Born Rule and Noncontextual Probability

The probabilistic rule that links the formalism of Quantum Mechanics (QM) to the real world was stated by Born in 1926. Since then, there were many attempts to derive the Born postulate as a theorem, Gleason's being the most prominent. The Gleason derivation, however, is generally considered rather intricate and its physical meaning, in particular in relation with the noncontextuality of probability (NP), is not quite evident. More recently, we are witnessing a revival of interest in possible demonstrations of the Born rule, like Zurek's and Deutsch's based on the decoherence and on the theory of decisions, respectively. Despite an ongoing debate about the presence of hidden assumptions and circular reasonings, these have the merit of prompting more physically oriented approaches to the problem. Here we suggest a new proof of the Born rule based on the noncontextuality of probability. Within the theorem we also demonstrate the continuity of probability with respect to the amplitudes, which has been suggested to be a gap in Zurek's and Deutsch's approaches, and we show that NP is implicitly postulated also in their demonstrations. Finally, physical motivations of NP are given based on an invariance principle with respect to a resolution change of measurements and with respect to the principle of no-faster-than-light signalling.Comment: 10 page

Physics on the Beach with Google EarthTM

In this paper, we present a proposal for teaching wave physics based on free software Google Earth. Taking advantage of its wide source of interesting satellite images, we use Google Earth photos to illustrate the physics of water waves and the Huygens principle in natural phenomena that occurs on sea and rivers. With basic physics, we explain the main characteristics of some beach structures and waves properties near the shore. The aim of this suggestion is to make wave physics a subject more attractive to high school and university students and the process of its learning more participative