"Cartan indeed noticed that teleparallelism implies completely geometric Einstein equations, through the expression of the metric curvature in terms of the torsion and its derivatives. Likely because of lack of receptivity by Einstein, it appears that Cartan did not attempt to connect the torsion with the electromagnetic field."
Theory of the Unified Field…
This web page is devoted to the development by Jose G. Vargas and Douglas G. Torr of the theory of the unified field that Einstein tried when he postulated Teleparallelism (TP), or absolute parallelism. Not to be confused with Einstein-Cartan theory, this theory extends overlooked work in physics of Élie Cartan, who gave Einstein unheeded correct advice on TP.
based on Teleparallelism…
Cartan indeed noticed that TP implies completely geometric Einstein equations, through the expression of the metric curvature in terms of the torsion and its derivatives. Likely because of lack of receptivity by Einstein, it appears that Cartan did not attempt to connect the torsion with the electromagnetic (EM) field.
that includes Quantum Mechanics…
We connect torsion with EM field using teleparallel affine connections in Finsler bundles on pseudo-Riemannian metrics of Lorentzian signature. This geometric structure is integrated with the Kähler calculus of differential forms, which, being based on Clifford algebra, generalizes Cartan’s exterior calculus. The Kähler equation, which is based on that calculus and which generalizes the Dirac equation, solves the fine structure of the hydrogen atom without gamma matrices. A Kaluza-Klein (KK) space results, where geometry and general relativity meet quantum mechanics.
where Geometry becomes Physics…
The first equation of structure (i.e. for the torsion) of the KK space is now the Kähler equation. The second equation of structure, whose contraction implies Einstein’s geometric equations, generates an electromagnetic energy-momentum tensor. The latter contains the usual terms and, in addition, one whose integral over all of space is zero. This “mute” term, however, implies gravitational consequences, as pointed out by Feynman (Lectures on Physics, Volume II, chapter 27, section 4).
classical and quantum mechanical…
Gravitation and quantum mechanics are thus unified ab initio, while preserving there respective identities. The weak and strong interactions, but also classical mechanics, start to emerge. Each does so, however, in its own idiosyncratic way.
and emergence marries reductionism.
All physical concepts are to be viewed as emergent. Emergence of this type and reductionism are as inseparable as the two faces of an ordinary surface.