We discuss the form of the special Lorentz transformation, and the corresponding transformation of the electromagnetic field, in which the transformation matrix is diagonal. We derive the diagonal form of the special Lorentz transformation directly, in a simple way, and show that it is sometimes more convenient to apply than the algebraically equivalent conventional form of the transformation. The convenience is especially evident in deriving the linear Doppler effect, and the relativistic addition of more than two parallel velocities. By writing Maxwell's equations in terms of linear combinations of coordinates which have simple transformation properties, we arrive at the transformation equations of the Maxwell fields in a diagonal form, as well as at the plane wave solutions, in a natural manner. The derivations and applications described above should be of use in a course on relativity because of their simplicity and directness.
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February 1970
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February 01 1970
Special Relativity and Diagonal Transformations Available to Purchase
Leonard Parker;
Leonard Parker
Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201
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Glenn M. Schmieg
Glenn M. Schmieg
Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201
Search for other works by this author on:
Leonard Parker
Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201
Glenn M. Schmieg
Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201
Am. J. Phys. 38, 218–222 (1970)
Article history
Received:
June 13 1969
Citation
Leonard Parker, Glenn M. Schmieg; Special Relativity and Diagonal Transformations. Am. J. Phys. 1 February 1970; 38 (2): 218–222. https://doi.org/10.1119/1.1976289
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