符合“欧氏几何”的洛伦兹变换图示法的设计A DESIGN OF GRAPHIC METHOD OF THE LORENTZ TRANSFORMATION ACCORDING WITH EUCLIDEAN GEOMETRY
刘远
摘要(Abstract):
文章将洛伦兹变换简化为几何函数形式,根据这些几何函数构造若干直角三角形,表示洛伦兹变换的两参考系时空坐标值相互关系,逐步设计了与"闵氏几何"的闵可夫斯基时空图不同的洛伦兹变换图示法,以符合"欧氏几何"的形式表示洛伦兹变换。设计过程中,提出一种"火车-铁轨"模型,结合图示法,描述了狭义相对论时空中的几种典型物理现象,包括两参考系相互观察、异地同时性的破坏和长度收缩。此图示法可以作为一种借鉴,帮助初学者和爱好者学习洛伦兹变换和狭义相对论。
关键词(KeyWords): 洛伦兹变换;图示法;异地同时性的破坏;长度收缩
基金项目(Foundation):
作者(Author): 刘远
参考文献(References):
- [1]邓魁英,楚天广.洛伦兹变换的几何导出[J].力学与实践,2017,39(1):82-86.DENG K Y,CHU T G.Geometric derivation of the Lorentz transformation[J].Mechanics in Engineering,2017,39(1):82-86.(in Chinese)
- [2]梁灿彬.相对论的几何表述(1)[J].大学物理,1998,17(5):2-6.LIANG C B.Geometric formulation of the theory of relativity[J].College Physics,1998,17(5):2-6.(in Chinese)
- [3]魏益焕,崔萧,李微.洛伦兹变换与二维旋转变换[J].渤海大学学报(自然科学版),2017,38(1):19-21.WEI Y H,CUI X,LI W.Lorentz transformation and twodimensional rotation transformation[J].Journal of Bohai University(Natural Science Edition),2017,38(1):19-21.(in Chinese)
- [4]缪劲松,胡海云.洛伦兹变换的引入及其时空图像讨论[J].物理与工程,2016,26(S1):10-16+21.MIAO J S,HU H Y.Introduction of Lorenz transformation and discussion about its space-time-image[J].Physics and Engineering.2016,26(S1):10-16+21.(in Chinese)
- [5]缪劲松,胡海云.狭义相对论中与长度或距离有关的典型问题的讨论[J].物理与工程,2017,27(S1):10-15.MIAO J S,HU H Y.Discussion about the representative problems concerning the length or distance in special theory of relativity[J].Physics and Engineering.2017,27(S1):10-15.(in Chinese)
- [6]黄献民.狭义相对论与时空图[M].北京:国防工业出版社,2008.
- [7]党兴菊,张瑶,吴文良.用斜交坐标轴画二维对称时空图[J].大理学院学报,2014,13(12):35-39.DANG X J,ZHANG Y,WU W L.Using oblique coordinate axes for two-dimentional symmetric space-time diagrams[J].Journal of Dali University,2014,13(12):35-39.(in Chinese)
- [8]张元仲.狭义相对论洛伦兹变换的推导及其他[J].物理与工程,2016,26(3):3-8.ZHANG Y Z.The derivation of Lorentz transformation in special relativity and others[J].Physics and Engineering,2016,26(3):3-8.(in Chinese)
- [9]张艳亮,张鲁殷.基于狭义相对论的同时性对长度收缩佯谬的认识[J].物理与工程,2012,22(2):7-9.ZHANG Y L,ZHANG L Y.Cognition on the paradox of length contraction based on simultaneity of special relativity[J].Physics and Engineering,2012,22(2):7-9.(in Chinese)
- [10]张三慧.大学物理学:力学、电磁学[M].3版.北京:清华大学出版社,2009:189.
- [11]王超群.关于时间膨胀和长度收缩的研究[J].陕西师范大学学报(自科版),2007(s2):39-41.WANG C Q.On the time expansion and length contraction[J].Journal of Shaanxi Normal University(Natural Science Edition),2007(s2):39-41.(in Chinese)
- [12]李勇,王玉连,刘慧,等.同时的相对性在长度收缩公式推导中的应用[J].湖南文理学院学报(自科版),2010,22(3):25-26.LI Y,WANG Y L,LIU H,et al.Application of relativity of simultaneity in deduction of the formula of length contraction[J].Journal of Hunan University of Arts and Science(Natural Science Edition),2010,22(3):25-26.(in Chinese)
- [13]张之翔.对长度收缩的另一种看法[J].大学物理,2005,24(10):13-14.ZHANG Z X.Another way of looking at length contraction[J].College Physics,2005,24(10):13-14.(in Chinese)
- [14]刘志明,刘春清.基于相对性原理的洛伦兹变换[J].长春工程学院学报(自然科学版),2018,19(2):105-109+121.LIU Z M,LIU C Q.The Lorentz transformation based on the principle of relativity[J].J.Changchun Inst.Tech.(Nat.Sci.Edi.),2018,19(2):105-109+121.(in Chinese)
- [15]舒幼生.狭义相对论中的几个佯谬(讲课札记)[J].大学物理,2014,33(8):55-60.SHU Y S.Several Paradoxes in the special relativity(Lecture note)[J].College Physics,2014,33(8):55-60.(in Chinese)