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

2.5. TENSOR AND VECTOR LAWS OF CLASSICAL DYNAMICS . . .
This result illustrates that the internal structure of the relation between field and
potential is different for each law of electrodynamics in ECE theory. Therefore
in a GCUFT such as ECE different types of field and potential exist for each
law, and also different types of spin connection.
For the orbital Gauss law of magnetism the internal structure of Eq. (2.136)
is:
A = A 01 i + A 02 j + A 03 k, (2.139)
ω = −(ω 01 0i + ω 02 0j + ω 03 0k). (2.140)
For the Ampère Maxwell law, a spin law, the internal structure of Eqs. (2.135)
and (2.136) are again different, and are defined as follows. The structure of Eq.
(2.135) is:
φ = cA 00 = cA 01 = cA 02 = cA 03 ,
AX = A 01 = A 11 = A 21 = A 31 ,
AY = A 02 = A 12 = A 22 = A 32 ,
AZ = A 03 = A 13 = A 23 = A 33 ,
ωX = ω 11 0 = ω 11 1 = ω 11 2 = ω 11 3,
ωY = ω 22 0 = ω 22 1 = ω 22 2 = ω 22 3,
ωZ = ω 33 0 = ω 33 1 = ω 33 2 = ω 33 3,
ω = cω 10 0 = cω 10 1 = cω 10 2 = cω 10 3
= cω 20 0 = cω 20 1 = cω 20 2 = cω 20 3
= cω 30 0 = cω 30 1 = cω 30 2 = cω 30 3
and the structure of Eq. (2.136) is:
BX = B 332 = ∂AZ
∂Y
BY = B 113 = ∂AX
∂Z
BZ = B 221 = ∂AY
∂X
− ∂AY
∂Z + ωZAY − ωY AZ,
− ∂AZ
∂X + ωXAZ − ωZAX,
− ∂AX
∂Y + ωY AX − ωXAY .
(2.141)
(2.142)
Finally the internal structures are again different for the Faraday law of induction.
In arriving at these conclusions the relation between field and potential in
the base manifold is:
F κµν = ∂ µ A κν − ∂ ν A κµ + (ω κµ
λ Aλν − ω κν λA λµ ). (2.143)
The Hodge dual of this equation is:
F κµν = (∂ µ A κν − ∂ ν A κµ + (ω κµ
λ Aλν − ω κν λA λµ ))HD
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(2.144)