Violations of Bell inequalities for measurements with macroscopic uncertainties: What it means to violate macroscopic local realism

We suggest a method to test the premise of “macroscopic local realism” that is sufficient to derive Bell inequalities when measurements of photon numbers 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” that 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.