Abstract Hans Primas

Complementary Time Concepts

Abstract:

The harmonic analysis of the noncommutative affine Weyl–Heisenberg group provides a natural setting and a unifying language for defining and analyzing complementary time concepts. For example, the affine Weyl–Heisenberg group is the invariance group of human music perception.

The ergodic representations of the two two affine subgroups E and F of the affine Weyl–Heisenberg group define two mathematically well-defined complementary time concepts. None of them is sufficient, none can replace the other, both are necessary. The F-related description defines a sequentially ordered F-time and a superselection rule which separates past and future. It is appropriate for a local analysis of parts, for causal descriptions, and allows a characterization of facts by emergent classical observables. The complementary E-related description is characterized by a superselection rule which separates positive and negative temporal energies. E-time represents an extended present which is not sequentially ordered. It is appropriate for a global synthesis of wholes and to describe parallel processing.