Geometric theory of fields in brief:
1) Each body describes a time-like curve in the space-time continuum.
2) All fields in vacuo are parameters of this curve.
3) Gravitation and accelerated motion are the relevant parts of the
curvature vector. Force = mass times curvature_vector
4) Electromagnetism is performed from a pair of special dual surfaces
accompanying the curve. Rainich knew this already in 1924.
U.E. Bruchholz: Geometry of Space-Time,
Progress in Physics, 5 (4), 2009, 65-66,
http://www.ptep-online.com/2009/PP-19-06.PDF,
5) The geometry is based on the known (!) Einstein-Maxwell equations.
Solutions different by zero follow with integration constants.
6) Numerically solving the Einstein-Maxwell equations, one sees the
basical states of the world:
a) Determinacy comes from the first approximations of the Einstein-
Maxwell equations (that are wave equations). The integration
constants are those of the wave equations, and identical with
particle parameters (for stationary solutions).
b) Indeterminacy is the consequence of the fact that there are
only 10 independent equations for 14 components, i.e. the
Einstein-Maxwell equations are underdetermined. That does not
vary the integration constants.
c) Deterministic chaos can be seen at numerical calculation of the
Einstein-Maxwell equations. It determines the discrete values
of the integration constants. Of course, these values are identical
with known particle values, resp., one can predict unknown values
as already done for supposed neutrinos.
7) There are always geometric limits. As well, singularities are only
in observer's coordinates, not in local coordinates.
You can see that all in
Ulrich Bruchholz: Quanta and Particles as Necessary Consequence
of General Relativity. LAP Lambert Academic Publishing, 2017,
ISBN 978-620-2-07669-2.
One can understand as it is with Planck's Constant in
U. E. Bruchholz, Derivation of Planck's Constant from Maxwell's
Electrodynamics, Progress in Physics 5 (4) (2009), 67.
http://www.ptep-online.com/2009/PP-19-07.PDF
A quintessence of the geometric theory is to see in
http://viXra.org/abs/1904.0328