Pub Date : 2021-12-31DOI: 10.1017/9781009039345.004
J. Ehlers
In Appendix III of the fifth edition of his book Space, Time, Matter [15] henceforth cited as W (which has not been translated into English), Hermann Weyl derived for the first time, motivated by cosmological considerations, the general frequency shift formula for sources and observers moving arbitrarily in a general spacetime. In his discussion of cosmology (W, 39) he argued for a non-stationary model. In support of this he cited astrophysical considerations (stellar ages and motions), used essentially Olbers’ argument against Einstein’s static model of 1917 [3], emphasized the significance of initial rather than (spatial) boundary conditions in GRT in relation to the difference between past and future, and asserted (in 1922!): “The present state of the system of stars on the sky does not resemble a final statistical state. The small stellar velocities are due to a common origin rather than to an adjustment, and it appears that the velocities between distant celestial objects on average increase with their mutual separations.” (My translation and underlining.) Weyl then constructed a corresponding model, an isotropically expanding substratum which occupies an initially small, but monotonically growing part of de Sitter’s hyperboloidal, globally non-stationary spacetime [7] depicted in Fig. 1, and applied to it his frequency shift formula. Using Slipher’s red shift data and Lundmark’s estimate of the distance of the Andromeda nebula, he obtained a ‘world radius’ (Hubble radius) of about 109 light years corresponding to a ‘Hubble constant’ of about 103 km/s/Mpc—6 years ahead of
Hermann Weyl在其著作《空间，时间，物质》第五版的附录三(下文简称为W)中，从宇宙学的考虑出发，首次推导出在一般时空中任意运动的源和观测者的一般频移公式。在他关于宇宙学的讨论中(W, 39)，他主张非平稳模型。为了支持这一点，他引用了天体物理学的考虑(恒星的年龄和运动)，基本上使用了奥伯斯的论点来反对爱因斯坦1917年的静态模型，强调了GRT中与过去和未来之间的差异有关的初始而不是(空间)边界条件的重要性，并断言(在1922年!):“天空中恒星系统的当前状态不像最终统计状态。小的恒星速度是由于一个共同的起源，而不是由于调整，似乎遥远天体之间的速度平均随着它们的相互分离而增加。(我的翻译和下划线。)Weyl随后构建了一个相应的模型，即一个各向同性膨胀的基底，它占据了图1所示de Sitter的双曲全局非平稳时空[7]中最初很小但单调增长的部分，并将其应用于他的频移公式。利用斯莱弗的红移数据和伦德马克对仙女座星云距离的估计，他得到了大约109光年的“世界半径”(哈勃半径)，对应于大约103公里/秒/ mpc的“哈勃常数”，提前6年
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Pub Date : 2021-12-31DOI: 10.1017/9781009039345.002
{"title":"Notation, Concepts, and Conventions in Relativity Theory","authors":"","doi":"10.1017/9781009039345.002","DOIUrl":"https://doi.org/10.1017/9781009039345.002","url":null,"abstract":"","PeriodicalId":101756,"journal":{"name":"300 Problems in Special and General Relativity","volume":"122 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132318429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-31DOI: 10.1017/9781009039345.003
G. Holton
{"title":"Special Relativity Theory","authors":"G. Holton","doi":"10.1017/9781009039345.003","DOIUrl":"https://doi.org/10.1017/9781009039345.003","url":null,"abstract":"","PeriodicalId":101756,"journal":{"name":"300 Problems in Special and General Relativity","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132183360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-31DOI: 10.1017/9781009039345.007
{"title":"Index to the Problems and Solutions","authors":"","doi":"10.1017/9781009039345.007","DOIUrl":"https://doi.org/10.1017/9781009039345.007","url":null,"abstract":"","PeriodicalId":101756,"journal":{"name":"300 Problems in Special and General Relativity","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124456269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-11-12DOI: 10.1002/9780470172407.OTH1
B. Gnedenko, Igor Pavlov, I. Ushakov
Balance sheet: The financial condition of Technica, Inc. at December 31, 2008 and 2009 is shown as a summary of assets and liabilities. Technica, Inc. has an excess of current assets over current liabilities, demonstrating liquidity. The firm’s fixed assets represent over one-half of total assets ($270,000 of $408,300). The firm is financed by short-term debt, long-term debt, common stock, and retained earnings. It appears that it repurchased 500 shares of common stock in 2009.
{"title":"Solutions to Problems","authors":"B. Gnedenko, Igor Pavlov, I. Ushakov","doi":"10.1002/9780470172407.OTH1","DOIUrl":"https://doi.org/10.1002/9780470172407.OTH1","url":null,"abstract":"Balance sheet: The financial condition of Technica, Inc. at December 31, 2008 and 2009 is shown as a summary of assets and liabilities. Technica, Inc. has an excess of current assets over current liabilities, demonstrating liquidity. The firm’s fixed assets represent over one-half of total assets ($270,000 of $408,300). The firm is financed by short-term debt, long-term debt, common stock, and retained earnings. It appears that it repurchased 500 shares of common stock in 2009.","PeriodicalId":101756,"journal":{"name":"300 Problems in Special and General Relativity","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127865053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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