Macroscopic Local Realism Incompatible with Quantum Mechanics: Failure of Local Realism where Measurements give Macroscopic Uncertainties

We show that quantum mechanics predicts a contradiction with local hidden variable theories for photon number measurements which have limited resolving power, to the point of imposing an uncertainty in the photon number result which is macroscopic in absolute terms. We show how this can be interpreted as a failure of a new premise, macroscopic local realism. Bell [1] in 1966 showed that the premises of local realism (or local hidden variable theories) were incompatible with the predictions of quantum mechanics. Experiments [2] support quantum mechanics, and the general viewpoint is to reject the premise of local realism. To date theoretical and experimental effort has focussed on situations where results of the relevant measurements need be only microscopically separated . The measurements performed are intrinsically microscopic, in that one requires to clearly distinguish between results (eigenvalues of the appropriate quantum operator) which are microscopically distinct. Theoretical work has shown a failure of local realism for multi-particle (or higher spin) systems , where the system and range of results can be macroscopic. There have also been proposals [4] which show failure of local realism for quantum superpositions of two macroscopically distinct states. However the violations are still apparently only indicated where measurements at some point must resolve microscopically different results, such as adjacent photon number or spin values. While the results indicate failure of local realism for macroscopic systems, it is not clear whether one is testing a premise different to that tested in the microscopic experiments. Schrodinger [5] raised the issue of quantum mechanics apparently predicting superpositions of states macroscopically distinct (“Schrodinger-cat states”), questioning the possibility of their true existence, based on the notion that such states apparently violate a type of macroscopic realism. Recent progress [6] in the experimental generation of such superpositions highlights a need to test objectively for a true incompatibility with a macroscopic realism. Progress has been made by Leggett and Garg [7] who predict an incompatibility of quantum mechanics with the premise of “macroscopic realism and noninvasive measurability”.