Derivation of the Geometrical Phase from the Evans Phase Law of Generally Covariant Unified Field Theory

Derivation of the Lorentz Boost from the Evans Wave Equation

“…It follows that the recently derived Evans wave equation of generally covariant unified field theory [3][4][5][6][7][8][9][10][11][12][13][14][15] must self-consistently and non-trivially reduce to the Lorentz boost, while also suggesting experimentally measurable developments such as the Evans spin field B (3) , observed in the magne-tization of matter by circularly or elliptically polarized electromagnetic radiation -the inverse Faraday effect [16]. The Lorentz boost must be derivable analytically from the structure of Evans' generally covariant unified field theory, and therefore the derivation serves as one of many checks available [3][4][5][6][7][8][9][10][11][12][13][14][15] on the self-consistency of the Evans theory. The Lorentz boost or transformation was originally devised by Lorentz following a suggestion by Fitzgerald in response to the crisis in physics posed by the Michelson-Morley experiment.…”

“…The first generally covariant unified field theory was devised by Evans in 2003 [5][6][7][8][9][10][11][12][13][14][15] using differential geometry to describe spacetime with both curvature and torsion [2]. The Evans theory has been tested experimentally and for analytical self consistency in many ways [5][6][7][8][9][10][11][12][13][14][15] and predicts from spacetime torsion the existence of the fundamental and experimentally well observed Evans spin field of electrodynamics, the B (3) field. Tiny (nanotesla) B (3) fields were first observed by Pershan et al [17], shortly after the laser first became available, as magnetization of matter with circularly polarized electromagnetic radiation at visible frequencies.…”

“…The fundamental concept in the Evans theory is the tetrad [2][3][4][5][6][7][8][9][10][11][12][13][14][15], which has a well-defined meaning in differential geometry [2], a the-ory which shows that the two differential forms that define the gauge invariant fields of nature are the Riemann (curvature) and torsion forms. These are defined, respectively, by the second and first Maurer-Cartan structure relations and in the Evans theory both are synthesized selfconsistently and in an entirely original manner [3][4][5][6][7][8][9][10][11][12][13][14][15] from the tetrad form of differential geometry.…”

“…These are defined, respectively, by the second and first Maurer-Cartan structure relations and in the Evans theory both are synthesized selfconsistently and in an entirely original manner [3][4][5][6][7][8][9][10][11][12][13][14][15] from the tetrad form of differential geometry. The tetrad (a vector-valued one-form) is the potential field, the Riemann form (a tensor-valued two-form) is the gauge invariant gravitational field, and the torsion form (a vectorvalued two-form) is the gauge-invariant electromagnetic field, whose fundamental spin invariant is the well observed Evans spin field B (3) .…”

“…They are therefore left-handed and right-handed spin labels, and originate in the fact that the tetrad must always be defined as a matrix linking two spaces in such as way as to create spin as well as mass in general relativity. The fundamental reason for this is that there are two Casimir invariants of the Einstein group (and also the Poincaré group): the mass and spin invariants [1,[3][4][5][6][7][8][9][10][11][12][13][14][15], which in differential geometry are defined respectively by the Riemann and torsion forms, i.e., by the second and first Maurer-Cartan structure relations [2][3][4][5][6][7][8][9][10][11][12][13][14][15], respectively. Only one of these appears in the original 1915 theory, the mass invariant, and then without recognition of the fact that the symmetric metric tensor used by Einstein is the dot product of two, more fundamental, tetrads.…”