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 ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{S}}_{\ensuremath{\theta}}$ defined by two macroscopically distinct states. The analyzers that realize the unitary operations ${U}_{\ensuremath{\theta}}$ determining the measurement settings $\ensuremath{\theta}$ 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 ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{S}}_{\ensuremath{\theta}}$ distinguishing between the states. Deterministic macroscopic realism assumes MR for the system defined prior to the interaction ${U}_{\ensuremath{\theta}}$ 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 ${U}_{\ensuremath{\theta}}$, at the time ${t}_{f}$---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 ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{S}}_{\ensuremath{\theta}}$ 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.