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

2.5. TENSOR AND VECTOR LAWS OF CLASSICAL DYNAMICS . . .
electromagnetic phase with ECE theory [1, 12] it has been demonstrated that
the phase is due to the well known B(3) spin field of ECE theory, first inferred in
1992 from the inverse Faraday effect. This generally relativistic development of
the electromagnetic phase is closely related to the AB effects and resolves basic
problems in the standard model electromagnetic phase [1, 12]. It has therefore
been shown that the B(3) field is ubiquitous in optics and electrodynamics,
because it derives from the ubiquitous spin connection of space-time itself.
These considerations have also been developed for the topological phases,
such as that of Berry, using for self consistency the same methodology as for the
electromagnetic, Dirac and Wu Yang phases [1, 12]. These well known phases
are again understood in ECE theory in terms of Cartan geometry by use of the
Stokes Theorem with D∧ in place of d∧. All phase theory in physics becomes
part of general relativity, and this methodology has been linked to traditional
Lagrangian methods based on the minimization of action.
2.5 Tensor and Vector Laws of Classical Dynamics
and Electrodynamics
The tensor law for the homogeneous field equation has been shown [1,12] to be:
∂µ F κµν = 0. (2.77)
For each κ index the structure of the matrix is:
F µν ⎡
0
⎢ −cBX
= ⎢
⎣ −cBY
cBX
0
EZ
cBY
−EZ
0
cBZ
EY
−EX
⎤
⎥
⎦
−cBZ −EY EX 0
=
⎡
⎢
⎣
0 F 01 F 02 F 03
F 10 0 F 12 F 13
F 20 F 21 0 F 23
F 30 F 31 F 32 0
⎤
⎥
⎦ .
(2.78)
The Gauss law of magnetism in ECE theory has been shown to be obtained
from:
and so:
i.e.:
with:
κ = ν = 0 (2.79)
∂1 F 010 + ∂2 F 020 + ∂3 F 030 = 0 (2.80)
∇ · B = 0 (2.81)
B = BXi + BY j + BZk (2.82)
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