参考文献 E1] A. Einstein, Annalen der Phys,, 49, 769(1916), For an English translation, see The Principle of Relativity (Methuen, 1923 reprinted by Dover Publications), p. 35 [2]Th ding English edition ig Euclid,s Elements with an introduction and commentary by T. I. Heath (rev, ed Cambridge, 1926) [3] These quotations are taken from George Sartor, Ancient Science and modern Civilitation (University of Nebraska PresB, 1954: reprinted by Harper and Brothers, New York, 1959),p. 26. E 41 Quoted by R. Bonola, in Non-Euclidean Geometry, trans. by H. 8. Carslaw (Dover Press, 1955), pp 65-67. [5]F. Kein,Math,An,,573(181);6,112(1873);37,544 (1890 quoted by H. Weyl, in Space-Time-Matter, trams. by H. L, Brose (Dover Press, 1952), p. 80, A Euclidean mc for the GausB-B6lyai-Lobachevski geometry was given in 1868 Beltrami, Saggio di interpretation della geo得etra第O混 euclidea, quoted by J. D. North in The Measure of the universe ( Orford,196),D.60. [6] Isaac Newton, Philosophiae Natwulis Principia Mathematica, traas. by Andrew Motte, revised and annotated by F. Cajorj University of California Press, 1966), p. 546 [7]R. v. Eotv &e, Math. nat. Ber. Ungarn, 8, 65(1890); R.v. Eotvos, D. Pekar, and E. Fekete, Ann. Phya, 68, 11(1922 Also see J. Renner, Hung. Acad. Sci, Vol 53. Part II(1985 [8] See, for example, A. Einstein, The Meaning of Relativity (2nd ed Princeton. 1946),p.56. [9] T, D. Lee and C. N: Yang Phys. Rev., 98, 1501(1955) [10 R. H. Dicke, in Relativity, Growps, and Topology, od, by C De Witt and B. S. Dewitt (Gordon and Breach, New York, 1964),p. 167; P.G. Roll, R, Krotkov, and R, H. Dicke, Ann. PhyA.(Nx.),26,生4(1967) I1」J.W.T.Dobk,J,A, Harve,D.Paya,and且.且 ortmann, Phy8,Be,139,B756(1965) [12] F. C. witteborn and W. M. Fairbank, Phys. Rev. Lettera. 19 1049(1967) [131 The most accessible edition ig that of Florian Carjori, ref. 6 114] S. Newcomb, Astronomical Papers of the American Ephemeris, 1,472(1882) 21
[15]8. Newcomb, article on (!Mercury in The Encyclopaedia Britannica, 11th ed. XVILL, 155(1910---1911). [16] Ref. 6, p. 6(a different translation is quoted here) 「17]rbi,p.10. 118] G.H. Alexander, The Lcibnie-Clarke Correspondence(manchester University Press, 1956). Excerpts are quoted by A. Koyre in from the Closed World to the Infinite Universe (harper and Row, New York, 1958), Chapter XI. (See especially Leihniz's fifth letter. 「1!〕L.Mach,Tλ 8 Science o∫ Mechanics, trans.byT.J. Mccormack (2nd ed, Open Court Publishing Co.. 1893) [20] L I. Schiff, Rev. Mod. Phys., 36, 510(1964);G. M.Clemence Rev.Mod,.Phy,19,36l(1947);29,2(1957) [21] James Clark Maxwell, artiele on "fElher'7 in The Encyolo paedia Britannica, 9th ed. (1875---1889); reprinted in The Scientifio Papers of James Clark Marwell, ed by W. D. Niven (Dover Publications, 1965),p. 763, Also gee Maxwel'y Treatise on Electricity and Magnetism, Vol. II (Dover Publications 1964),pp.492-493. [22] For an account of these experiments see C. MOller, The Theory of relatiuity (Oxford Press, London, 1952). (hapter I [23 A.A. Michelson and E. W. Morley, Am, J. Sei, 34, 333(1887); reprinted in Relatinity Theory: Itis Origing and Impact on Modern Thought, ed by L. Pearec Williams (John Wilcy and Sons, New York, 1968. [ 24]T S. Jaseja, A, Javan, J. Murray, and C. H. TowmoB, Phys, Rev., 13,A1221(1964) [251 G. F. Fitzgerald, quoted by 0. Lodge, Nature, 46, 165(1892) Also Bce O, Iodge, Phil Trans. Roy. Soe, ISA(I893) [26] H. A Lorentz, Zittungsyerslagen der Akad. van Wettensehappe 1, 74(November 26, 1892); Verguch einer Theorie der elektrischen und optische Erscheinungen in bewegten Korpern(E.J.Brill Leiden, 1895); Proc. Acad. Sci. Amsterdam (English version) 6, 800(1904), The third reference, and a translated excerpt from the second, are available in The Principle of Relativity, ref 1. [27] J. H. Poincare, Rapports presentes au Congres International de Physique reuni d Paris (Gauthier-Villiers, Paris. 1900): spccch at the St. Louis International Exposition in 1904, trans, by G B. Halstead, The Monist, 15. 1(1905), reprinted in Relativity Theory: its Origins and Impact on Modern Thought, ref. 23
Rend. Ciro. Mat. Palermo, 2, 129(1906) [28] Sir F'dhnund whittaker A History of The Theories of Aether and Electricity, Vol. II. (Thomas Nelson and Sons, London 1953), Chapter工 [29 For a balanced viow of thig question, gee G. Bolton, A. J. 28,627(1960) t in Relativity Th Ite Origins and Impact on Modern Thought, ref. [30 A. Einstein, Ann. Physik, 17, 891(1905); 18, 639(1905): Transla tions are given in The Principie of retativity, ref. 1 [31]G. Holton, ref. 99, and Isis, 60, 183(1969) [32] See ref. 30, and also A. Griinbaum, in Current Issues in the Philosophy of Science, ed, by I. Feigl and G. Maxwell (Holt, Rinehart, and Winston, New York, 1961). reprinted in part in Relativity Theory: Its Origina and impact on Modern Thought re,23 [38] A. Einstein, Jahrb. Raaioakt, 4, 411(1907) Bitzungsber. preuss. Akad. Wiss June 13 Phys. Leipzig, 26(1908) [34]A. Einstein, An, Phys, Leipzig, 35, 898(1911). For an engligh translation, see The Primoiple of Relativity, ref. 1 35] A Einstein, Ann. Phys. Leipzig, 38, 355, 443(1912) [36] M. Abraham, Iincet Atti, 20, 678(1911): Phys. Z, I3, 1.4 176,310,311793(1912); Nuoro Cimento,4.459(1912) [37] G. Nordstrom, Phys. Z, 13, 1126(1912): Ann. Phys. leipzig 4D,856(1913);42,533(1913);43,1101(1914);Phys.z.,15, 375(1914);An.Aa,soi,femn.57(19141915) 38]A. Einstein, Phys. Z, 14, 1240(1913):A, Einstein and M. Grossmann,z.Mat,Phy,62,225(1913);63,215(1914);A Einstein, Vierteljahr Nat. Ges. Zurich, 58, 284(1913): Archives a- phys, nat,7,6(1914);Pys.z,141249(I913). [39 A. Einstein, Sitzungsbor. preuss. Akad. Wiss. 1914, p. 1030, 1915, pp. 718, 799, 831, 844. Also see D. Hilbert, Nachschr. Ges Wiss, Gottingen, November 20, 1915, p. 395. [40] This famous erperiment may in fact be a myth. See A. I. Miller, IBis, to be. published (1972). 26◆
第二章狭义相对论 我们现在复习一下 Einstein的狭义相对论.本章虽然是 齐全的,但只是一个简明的总结.主要目的在于建立我们用 到的符号体系和汇集一些以后有用的公式。需要对狭义相对 论有更广泛了解的读者最好先看本章末所列参考书之一,然 后再回过头来学习本章.至于那些对狭义相对论已颇熟悉的 读者则可立即阅读第三章 1. Lorentz变换 狭义相对性原理说,自然定律对 rentz变换群(一个特 定的空一时坐标变换群)是不变的.我们在第一章末曾看到 Newton运动定律对 Galileo坐标变换(132)不变,而 Maxwell 方程则不然. Einstein通过把 Galileo不变性换成 Lorentz不 变性解决了这一矛盾.我们不准备按照历史发展的顺序进行 讨论,而只是先定义 Lorentz变换,再示明 Lorent不变性如 何指导我们研究自然定律 Lorentz变换是由一个空一时坐标系x到另一个坐标系x 的变换,这种变换具有如下形式 A°sx3 式中““和Ap是常数,且满足条件 1oA at 而
+1 1,2或3 2.1 我们所采用的符号a,B,Y等遍取1,2,3,0这4个值而x2 x2x2是位置向量x的 Descartes分量,x是时间t,我们采用 光速等于1的自然单位制,因而所有的x都具有长度的量纲 任何指标(例如象方程(211)中的),出现二次时,如果 次在上另一次在下,则都理解为求和(除非另有说明);邸方程 (2L1)是下面方程的缩写 Moro+41r+A2x2+43x3+a 标志 Lorentz变换的基本性质是它保持“原时”ax不变, 而dr的定义是 dr= de- dx?=-naBdxodx (214) 在新坐标系x中,由(21.1)得出坐标的微分为 故新的原时将是 mapdr°dx eArA° dxrd mrodx' drd 因而有 (215) 正是这个性质解释了 Michelson和 Morley观测到的光速在全 部惯性系中都相同的现象,光的波阵面的|4x/dl就等于光 速,它在我们的单位制中等于1;因此光的传播为下列陈述所 描写 (216) 实行一个 Lorentz变换后并不改变dr,因而dx'=0,所以 x'ldl!l-1;即光速在新坐标系中仍等于1. 28