{"title":"可视相对论力学","authors":"Karol Urbański","doi":"arxiv-2408.07036","DOIUrl":null,"url":null,"abstract":"Many formalisms of special relativity are shown in various textbooks.\nHowever, even in those where the underlying geometry of Minkowski space is\nemphasized, the visualisations are lacking. This article aims to remedy this by\nexpressing relativistic concepts in a visual manner, using the full power of\nhyperbolic trigonometric functions. Minkowski diagrams in energy-momentum space\nare used and then augmented in comparison with previous uses in literature by\ndirect usage of triangles in Minkowski space. As a proof-of-concept for the\nadvantages of this holistic approach, elegant new derivations of the\nrelativistic rocket equation and the relativistic Doppler effect are presented.","PeriodicalId":501565,"journal":{"name":"arXiv - PHYS - Physics Education","volume":"6 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Visual relativistic mechanics\",\"authors\":\"Karol Urbański\",\"doi\":\"arxiv-2408.07036\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Many formalisms of special relativity are shown in various textbooks.\\nHowever, even in those where the underlying geometry of Minkowski space is\\nemphasized, the visualisations are lacking. This article aims to remedy this by\\nexpressing relativistic concepts in a visual manner, using the full power of\\nhyperbolic trigonometric functions. Minkowski diagrams in energy-momentum space\\nare used and then augmented in comparison with previous uses in literature by\\ndirect usage of triangles in Minkowski space. As a proof-of-concept for the\\nadvantages of this holistic approach, elegant new derivations of the\\nrelativistic rocket equation and the relativistic Doppler effect are presented.\",\"PeriodicalId\":501565,\"journal\":{\"name\":\"arXiv - PHYS - Physics Education\",\"volume\":\"6 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Physics Education\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.07036\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Physics Education","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.07036","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Many formalisms of special relativity are shown in various textbooks.
However, even in those where the underlying geometry of Minkowski space is
emphasized, the visualisations are lacking. This article aims to remedy this by
expressing relativistic concepts in a visual manner, using the full power of
hyperbolic trigonometric functions. Minkowski diagrams in energy-momentum space
are used and then augmented in comparison with previous uses in literature by
direct usage of triangles in Minkowski space. As a proof-of-concept for the
advantages of this holistic approach, elegant new derivations of the
relativistic rocket equation and the relativistic Doppler effect are presented.
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