New Transformation Equations and the Electric Field Four-vector

Introduction

In special relativity, Einstein introduced two postulates: The first postulate is that the speed of light is invariant for all inertial observers. In this theory, unlike in relativity, we use a Euclidean metric to describe spacetime, leading to a redefinition of the invariance of the speed of light in terms of a four-vector, rather than a three-vector. The second postulate of relativity is that the laws of physics are the same for all inertial observers. This requires that the laws have a covariant form under a Lorentz transformation between inertial reference frames. Our intention is to show that the Lorentz equations are incomplete. Since these equations are used to determine the covariance of the laws of physics, any change in their form requires a change in the form and scope of these laws. We will introduce the new version of the Lorentz transformation equations and some of its consequences.

Unlike the Maxwell tensor, its analog, the electric field tensor, includes nonzero terms along the main diagonal. These terms are responsible for the appearance of additional terms in many of the existing laws of physics, for example, Maxwell's electromagnetic field equations, the Lorentz four-force equations, and the electromagnetic energy-momentum tensor.

The Euclidean nature of spacetime, in this theory, leads directly to the invariance of charge density as well as the dependence of the magnitude of a charge on its velocity.

E-mail: drutherford@softcom.net