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

CHAPTER 2. A REVIEW OF EINSTEIN CARTAN EVANS (ECE) . . .
and have O(3) symmetry as follows:
q (1) × q (2) = iq (3)∗ , (2.182)
q (2) × q (1) = iq (1)∗ , (2.183)
q (3) × q (1) = iq (2)∗ . (2.184)
In the absence of rotation about Z :
∇ × A (1) = ∇ × A (2) = 0, (2.185)
A (3) = A (0) k. (2.186)
In the complex circular basis:
∇ × E (1) + ∂B (1) /∂t = 0, (2.187)
∇ × E (2) + ∂B (2) /∂t = 0, (2.188)
∇ × E (3) + ∂B (3) /∂t = 0. (2.189)
Therefore from Eqs. (2.176) to (2.189) the only field present is:
B (3)∗ = B (3) = −iB (0) q (1) × q (2)
= B (3)
z k = Bzk
(2.190)
which is the static magnetic field of the bar magnet.
Now mechanically rotate the disk at an angular frequency Ω to produce:
A (1) = A(0)
√ 2 (i − ij) exp(iΩt), (2.191)
A (2) = A(0)
√ 2 (i + ij) exp(−iΩt). (2.192)
From Eqs. (2.176) to (2.192) electric and magnetic fields are induced in a direction
transverse to Z, i.e. in the XY plane of the spinning disk as observed
experimentally. However, the Z axis magnetic flux density is unchanged by
physical rotation about the same Z axis. This is again as observed experimentally.
The (2) component of the transverse electric field spins around the rim of
the disk and is defined from Eq. (2.151) as:
E (2) = E (1)∗
∂
= − + iΩ A
∂t (2) . (2.193)
It can be seen from section 2.5 that iΩ is a type of spin connection. The latter
is caused by mechanical spin, which in ECE is a spinning of space-time itself.
The real and physical part of the induced E (1) is:
Real(E (1) ) = 2
√ 2 A (0) Ω(i sin Ωt − j cos Ωt) (2.194)
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