New Transformation Equations and the Electric Field Four-vector

1. The Energy-Momentum Tensor

The energy-momentum tensor is defined here as

These equations were obtained by assuming that the method used to derive the current density and force four-vector equations as described in "Additions: July 12, 1999" might be applicable to the energy-momentum tensor as well. The analogs of the equations in parentheses might now be written more succinctly as

where the brackets mean that the terms are summed over all possible permutations of the subscripts. When two subscripts are repeated, there is an additional implied sum in that term. The Lorentz homogeneous force equations say that a charged particle moving parallel to a magnetic field feels no magnetic force.

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