|
) |
|
|
</mo> |
|
|
</mrow> |
|
|
<annotation encoding="application/x-tex"> |
|
|
(+,-,\cdots, -) |
|
|
</annotation> |
|
|
</semantics> |
|
|
</math> |
|
|
(depending on convention). The null-vectors in this metric characterize the |
|
|
<a class="existingWikiWord"> |
|
|
speed of light |
|
|
</a> |
|
|
. The linear |
|
|
<a class="existingWikiWord"> |
|
|
isometries |
|
|
</a> |
|
|
of this metric are the |
|
|
<a class="existingWikiWord"> |
|
|
Lorentz transformations |
|
|
</a> |
|
|
and the fact that with the Minkowski metric these also preserve, hence, null rays is the mathematical model for the famous |
|
|
<a class="existingWikiWord"> |
|
|
phenomenological |
|
|
</a> |
|
|
observation that “the speed of light is the same in all reference systems”. |
|
|
</p> |
|
|
<h2 id="related_concepts"> |
|
|
2. Related concepts |
|
|
</h2> |
|
|
<ul> |
|
|
<li> |
|
|
<p> |
|
|
<a class="existingWikiWord"> |
|
|
speed of light |
|
|
</a> |
|
|
</p> |
|
|
<p> |
|
|
<a class="existingWikiWord"> |
|
|
Michelson-Morley experiment |
|
|
</a> |
|
|
</p> |
|
|
</li> |
|
|
<li> |
|
|
<p> |
|
|
<a class="existingWikiWord"> |
|
|
theory (physics) |
|
|
</a> |
|
|
</p> |
|
|
</li> |
|
|
<li> |
|
|
<p> |
|
|
<a class="existingWikiWord"> |
|
|
electromagnetism |
|
|
</a> |
|
|
</p> |
|
|
</li> |
|
|
<li> |
|
|
<p> |
|
|
<a class="existingWikiWord"> |
|
|
general relativity |
|
|
</a> |
|
|
, |
|
|
<a class="existingWikiWord"> |
|
|
gravity |
|
|
</a> |
|
|
</p> |
|
|
</li> |
|
|
</ul> |
|
|
<h2 id="references"> |
|
|
3. References |
|
|
</h2> |
|
|
<ul> |
|
|
<li> |
|
|
Wikipedia, |
|
|
<em> |
|
|
<a> |
|
|
Special relativity |
|
|
</a> |
|
|
</em> |
|
|
</li> |
|
|
</ul> |
|
|
</body> |
|
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</html> |
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</div> |
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|
<div class="revisedby"> |
|
|
<p> |
|
|
Last revised on January 26, 2019 at 11:38:24. |
|
|
See the |
|
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<a style="color: #005c19"> |
|
|
history |
|
|
</a> |
|
|
of this page for a list of all contributions to it. |
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