{"title":"关于 \"各向同性介质中电动力学的共变公式 \"的评论","authors":"Jerrold Franklin","doi":"10.1088/1361-6404/ad0de9","DOIUrl":null,"url":null,"abstract":"A recent paper Pal (2022 <italic toggle=\"yes\">Eur. J. Phys.</italic>\n<bold>43</bold> 015204) puts into covariant form an extension of relativistic classical electromagnetism from free space to a linearly polarizable medium. The paper is based on the assumption that the relativistic tensor, <italic toggle=\"yes\">F</italic>\n<sup>\n<italic toggle=\"yes\">μ</italic>\n<italic toggle=\"yes\">ν</italic>\n</sup>, which is a tensor in free space, will also be a tensor in a linear medium. Pal constructs a proposed covariant formulation that gives <inline-formula>\n<tex-math>\n<?CDATA ${F}^{\\mu \\nu }$?>\n</tex-math>\n<mml:math overflow=\"scroll\"><mml:msup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi><mml:mi>ν</mml:mi></mml:mrow></mml:msup></mml:math>\n<inline-graphic xlink:href=\"ejpad0de9ieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> for a medium moving with constant velocity, <bold>v</bold>, in terms of <italic toggle=\"yes\">F</italic>\n<sup>\n<italic toggle=\"yes\">μ</italic>\n<italic toggle=\"yes\">ν</italic>\n</sup> for the medium at rest. However, although <italic toggle=\"yes\">F</italic>\n<sup>\n<italic toggle=\"yes\">μ</italic>\n<italic toggle=\"yes\">ν</italic>\n</sup> has been proven to be a relativistic tensor in free space, we show that it is not a tensor in a linear medium. This means that the covariant extension proposed by Pal fails.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"11 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Comment on ‘Covariant formulation of electrodynamics in isotropic media’\",\"authors\":\"Jerrold Franklin\",\"doi\":\"10.1088/1361-6404/ad0de9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A recent paper Pal (2022 <italic toggle=\\\"yes\\\">Eur. J. Phys.</italic>\\n<bold>43</bold> 015204) puts into covariant form an extension of relativistic classical electromagnetism from free space to a linearly polarizable medium. The paper is based on the assumption that the relativistic tensor, <italic toggle=\\\"yes\\\">F</italic>\\n<sup>\\n<italic toggle=\\\"yes\\\">μ</italic>\\n<italic toggle=\\\"yes\\\">ν</italic>\\n</sup>, which is a tensor in free space, will also be a tensor in a linear medium. Pal constructs a proposed covariant formulation that gives <inline-formula>\\n<tex-math>\\n<?CDATA ${F}^{\\\\mu \\\\nu }$?>\\n</tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:msup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi><mml:mi>ν</mml:mi></mml:mrow></mml:msup></mml:math>\\n<inline-graphic xlink:href=\\\"ejpad0de9ieqn1.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> for a medium moving with constant velocity, <bold>v</bold>, in terms of <italic toggle=\\\"yes\\\">F</italic>\\n<sup>\\n<italic toggle=\\\"yes\\\">μ</italic>\\n<italic toggle=\\\"yes\\\">ν</italic>\\n</sup> for the medium at rest. However, although <italic toggle=\\\"yes\\\">F</italic>\\n<sup>\\n<italic toggle=\\\"yes\\\">μ</italic>\\n<italic toggle=\\\"yes\\\">ν</italic>\\n</sup> has been proven to be a relativistic tensor in free space, we show that it is not a tensor in a linear medium. This means that the covariant extension proposed by Pal fails.\",\"PeriodicalId\":50480,\"journal\":{\"name\":\"European Journal of Physics\",\"volume\":\"11 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-12-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1361-6404/ad0de9\",\"RegionNum\":4,\"RegionCategory\":\"教育学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"EDUCATION, SCIENTIFIC DISCIPLINES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1361-6404/ad0de9","RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"EDUCATION, SCIENTIFIC DISCIPLINES","Score":null,"Total":0}
引用次数: 0
摘要
最近的一篇论文 Pal (2022 Eur. J. Phys.43 015204) 以共变形式将相对论经典电磁学从自由空间扩展到线性可极化介质。论文基于这样一个假设:相对论张量 Fμν 在自由空间中是一个张量,在线性介质中也是一个张量。Pal 提出了一种协变公式,用静止介质的 Fμν 来表示以恒定速度 v 运动的介质的 Fμν。然而,尽管 Fμν 已被证明是自由空间中的相对论张量,但我们证明它在线性介质中并不是张量。这意味着帕尔提出的协变扩展失败了。
Comment on ‘Covariant formulation of electrodynamics in isotropic media’
A recent paper Pal (2022 Eur. J. Phys.43 015204) puts into covariant form an extension of relativistic classical electromagnetism from free space to a linearly polarizable medium. The paper is based on the assumption that the relativistic tensor, Fμν, which is a tensor in free space, will also be a tensor in a linear medium. Pal constructs a proposed covariant formulation that gives Fμν for a medium moving with constant velocity, v, in terms of Fμν for the medium at rest. However, although Fμν has been proven to be a relativistic tensor in free space, we show that it is not a tensor in a linear medium. This means that the covariant extension proposed by Pal fails.
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