Realism and the physical world

I consider the extent to which the applicability of the concept of classical realism is constrained, irrespective of the validity or not of the quantum formalism, by existing experiments both in the EPR-Bell setup, including recent experiments testing 'nonlocal realistic' theories, and in the area of 'macroscopic quantum coherence'. Unless we are willing to sacrifice one or more other intuitively plausible notions such as that of the conventional 'arrow of time', it appears impossible, in either context, to maintain the classical notion of realism.