Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2002-10-18
NATO Sci.Ser.II 95:165-174,2003
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
11 pages, Talk presentedat NATO Advanced Research Workshop "The Nature of Time: Geometry, Physics & Perception", May 2002, Tat
Scientific paper
The geometric calculus based on Clifford algebra is a very useful tool for geometry and physics. It describes a geometric structure which is much richer than the ordinary geometry of spacetime. A Clifford manifold (C-space) consists not only of points, but also of 1-loops, 2-loops, etc.. They are associated with multivectors which are the wedge product of the basis vectors, the generators of Clifford algebra. Within C-space we can perform the so called polydimensional rotations which reshuffle the multivectors, e.g., a bivector into a vector, etc.. A consequence of such a polydimensional rotation is that the signature can change: it is relative to a chosen set of basis vectors. Another important consequence is that the well known unconstrained Stueckelberg theory is embedded within the constrained theory based on C-space. The essence of the Stueckelberg theory is the existence of an evolution parameter which is invariant under the Lorentz transformations. The latter parameter is interpreted as being the true time - associated with our perception of the passage of time.
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