Spin Connection Resonance in the Bedini Machine - Alpha Institute ...

A
Appendix 1: Reduction of Form Notation to
Vector Notation
In differential form notation the electromagnetic field in ECE theory is:
which in tensor notation is 1–10:
The electromagnetic potential is:
F a = d ∧ A a + ω a b ∧ A b
(A.1)
F a µν = ∂µA a ν − ∂νA a µ + ω a µbA b ν − ω a νbA b µ. (A.2)
A a µ = A (0) q a µ
where q a µ is a rank two mixed index tensor defined by:
(A.3)
V a = q a µV µ . (A.4)
Here V a and V µ are four vectors in different frames of reference labeled a and
µ in four dimensional space-time. Consider a particular example of Eq. (A.2):
F 1 23 = ∂2A 1 3 − ∂3A 1 2 + ω 1 2bA b 3 − ω 1 3bA b 2. (A.5)
Either side of the equation there are rank three tensors whose components
must correspond to each other on both sides. Thus:
F 1 23 =(∂2A3 − ∂3A2) 1 + ω2bA b 3 − ω3bA b 2
1 . (A.6)
Inside the brackets on the right hand side are anti-symmetric tensor components
which correspond to the components of an axial vector (magnetic field)