1. Auflage 2000, Universität Basel.
Content: Introduction – Geometric Algebra – Completely Dual Approach – Projective Geometry – Principle of Duality – Space and Counterspace – Momentum as a Plane-like Vector – Mechanics in Space and Counterspace – Symplectic Geometry – Dual Mechanics – Lorentz Transformations – Electrodynamics – Conclusion and Outlook – Appendix – Dank.
About this book: This PhD thesis originates in the quest of the role played by the projective principle of duality in physics. The investigations are performed in terms of the numbers of Geometric Clifford Algebra.
The first part presents the completely dual approach to Geometric Algebra, the formulation of the principle of duality in the universal language of Geometric Algebra, and an introduction to the new and powerful concept of space and counterspace.
The second part is devoted to physical applications. Lagrangian mechanics, Hamiltonian mechanics, Lorentz transformations, and relativistic electrodynamics are embedded into the dual framework of space and counterspace. Guided by the principle of duality the counterpart theories to Lagrangian and Hamiltonian mechanics are derived. They are promising candidates for a completely new perspective to optics.
The third part connects our investigations to the old question whether there are absolute spatial quantities. More than 100 years ago, Einstein's interpretation of the Michelson-Morley null experiment removed the ether as an element of the natural sciences and with it Newton's absolute space. Instead of the absolute quantities `space' and `ether', Einstein postulated the universal principle of relativity and the universal law of constant light velocity. Without violating any of these postulates our investigations prove that the origin of counterspace is an absolute spatial quantity with respect to the nature of the physical laws.