This web site is concerned with demonstrating a paradigm shift in the development and application of quantum theory.

My research on incommensurate behaviour in order-disorder transitions has led me to a new awareness of the role of translational symmetry in quantum mechanics.

The relevant Lie matrix group SO(2) in translation, demands the use of a dual k-wave system associated with quantum harmonic oscillations. This group provides essential gradient and energy invariance in space and time.

Proof of the importance of the dual k-wave system is provided by electron-optical resolution of the dual system of quantum wave modulations related to the e and f reflections in the plagioclase feldspars.

Two new translation groups based on Lie group O(2) are presented. The first, which I describe as the Lie group O(2), provides the answer to the EPR paradox, and the second, which I describe as the Landau group, has been designed to provide a new quantum solution of the order-disorder transition, and related incommensurate behaviour, in the binary solid solution system of the plagioclase feldspars.