PART I. THE FOUNDATIONS OF THE SPECIAL THEORY
OF RELATIVITY

1. Historical background (Lorentz, Poincaré, Einstein)

The transformation in physical concepts which was brought about by the theory of relativity, had been in preparation for a long time. As long ago as 1887, in a paper still written from the point of view of the elastic- solid theory of light, Voigt1 mentioned that it was mathematically convenient to introduce a local time tʹ into a moving reference system. The origin of tʹ was taken to be a linear function of the space coordinates, while the time scale was assumed to be unchanged. In this way the wave equation

could be made to remain valid in the moving reference system, too. These remarks, however, remained completely unnoticed, and a similar transformation was not again suggested until 1892 and 1895, when H. A. Lorentz2 published his fundamental papers on the subject. Essentially physical results were now obtained, in addition to the purely formal recognition that it was mathematically convenient to introduce a local time tʹ in a moving coordinate system. It was shown that all experimentally observed effects of first order in v/c (ratio of the translational velocity of the medium to the velocity of light) could be explained quantitatively by the theory when the motion of the electrons embedded in the aether was taken into account. In particular, the theory gave an explanation for the fact that a common velocity of medium and observer relative to the aether has no influence on the phenomena, as far as quantities of first order are concerned.3

However, the negative result of Michelson's interferometer experiment4,

____________________
1
W. Voigt, "'Über das Dopplersche Prinzip'", Nachr. Ges. Wiss. Göttingen ( 1887) 41. Voigt's formulae are obtained by substituting κ = √(1-β2) in Eqs. (1), below.
2
H. A. Lorentz, "'La théorie électromagnétique de Maxwell et son application aux corps mouvants'", Arch. néerl. Sci., 25 ( 1892) 363; Versuch einer Theorie der elektrischen und magnetischen Erscheinungen in bewegten Körpern (Leyden 1895).
3
Fizeau's result purported to show the effect of the earth's motion on the change in the azimuth of polarization when polarized light is obliquely incident on a glass plate. This contradicted both the relativity principle and Lorentz's theory and was later shown to be wrong by D. B. Brace ( Phil. Mag., 10 ( 1908) 591) and B. Strasser ( Ann. Phys., Lpz., 24 ( 1907) 137). It should further be mentioned that in Lorentz's theory it might be possible to obtain first-order effects of the "aether wind" by considering gravitation. Thus, as mentioned by Maxwell, the motion of the solar system relative to the aether would produce first-order differences in the times of the eclipses of the Jupiter satellites; but it was found by C. V. Burton ( Phil. Mag., 19 ( 1910) 417; of. also H. A. Lorentz, "'Das Relativitätsprinzip'", 3 Haarlemer Vorträge ( Leipzig 1914), p. 21) that the inherent observational errors would be as large as the expected magnitude of the effect. Observations on the satellites would therefore not help in deciding for or against the old aether theory.
4
A description of this experiment is given by Lorentz in article V14 of the Encykl. math. Wiss. ( Leipzig 1904).

-1-

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Theory of Relativity
Table of contents

Table of contents

  • Title Page iii
  • Preface v
  • Acknowledgments in the Original Article vi
  • Contents vii
  • Preface xi
  • Bibliography xiii
  • Part I. the Foundations of the Special Theory of Relativity 1
  • Part Ii. Mathematical Tools 21
  • Part Iii. Special Theory of Relativity. Further Elaborations. 71
  • Part Iv. General Theory of Relativity 142
  • Part V. Theories on the Nature of Charged Elementary Particles 184
  • Supplementary Notes 207
  • Author Index 233
  • Subject Index 236
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