Alternative Einstein-Podolsky-Rosen argument based on premises not falsified by Bell's theorem: weak macroscopic realism and weak local realism

The Einstein-Podolsky-Rosen (EPR) paradox gives an argument for the incompleteness of quantum mechanics based on a plausible criterion for reality, as well as the assumption of locality. A general view is that the argument is compromised, because EPR's premises are falsified by Greenberger-Horne-Zeilinger (GHZ) and Bell experiments. In this paper, we present an EPR argument based on premises not falsified by these experiments. First, we consider macroscopic EPR-Bohm, Bell, and GHZ experiments using spins ̂ \^S_θ defined by two macroscopically distinct states. The analyzers that realize the unitary operations U_θ determining the measurement settings θ are nonlinear devices creating macroscopic superposition states. We note two definitions of macroscopic realism (MR). For a system with two macroscopically distinct states available to it, MR posits a predetermined outcome for the measurement ̂ \^S_θ distinguishing between the states. Deterministic macroscopic realism assumes MR for the system defined prior to the interaction U_θ being carried out but is falsifiable by the macroscopic Bell and GHZ proposals. Motivated by arguments to uphold MR (without resorting to decoherence), as well as no-signaling and the properties of a meter, we define a set of premises referred to as weak macroscopic realism (wMR). Weak macroscopic realism (wMR) posits MR for the system after U_θ, at the time tf---when the system is prepared with respect to the measurement basis, ready for a ``pointer'' measurement and readout. For this system, wMR posits that the outcome of ̂ \^S_θ is determined and not changed by interactions that might subsequently occur at a remote system B. The premise wMR also posits a weaker version of EPR's criterion for reality. Importantly, we show that the GHZ and Bell predictions are consistent with wMR. Yet, an EPR paradox arises for a macroscopic EPR-Bohm state, based on wMR. As considered by Schr\"odinger, it is possible to measure two complementary spins of system A simultaneously, ``one by direct, the other by indirect measurement'': If we assume wMR, then once both settings are fixed, the outcomes of the two spins are both determined. We revisit the original EPR paradox and find a similar result: An EPR argument can be based on a set of premises, weak local realism, which we show are not falsifiable by GHZ or Bell experiments.