3. GENERAL WAVE, FIELD AND FORCE EQUATIONS OF THE EVANS THEORY

The wave and field equations of this section are generalizations to unified field theory of the well-known wave and gauge field equations of electrodynamics [19]. Consider the Evans field equation in the form

        G q^a_μ = kT q^a_μ .                                                                         (62)

The unified potential field is the tetrad or vector-valued one-form q^a_μ , which is in general an asymmetric square matrix. The latter can always be written as the sum of symmetric and antisymmetric component square matrices, components that are physically meaningful potential fields of nature:

        q^a_μ = q^a_μ^(S) + q^a_μ^(A) .                                                                 (63)

This decomposition is correct. However, it is useless because of not transforming covariantly.

The symmetric and antisymmetric parts of q^a_μ do NOT transform covariantly
and hence have NO PHYSICAL MEANING.

In the Evans unified field theory the gravitational potential field is identified [1-10] as the tetrad q^a_μ and the electromagnetic potential field as A^(o)q^a_μ , where A^(o) is measured in volts. The unit of magnetic flux, i.e., the weber (or V ·s) belongs to h^-/e, the magnetic fluxon, and both h^- and e are manifestations of the principle of least curvature [1-10] of the Evans unified field theory. Both the gravitational and the electromagnetic potential fields can in general have symmetric and antisymmetric components:

        A^a_μ = A^(o) q^a_μ = A^a_μ^(S) + A^a_μ^(A) ,                                                 (64)

The symmetric and antisymmetric parts of A^a_μ do NOT transform covariantly
and hence have NO PHYSICAL MEANING.

and all four components appearing in Eqs. (63) and (64) are objectively measurable fields of nature. Geometry shows that there can be two types of gravitational potential fields: q^a_μ^(S) and q^a_μ^(A) , and two types of electromagnetic potential field, A^a_μ^(S) and A^a_μ^(A). These four types of field are governed by four Evans field equations:

        R₁ q^a_μ^(S) = − kT₁ q^a_μ^(S) ,                                                                 (65)

        R₂ q^a_μ^(A) = − kT₂ q^a_μ^(A) ,                                                               (66)

        R₃ A^a_μ^(S) = − kT₃ A^a_μ^(S) ,                                                               (67)

        R₄ A^a_μ^(A) = − kT₄ A^a_μ^(A) ,                                                             (68)

in which appear four types of canonical energy momentum tensor: symmetric gravitational, antisymmetric gravitational, symmetric electromagnetic, and antisymmetric electromagnetic. . . . We conclude that the symmetric part of the tetrad q^a_μ^(S) represents the central, gravitational potential field, and the symmetric A^a_μ^(S) represents the central, electrostatic potential field. The antisymmetric A^a_μ^(A) represents the rotating and translating electrodynamic potential field.
The antisymmetric q^a_μ^(A) represents a type of spinning potential field which is C positive, where C is charge conjugation symmetry [20]. This fundamental potential field of nature is not present in the Einsteinian or Newtonian theories of gravitation as argued and is a field that is governed by the Evans equation (66). It may be the potential field of dark matter [13], which is observed to constitute the great majority of mass in the vicinity of spiral galaxies. Significantly, the latter are thought to be formed by spinning motion, responsible for their characteristic spiral shape. The field q^a_μ^(A) is not centrally directed and so does not manifest itself in the Newtonian inverse square law in the weak-field limit. (Similarly, the antisymmetric electrodynamic A^a_μ^(A) µdoes not reduce to the Coulomb inverse square law, which must be obtained [1-10] from the symmetric electrostatic A^a_μ^(S) .) The antisymmetric q^a_μ^(A) is also the root cause of the well-known Coriolis and centripetal accelerations, which conventionally require a rotating frame not present in Newtonian dynamics.

The above Eqs.(65)-(68) have NO PHYSICAL MEANING because of referring to unphysical quantities,
namely to q^a_μ^(S), q^a_μ^(A), A^a_μ^(S) and A^a_μ^(A).

. . .

All of these fields emerge systematically from the tetrad q^a_μ by splitting it into its symmetric and antisymmetric components and by multiplying them by a C negative coefficient whose unit is the volt. The original asymmetric tetrad is the unified potential field of nature. The C negative manifestation of the unified field is ζ^(o) q^a_μ , where ζ^(o) must be determined experimentally. The coefficient ζ^(o) determines for example the way in which an electrostatic field affects the gravitational field. All forms of energy-momentum are interconvertible, implying that

        T^a_μ = T^a_μ^(S) + T^a_μ^(A) .                                                                 (69)

A useless decomposition as well.

. . . the Cartan convention [11]

        q^a_μ q^μ_a = 1,                                                                                 (20)

The unspecified reference [11] is pointing to S.M. Carroll's Lecture Notes in General Relativity where, of course, such nonsense cannot be found.

References