How Much and What Kind of Nonlocality? A Sufficient Condition for Singlet Spin Correlations

We give a sufficient condition of nonlocality in order to reproduce singlet spin correlations. For a given pair of hidden variables and measurement directions this condition determines only the product of the outcomes and reproduces statistical correlations for all measurement directions; but fails to give a complete description of sub-systems, provides no means to calculate all joint probabilities and puts no constraints on signaling. In order to complete the model we introduce an additional condition. In this case we observe that the character of the nonlocality changes (outcome independence is violated) and nonlocality applies asymmetrically to the spacelike separated parties. At first sight it seems possible to explain this asymmetry by assuming that the observer that measures first determines his outcome locally. However this assumption has no meaning without adopting a privileged reference frame.