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(2017) From Riemann to differential geometry and relativity, Dordrecht, Springer.
Some remarks on "a contribution to electrodynamics" by Bernhard Riemann
Hubert F. M. Goenner
pp. 111-123
Around 1850, the idea originated that electromagnetic forces between moving charges in circuits are propagated with the velocity of light. After such a speculation by C. F. Gauss in 1845, B. Riemann, in 1858, suggested the inhomogeneous wave equation in 3-dimensional space for the modeling of this propagation. He found a particular solution replacing Coulomb's potential, now called the retarded potential. His attempt failed to derive from this solution Weber's action-at-a-distance potential. Riemann withdrew his pertinent paper before it became printed. After a description of some aspects of research by Gauss, Weber and Riemann, a likely reason for Riemann's withdrawal is specified differing from recent suggestions by historians of mathematics.
Publication details
DOI: 10.1007/978-3-319-60039-0_3
Full citation:
Goenner, H. F. (2017)., Some remarks on "a contribution to electrodynamics" by Bernhard Riemann, in L. Ji, A. Papadopoulos & S. Yamada (eds.), From Riemann to differential geometry and relativity, Dordrecht, Springer, pp. 111-123.