The Physical Implications of Multidimensional Geometries and Measurement

We have developed Non-Abelian gauge groups for real and complex amended Maxwell's equations in a complex 8-Dimensional Minkowski space to describe nonlocality in quantum theory and relativity which has quantum gravitational implications. We demonstrate a mapping between the twistor algebra of the complex 8-space and the spinor calculus of 5D Kaluza-Klein geometry which attempts to unify Gravitational and EM theory. Our quantum formalism demonstrates that solving the Schrödinger equation in a complex 8D geometry yields coherent collective state phenomena with soliton wave solutions. The model shows that standard quantum theory is a linear approximation to a higher Dimensional complex space. Through this formalism we can assess that complex systems can be defined within conventional quantum theory as long as we express that theory in a hyper-geometric space. We utilize our complex dimensional geometry to formulate nonlocal correlated phenomena, including the quantum description of the 1935 EPR paradox formulated with Bell's theorem. Tests by Clauser, Aspect, Gisin have demonstrated that particles emitted with approximde simultaneity at c remain correlated nonlocally over meter and kilometer distances. As Stapp has said, Bell's theorem and its experimental verification is one of the most profound discoveries of the 20th century. We will demonstrate the application of our formalism for complex systems and review the history of our model from 1974.