{"id":33559,"date":"2022-07-11T00:00:20","date_gmt":"2022-07-11T00:00:20","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=33559"},"modified":"2025-07-27T00:35:31","modified_gmt":"2025-07-27T00:35:31","slug":"principium-relativitatis-specialis","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/la\/principium-relativitatis-specialis\/","title":{"rendered":"Principium Relativitatis Specialis"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>Principium Relativitatis<\/h1>\n<p><\/p>\n<p class=\"eq\"><em><strong>Summarium:<\/strong> Principium relativitatis statuit observationes a structura inertiali pendere, ita tamen ut leges physicae permaneant. In hac lectione exhibebuntur notiones referentiae inertialis et fundamenta quae sinunt obtinere transformationes inter coordinatas observatas a diversis referentiis inertialibus in contextibus physicae Newtonianae et relativitatis specialis.<\/br><\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>OBJECTIVA DISCENDI:<\/strong><br \/>\nPost hanc lectionem discipulus erit capax:\n<\/p>\n<ol>\n<li><strong>Describere<\/strong> notiones fundamentales principii relativitatis et systematum referentialium inertialium.<\/li>\n<li><strong>Explicare<\/strong> momentum referentiae inertialis in contextu principii relativitatis et distinguere inter physicam Newtonianam et relativitatem specialem.<\/li>\n<li><strong>Applicare<\/strong> transformationes Lorentzianas et Galileianas ad solvenda problemata simplicia et demonstrandum quomodo observationes inter diversos systemata referentialia inertialia mutantur.<\/li>\n<\/ol>\n<p><center><\/p>\n<p><strong>INDEX<\/strong><br \/>\n<a href=\"#1\"><strong>Referentia Inertialis<\/strong><\/a><br \/>\n<a href=\"#2\"><strong>Principium relativitatis in physica Newtoniana et in relativitate speciali<\/strong><\/a><br \/>\n<a href=\"#3\">Simplicans transformationes inter referentias inertiales<\/a><br \/>\n<a href=\"#4\">Transformationes Lorentzianae et Galileianae<\/a><br \/>\n<a href=\"#5\"><strong>Conclusiones<\/strong><\/a>\n<\/p>\n<p><\/center><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/Z1IWvfnSNe8?si=VxQeeMn9VC8NhFi_\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/center>\n<\/div>\n<p><a name=\"1\"><\/a><\/p>\n<h2>Referentia Inertialis<\/h2>\n<p>Cum physica exercetur, semper possibile est eligere structuram referentialem ex qua eventus mensurantur, et hae structurae possunt variari tum orientatione tum motu relativo. Ex omnibus possibilibus systematis referentialibus classis quaedam praecipua est quae nobis permittit physicam uti cognoscimus facere; hi sunt <strong>systemata referentialia inertialia.<\/strong> Dicitur structuram referentialem inertiale esse cum in ea satisfacta est <strong>prima lex Newtoni,<\/strong> quae enuntiat quod, in absentia agentium externorum, particulae conservant statum suum motus et propterea:<\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{dx^2}{dt^2} = \\frac{dy^2}{dt^2} = \\frac{dz^2}{dt^2} = 0.<\/span>\n<p>Hinc sequitur quod, in absentia gravitatis, si duo systemata <span class=\"katex-eq\" data-katex-display=\"false\">S<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span> inertialia sunt, tunc <span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span> solum a <span class=\"katex-eq\" data-katex-display=\"false\">S<\/span> differre potest in:<\/p>\n<ul>\n<li>translatione una,<\/li>\n<li>rotatione una,<\/li>\n<li>motu relativo inter utrumque systema celeritate constanti.<\/li>\n<\/ul>\n<p>Conceptus referentiae inertialis fundamentalis est pro <strong>principio relativitatis,<\/strong> quod statuit leges physicae eandem formam habere in omnibus systematibus inertialibus. Hoc principium aeque valet tam in physica Newtoniana quam in relativitate speciali.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h3>Principium relativitatis in physica Newtoniana et in relativitate speciali<\/h3>\n<p>Descriptiones Newtonianae et relativitatis specialis differunt quomodo coordinatae eventus, ad systema inertiale relata, ad coordinatas alterius systematis inertialis referantur.<\/p>\n<p>Consideremus duo systemata inertialia cartesiana <span class=\"katex-eq\" data-katex-display=\"false\">S<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span> in \u00abconfiguratione standardi\u00bb, id est, ubi <span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span> movetur per axem <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span> systematis <span class=\"katex-eq\" data-katex-display=\"false\">S<\/span> celeritate constanti <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{v}_{ss^\\prime} = v_{ss^\\prime_x} \\hat{x}<\/span>  et axes respectivos <span class=\"katex-eq\" data-katex-display=\"false\">S<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span> sunt aligati et coincidunt in <span class=\"katex-eq\" data-katex-display=\"false\">t=t^\\prime = 0<\/span>.<\/p>\n<figure>\n<img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/coordenadas-cambio.png\" alt=\"\" width=\"1374\" height=\"741\" class=\"aligncenter size-full wp-image-25502 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/coordenadas-cambio.png\" alt=\"\" width=\"1374\" height=\"741\" class=\"aligncenter size-full wp-image-25502 lazyload\" srcset=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/coordenadas-cambio.png 1374w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/coordenadas-cambio-300x162.png 300w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/coordenadas-cambio-1024x552.png 1024w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/coordenadas-cambio-768x414.png 768w\" sizes=\"(max-width: 1374px) 100vw, 1374px\" \/><\/noscript><br \/>\n<\/figure>\n<p>Ita, si exstat transformata linearis quae coordinatas eventus visum ex <span class=\"katex-eq\" data-katex-display=\"false\">S<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span> inter se relinque, hae inter se referuntur per sequentem systema aequationum linearum<\/p>\n<p><a name=\"eq1\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\nt^\\prime &amp;= At + Bx,\\\\\n\nx^\\prime &amp;= Dt + Ex,\\\\\n\ny^\\prime &amp;= y, \\\\\n\nz^\\prime &amp;=z,\n\n\\end{array}\\;\\;\\;[\\triangle]<\/span>\n<p>ubi <span class=\"katex-eq\" data-katex-display=\"false\">A,<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">B,<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">D<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">E<\/span> sunt constantes determinandae.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>Simplificans transformationes inter referentias inertiales<\/h3>\n<p>Hae transformationes simplicari possunt si has observationes facimus:<\/p>\n<ul>\n<li>\n<p>Quoniam transformationes implendae sunt pro quolibet <span class=\"katex-eq\" data-katex-display=\"false\">x^\\prime<\/span>, si eventum ponimus in origine <span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span>, habebimus <span class=\"katex-eq\" data-katex-display=\"false\">x^\\prime =0<\/span>. Hoc implicat eventum simul cum <span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span> moveri et eius positio respectu <span class=\"katex-eq\" data-katex-display=\"false\">S<\/span> erit <span class=\"katex-eq\" data-katex-display=\"false\">x=v_{{ss^\\prime}_x}t.<\/span>\n<p>Substituendo <span class=\"katex-eq\" data-katex-display=\"false\">x=v_{{ss^\\prime}_x}t.<\/span> in secunda aequatione <a href=\"#eq1\"><span class=\"katex-eq\" data-katex-display=\"false\">[\\triangle]<\/span><\/a>, obtinebimus <span class=\"katex-eq\" data-katex-display=\"false\">D=-Ev_{{ss^\\prime}_x}.<\/span>\n<p>Analogi modo, transformationes valent quoque pro quolibet <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span>; si igitur eventum in origine <span class=\"katex-eq\" data-katex-display=\"false\">S<\/span> ponimus, tunc visum ex <span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span> positionem habebit <span class=\"katex-eq\" data-katex-display=\"false\">x^\\prime = -v_{{ss^\\prime}_x}t^\\prime<\/span>.<\/p>\n<p>Substituendo hoc in primam et secundam aequationem <a href=\"#eq1\"><span class=\"katex-eq\" data-katex-display=\"false\">[\\triangle]<\/span><\/a> pervenitur ad <span class=\"katex-eq\" data-katex-display=\"false\">t^\\prime=At<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">-v_{{ss^\\prime}_x}t^\\prime =Dt<\/span>. Dividendo has duas aequalitates concluditur <span class=\"katex-eq\" data-katex-display=\"false\">D=-v_{{ss^\\prime}_x}A<\/span>.<\/p>\n<\/li>\n<li>\n<p>Hoc modo, sola via conciliandi praedicta est imponere <span class=\"katex-eq\" data-katex-display=\"false\">A=E,<\/span>, et hoc facto transformationes reducuntur ad:<\/p>\n<p><a name=\"eq2\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\nt^\\prime &amp;= At + Bx,\\\\\n\nx^\\prime &amp;= A(x - v_{ss^\\prime_x} t), \\\\\n\ny^\\prime &amp;= y, \\\\\n\nz^\\prime &amp;= z.\n\n\\end{array}\\;\\;\\;[2]<\/span>\n<\/li>\n<\/ul>\n<p><a name=\"4\"><\/a><\/p>\n<h3>Transformationes Lorentzianae et Galileianae<\/h3>\n<p>In casu physicae Newtonianae habemus relativitatem Galileianam, in qua tempus eodem modo transit in omnibus systematibus inertialibus et propterea <span class=\"katex-eq\" data-katex-display=\"false\">t=t^\\prime.<\/span> Ex hoc sequitur quod <span class=\"katex-eq\" data-katex-display=\"false\">A=1<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">B=0.<\/span> Hoc ducit ad celebres <strong>transformationes Galileianas<\/strong> quae permittunt observationes inter duo systemata inertialia transformare<\/p>\n<p><a name=\"eq2\"><\/a><\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\nt^\\prime &amp;= t\\\\\n\nx^\\prime &amp;= x - v_{ss^\\prime_x} t, \\\\\n\ny^\\prime &amp;= y, \\\\\n\nz^\\prime &amp;= z.\n\n\\end{array}\\;\\;\\;[3]<\/span>\n<\/li>\n<\/ul>\n<p>Ex altera parte, in physica relativistica habemus principium relativitatis Einsteinianum, quod pro sua vice considerat velocitatem luminis in vacuo aequalem esse in omnibus systematibus inertialibus. Hoc ducit ad celebres Transformationes Lorentzianas relativitatis specialis et, ut in posteriis sectionibus videbimus, sequentem formam accipiunt:<\/p>\n<p id=\"eq\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\nct^\\prime &amp;=\\gamma_x \\left( ct - \\beta_x x \\right) \\\\\n\nx^\\prime &amp;= \\gamma_x(x - \\beta_x ct) \\\\\n\ny^\\prime &amp;= y \\\\\n\nz^\\prime &amp;= z\n\n\\end{array}\n\n<\/span>\n<p>ubi <span class=\"katex-eq\" data-katex-display=\"false\">\\beta_x=v_{ss^\\prime_x}\/c<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">\\gamma= 1\/\\sqrt{1-\\beta_x^2}.<\/span>\n<p><a name=\"5\"><\/a><\/p>\n<h2>Conclusiones<\/h2>\n<p>Principium relativitatis non solum cognitionem nostram universi vertit, sed etiam perceptiones nostras fundamentales de tempore et spatio provocat. Per analysim systematum referentialium inertialium vidimus quomodo leges physicae formam suam constantem servent, quocumque observatore, tam in physica Newtoniana quam in relativitate speciali. Transformationes Lorentzianae et Galileianae singulariter illustrant subtilia et profunda discrimina inter hos duos approches. Hoc principium, quod in corde physicae modernae versatur, non solum essentiale est ad comprehensionem theoricam phaenomenorum physicorum sed etiam ad applicationes practicas quae ab technologia GPS ad explorationem spatiale pertinent. Enodando complexitates Principii Relativitatis, paulum propius accedimus ad intellegendam intricatum textum cosmos et locum nostrum in eo.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Principium Relativitatis Summarium: Principium relativitatis statuit observationes a structura inertiali pendere, ita tamen ut leges physicae permaneant. In hac lectione exhibebuntur notiones referentiae inertialis et fundamenta quae sinunt obtinere transformationes inter coordinatas observatas a diversis referentiis inertialibus in contextibus physicae Newtonianae et relativitatis specialis. OBJECTIVA DISCENDI: Post hanc lectionem discipulus erit capax: Describere notiones fundamentales [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":25506,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":1,"footnotes":""},"categories":[1250,1286],"tags":[],"class_list":["post-33559","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-physica","category-relativitas"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Principium Relativitatis Specialis - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Detege mysteria Principii Relativitatis circa quomodo perceptio nostra temporis et spatii transformetur.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/toposuranos.com\/material\/la\/principium-relativitatis-specialis\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Principium Relativitatis Specialis\" \/>\n<meta property=\"og:description\" content=\"Detege mysteria Principii Relativitatis circa quomodo perceptio nostra temporis et spatii transformetur.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/toposuranos.com\/material\/la\/principium-relativitatis-specialis\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2022-07-11T00:00:20+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-07-27T00:35:31+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/RELATIVIDAD-ESPECIAL-1024x585.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"Principium Relativitatis Specialis\" \/>\n<meta name=\"twitter:description\" content=\"Detege mysteria Principii Relativitatis circa quomodo perceptio nostra temporis et spatii transformetur.\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/RELATIVIDAD-ESPECIAL.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/toposuranos.com\/material\/la\/principium-relativitatis-specialis\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/toposuranos.com\/material\/la\/principium-relativitatis-specialis\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Principium Relativitatis Specialis\",\"datePublished\":\"2022-07-11T00:00:20+00:00\",\"dateModified\":\"2025-07-27T00:35:31+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/toposuranos.com\/material\/la\/principium-relativitatis-specialis\/\"},\"wordCount\":929,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"https:\/\/toposuranos.com\/material\/la\/principium-relativitatis-specialis\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/RELATIVIDAD-ESPECIAL.jpg\",\"articleSection\":[\"Physica\",\"Relativitas\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/toposuranos.com\/material\/la\/principium-relativitatis-specialis\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/toposuranos.com\/material\/la\/principium-relativitatis-specialis\/\",\"url\":\"https:\/\/toposuranos.com\/material\/la\/principium-relativitatis-specialis\/\",\"name\":\"Principium Relativitatis Specialis - 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