While we know that in principle quantum mechanics is needed for a comLecture 3 9/29/09 continued from N4 pletely correct theory of the microscopic behavior of materials, it is also well understood that classical mechanics is a very good approximation for many purposes. In particular, as long as we are not concerned with very low temperatures or high frequency vibrations, then classical mechanic...

Sergio Chibbaro and Lamberto Rondoni and Angelo Vulpiani 1 Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR7190, Institut Jean Le Rond d’Alembert, F-75005 Paris, (France) 2 Dip. Scienze Matematiche, Politecnico di Torino, C. Duca degli Abruzzi 24, Torino. 3 INFN, Sezione di Torino, Via P. Giuria 1, Torino (Italy). 4 Dipartimento di Fisica, Università”La Sapienza” Roma (Italy) 5 ISC-CNR, Piaz...

We formulate physically-motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to Quantum Mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement th...