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Copyright © 1999-2008 David E. Rutherford
All Rights Reserved
Fifth edition published: January 17, 2001
Last revised: June 7, 2008
In special relativity, spacetime can be described as Minkowskian. We intend to show that spacetime, as well as the laws of electromagnetism, can be described using a four-dimensional Euclidean metric as a foundation. In order to formulate these laws successfully, however, it is necessary to extend the laws of electromagnetism by replacing the Maxwell tensor with an electric field four-vector. In addition, to assure the covariance of the new laws, we introduce equations that, completely, replace the Lorentz transformation equations and Lorentz group. The above replacements, we believe, lead naturally to a unification of the electromagnetic field with the gravitational and nuclear fields. We introduce, also, a new mathematical formalism which facilitates the presentation of our laws.