On the conflict between local realism and classical physics
  In contrast to the intuitively plausible assumption of local realism, entangled particles, even when isolated, are not allowed to possess definite properties in their own right, as quantitatively expressed by violations of Bell's inequalities [1]. Even as entanglement is now a key feature of quantum information and communication technology [2,3], it remains the most puzzling feature of quantum mechanics [4] and its conceptual foundation is still widely debated. Here we demonstrate that physical systems providing dicotomic outcomes are not able to guarantee both the rotation properties of physical quantities and local realism. This result opens the way to a new formulation of quantum mechanics based on only two elementary physical principles replacing the abstract mathematical axiomes of the present theory. According to this formulation, the coexistence of discrete outcomes with the classical continuous transformation properties of physical quantities under coordinate transformation inevitably implies quantum probabilities. These results, provide a simple physical explanation to the most debated quantum features and put into question the existence of physical quantities displaying continuous outcomes in agreement with approaches that attempt to integrate quantum theory with general relativity [5-8]. 
S. Savasta, O. DiStefano, R. Girlanda