Abstract
The study of an electric charge in hyperbolic motion is an important aspect of Minkowski’s geometrical formulation of electrodynamics. In “Space and Time”, his last publication before his premature death, Minkowski gives a brief geometrical recipe for calculating the four-force with which an electric charge acts on another electric charge. The subsequent work of Born, Sommerfeld, Laue, and Pauli filled in the missing derivation details. Here, we bring together these early contributions, in an effort to provide a more modern, accessible, and unified exposition of the early history of the electric charge in hyperbolic motion.
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References
Born, Max. 1909. Die Theorie des starren Elektrons in der Kinematik des Relativitätsprinzips. Annalen der Physik 30: 1–56.
Franklin, Joel, and David J. Griffiths. 2014. The fields of a charged particle in hyperbolic motion. American Journal of Physics 82: 755–763.
Liénard, Alfred-Marie. 1898. Champ électrique et magnétique produit par une charge électrique concentrée en un point et animée d’un mouvement quelconque. L’Eclairage Electrique 16: 5–14, 53–59, 106–112.
Minkowski, Hermann. 1908. Raum und Zeit, Vortrag gehalten auf der 80. Naturforscher-Versammlung zu Köln am 21. Leipzig: Teubner, 1909. A recent English translation (by D. Lehmkuhl) can be found in: Minkowski space–time: A hundred years later, ed. Vesselin Petkov, xiv–xlii. Springer, 2010.
Pauli, Wolfgang. 1921. Relativitätsttheorie. In Encyclopädie der mathematischen Wissenschaften, mit Einschluss ihrer anwendungen, ed. Arnold Sommerfeld, 5, Physik, part 2, 539–775. Leipzig: Teubner, 1904–1922. Reprinted in translation (by G. Field) with supplementary notes as Theory of relativity. London: Pergamon Press, 1958.
Sommerfeld, Arnold. 1910. Zur Relativitätstheorie. II. Vierdimensional Vektoranalysis. Annalen der Physik 33: 649–689.
von Laue, Max. 1911. Das Relativitätsprinzip. Braunschweig: Vieweg.
Walter, Scott. 2007. Breaking in the 4-vectors: The four-dimensional movement in gravitation, 1905–1910. In The genesis of general relativity, vol. 3, ed. Jürgen Renn, 193–252. Berlin: Springer.
Wiechert, Emil J. 1900. Elektrodynamishe Elementargesetze. Archives Néerlandaises de Sciences Exactes et Naturelles 5: 549.
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The author in much indebted to the anonymous reviewers for very helpful and detailed comments.
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Communicated by Tilman Sauer.
Appendix
Appendix
The original publications of Minkowski, Sommerfeld, Laue, and Pauli that have been used for this review article do not share a common notation. In order to facilitate the comparison of these early contributions to one another, and to this article, we are providing Table 1 with the different notations. Our variables a and \(\rho \) are the same as Pauli’s, and our variable r is the same as Minkowski’s. There is no corresponding diagram in Pauli’s book.
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Galeriu, C. Electric charge in hyperbolic motion: the early history. Arch. Hist. Exact Sci. 71, 363–378 (2017). https://doi.org/10.1007/s00407-017-0191-x
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DOI: https://doi.org/10.1007/s00407-017-0191-x