The fundamental geometrical structure of ECE theory is well known differential geometry, which is transformed into physics according to the Ockham Razor, by use of the simplest possible hypotheses, and minimum possible number of hypotheses.

1) Geometrical Structure

T = D ^ q

R = D ^ omega

D ^ T := R ^ q = q ^ R

where

D ^ = d ^ + omega ^

These are the two Cartan structure equations and the Cartan identity, which are well known in differential geometry. This notation is meant to be shorthand notation with all indices suppressed. The symbol T denotes the Cartan torsion form, R denotes the Cartan curvature form, omega the Cartan spin connection, q the Cartan tetrad form, and d ^ the Cartan exterior derivative. The Cartan identity may also be written as:

D ^ T tilde := R tilde ^ q = q ^ R tilde.

where tilde denotes Hodge dual. This is simply because the Hodge duals of the two-forms T and R are themselves two forms.

2) The hypotheses transform the geometry into physics in the simplest manner possible. The electromagnetic potential form is by hypothesis:

A = A(0) q

The gravitational potential form is:

phi = phi(0) q

These define the field equations of physics and the ECE engineering models for new energy and counter gravitation.

3) Quantum mechanics is derived from the very fundamental tetrad postulate of differential geometry, using one additional hypothesis:

R = – kT

where R is a scalar curvature defined directly by the tetrad postulate and k is the Einstein constant. So T is a scalar valued quantity with units of kilograms per metres cubed, or mass density. The minus sign is a convention.

ECE theory is basically very simple, and wholly original, and the only ideas that now survive from the twentieth century physics are the use of k and the minus sign by convention. It unifies quantum mechanics, classical mechanics and electrodynamics, and paves the way for a wholly new particle / field theory.

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