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

2.3. THE FIELD AND WAVE EQUATIONS OF ECE THEORY
clarified. The field equations were subsequently developed from the Bianchi
identity discussed in Section 2.2. This section summarizes the main equations
and methods of derivation. More detail of the equations is given in technical
appendices. The field equations are relevant to classical gravitation and electrodynamics,
and the wave equation to causal and objective quantum mechanics.
Full details of derivations are available in the literature [1, 12], the aim of this
section is to summarize the main inferences of ECE theory to date.
The Bianchi identity (2.5) and its Hodge dual (2.9) become the homogeneous
and inhomogeneous field equations of ECE respectively. These field equations
apply to the four fundamental fields of force: gravitational, electromagnetic,
weak and strong and can be used to describe the interaction of the fundamental
fields on the classical level. For example the electromagnetic field is described
by making the fundamental hypothesis:
A = A (0) q (2.19)
where the shorthand (index-less) notation has been used. Here A represents the
electromagnetic potential form and cA (0) is a primordial quantity with the units
of volts, a quantity which is proportional to the charge, −e, on the electron. The
hypothesis (2.19) implies that:
F = A (0) T (2.20)
where F is shorthand notation for the electromagnetic field form. The homogeneous
ECE field equation of electrodynamics follows from the Bianchi identity
(2.5):
d ∧ F + ω ∧ F = A (0) R ∧ q (2.21)
and the inhomogeneous ECE field equation follows from the Hodge dual (2.9)
of the Bianchi identity:
d ∧ F + ω ∧ F = A (0) R ∧ q. (2.22)
Therefore the ECE field equations are duality invariant, a basic symmetry which
means that they transform into each other by means of the Hodge dual [1, 12].
The Maxwell Heaviside (MH) field equations of the standard model do not have
this fundamental symmetry and in differential form notation the MH equations
are:
and
d ∧ F = 0 (2.23)
d ∧ F = J/ɛ0
(2.24)
where J denotes the inhomogeneous charge/current density and ɛ0 is the S. I.
vacuum permittivity. Duality symmetry is broken by the fact that there is no
16