The equation for a 10 dimension spacetime manifold is given. The values for r are approximate. R1 is the curvature for gravity, the other r values are for electron, weak and strong force, respectively.

Present work expects a Calabi-Yau manifold to provide solutions for the M-theory, but it presently it has too many symmetries. This formula shows the number of dimensions and also shows how the symmetry breaks. Symmetry is broken because r is of different sizes for the different dimensions, therefore has fewer symmetries than a Calabi-Yau manifold with the same number of dimensions. The formula is of a torus within a torus within a torus. When r1 = r2 = r3 = r4= r, the formula becomes that of a 10 dimension hypersphere in 11-space:

Full symmetry is restored geometrically.

The differential equation to be solved on this manifold is simply the transport equation. The quantum mechanical equation simplifies since mass is defined as momentum in the general theory of particles and forces, E=cp and (x·p)=h. x is defined to be the path length along a geodesic on the manifold, x=2p r when the path circles along a single dimension. Using the quantum differential operator for momentum, the differential equation becomes:

This equation is based on E=cp and assumes that mass is simply a momentum component traveling along an orthogonal vector.

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Last Updated on Novemer 20, 1999

©1999 Robert D Rutkiewicz