New inequalities from local realism

The probabilistic formulation of local realism is shown to imply the existence of physically meaningful limits for arbitrary linear combinations of joint probabilities. The set of the so generated inequalities (setA) is wider than the previously known set of inequalities for linear combinations of correlation functions (setB). One particular inequality of the setA is shown to be violated by the probabilities of the Garg-Mermin model. The same model satisfies instead all the inequalities of the setB. As a consequence, the Garg-Mermin model is nonlocal and the setA provides physical restrictions not contained in the setB. 1. In the adopted formalism it is implicitly assumed that physical properties of the type are not created in the act of measurement. IfB(b) is measured on the systems, the setT is split into two parts,T(b _±), corresponding to the resultsB(b) = ±1, respectively. AlsoS is split intoS(b _±) from the existing correlation between and systems. If it is possible to predict that a measurement ofA(a) on the's of, say,S(b ₊) will give the results ±1 with respective probabilitiesP _±, then, on the basis of the probabilistic criterion of reality, we can attribute a physical property ₊ toS(b ₊) such that p(a ₊, ₊) is the probability ofA(a) = +1 inS(b ₊), p(a _–, ₊) is the probability ofA(a) = –1 inS(b ₊).It is natural to assume that ₊ belongs toS(b ₊) also ifA(a) isnot measured. In so doing, we exclude that future measurements create, with a retroaction in time, the physical properties of the statistical ensembles on which these measurements are performed.