criticisms of the einstein field equation - Alpha Institute for Advanced ...

2.5. TENSOR AND VECTOR LAWS OF CLASSICAL DYNAMICS . . .
using the symmetric canonical energy momentum density tensor:
T κµ = T µκ
(2.116)
and the components of the electric and magnetic fields are components of J κµν
as follows:
E 00i = c2
eω J 00i , i = 1, 2, 3, (orbital),
E ii0 = c2
eω J ii0 , i = 1, 2, 3, (spin),
B 112 = c
eω J 112 , B 221 = c
eω J 221 , B 331 = c
eω J 331 .
(2.117)
The two index angular energy/momentum tensor of the electromagnetic field
is an integral over the three index density tensor. Ryder gives one example of
such an integral in Minkowski space-time [18]:
M µν
= M 0µν d 3 x. (2.118)
Therefore the four laws of electrodynamics in ECE theory are:
∇ × E + ∂B
∂t
∇ · B = 0, (2.119)
= 0, (2.120)
∇ · E = ρ/ɛ0, (2.121)
∇ × B − 1
c2 ∂E
∂t = µ0J, (2.122)
and therefore have the same vector structure as the familiar MH equations.
However, as argued in this section, the ECE theory gives additional information.
In the four laws the components of the magnetic and electric fields are as follows.
The Gauss law of magnetism in ECE theory is, for all practical purposes (FAPP):
∇ · B = 0 (2.123)
which is an orbital law in which the components of the magnetic field are proportional
to orbital components of the angular momentum/energy density tensor
and are:
B = B 001 i + B 002 j + B 003 k. (2.124)
The Faraday law of induction in ECE is a spin law with electric and magnetic
field components as follows:
E = E 332 i + E 113 j + E 221 k, (2.125)
B = B 101 i + B 202 j + B 303 k. (2.126)
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