Violations of Bell Inequalities for Measurements with Macroscopic Uncertainties: What does it Mean to Violate Macroscopic Local Realism?

We suggest to test the premise of “macroscopic local realism” which is sufficient to derive Bell inequalities when measurements of photon number are only accurate to an uncertainty of order n photons, where n is macroscopic. Macroscopic local realism is only sufficient to imply, in the context of the original Einstein-Podolsky-Rosen argument, fuzzy “elements of reality” which have a macroscopic indeterminacy. We show therefore how the violation of local realism in the presence of macroscopic uncertainties implies the failure of “macroscopic local realism”. Quantum states violating this macroscopic local realism are presented.