Proper-Time Formulation of Classical Electrodynamics

DOI

10.2991/jnmp.1997.4.3-4.17How to use a DOI?

Abstract

We show that Maxwell's equations have a generalization associated with the propertime of the source and a new invariance group which leaves this variable fixed for all observers. We show that the second postulate (of Einstein) depends on the anthropocentric view that the only clock to use is the proper-clock of the observer. Our work is motivated by the results of Fushchych and Shtelen (F-S), who showed that the free Maxwell equations have an additional invariance group which is Galilean. This work makes it clear that our group is distinct from but closely related to the Lorentz group, and is not Galilean. Since our present (constructive) approach requires a source, it does not apply to the free field case. In an earlier paper, we showed that the F-S transformation is an element of the proper-time (canonical) group which includes the group constructed here. This work is also related to the work of Wegener who showed that use of the proper time allows the construction of Galilean transformations from Lorentz transformations. 0. Introduction Background In the 40 years between Maxwell's theory of electrodynamics [13] in 1865 and the introduction of the special theory of relativity by Einstein [3], Lorentz [12], and Poincaré [16] in

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Tepper L. Gill
AU  - W.W. Zachary
PY  - 1997
DA  - 1997/09/01
TI  - Proper-Time Formulation of Classical Electrodynamics
JO  - Journal of Nonlinear Mathematical Physics
SP  - 418
EP  - 425
VL  - 4
IS  - 3-4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1997.4.3-4.17
DO  - 10.2991/jnmp.1997.4.3-4.17
ID  - Gill1997
ER  -