Testing macroscopic local realism using local nonlinear dynamics and time settings

We show how one may test macroscopic local realism where, differently from conventional Bell tests, all relevant measurements that lead to a violation of a Bell inequality need only distinguish between two macroscopically distinct states of the system being measured. Here, measurements give macroscopically distinct outcomes for some property of the system and do not resolve microscopically (of order (h) over bar over bar). To obtain a quantifiable test, we define N-scopic local realism where the outcomes are separated by an amount similar to N. We show for N up to 20 that violations of N-scopic local realism are predicted for entangled systems of N bosons at each of two sites. We further demonstrate for arbitrarily large alpha the violation of alpha-scopic local realism, for entangled superpositions of coherent states with amplitudes-alpha, infinitely separated in phase space, as alpha -> infinity. To achieve the Bell violations, the two separated subsystems evolve dynamically according to a local nonlinear unitary interaction. The tests may be understood in two ways. First, they are macroscopic Bell tests involving spacelike separated measurement events, where the choice of measurement setting at each site corresponds to a choice between two different times of local interaction. The interaction may be seen as the unitary stage of a local measurement process. Second, the proposal is a strong version of a Leggett-Garg test of macrorealism that uses two trajectories, where the usual assumption of noninvasive measurability as applied to measurements at one site is replaced by that of macroscopic locality. For N = 1, tests are feasible and give a way to demonstrate no classical trajectories without the assumption of noninvasive measurability, using instead that of locality.