Article révisé par les pairs
| Résumé : | The role of “chaos” in the fundamental dynamical description, both classical and quantum, is discussed. It is shown that it leads to a new formulation of laws of nature which is irreducible ( it can only be applied to probability distributions, or in quantum mechanics, to the density matrices ) and includes time symmetry breaking. This formulation is first applied to chaotic maps and then to Hamiltonian systems, classical or quantum, which belong to the class of non-integrable systems in the sense of Poincaré. Those are the Large Poincaré Systems ( LPS ) which include all systems studied in non-equilibrium statistical mechanics as well as interacting fields. This formulation requires the giving up of the traditional Hilbert space description and going to generalized spaces ( such as “rigged” Hilbert spaces ). In these spaces we obtain a complex spectral representation which includes irreversible processes. Moreover the solutions of the Liouville-von Neumann equation are not factorisable ( in quantum mechanics ). This leads to a purely dynamical interpretation of the “collapse” of the wave function. In this paper emphasis is put on simple physical examples in preference to general theory to introduce the reader to the ideas at the basics of the extension of the traditional formulation of classical or quantum mechanics. |
