New Transformation Equations and the Electric Field Four-vector

2. Introduction

In special relativity, Einstein introduced two postulates: The first postulate 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 incorrect. 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 coordinate transformation equations and some of its consequences. The second postulate of special relativity 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 and the propagation of light in four dimensions rather than three.

Unlike the Maxwell tensor, its replacement, the electric field tensor, includes nonzero terms along the principle diagonal. These terms are responsible for the appearance of additional terms in many of the existing laws of physics. 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 the charge on its velocity.

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