  Paul Busch has emphasized on various occasions the importance for physics of
going beyond a merely instrumentalist view of quantum mechanics. Even if we
cannot be sure that any particular realist interpretation describes the world
as it actually is, the investigation of possible realist interpretations helps
us to develop new physical ideas and better intuitions about the nature of
physical objects at the micro level. In this spirit, Paul Busch himself
pioneered the concept of ``unsharp quantum reality'', according to which there
is an objective non-classical indeterminacy---a lack of sharpness---in the
properties of individual quantum systems.
  We concur with Busch's motivation for investigating realist interpretations
of quantum mechanics and with his willingness to move away from classical
intuitions. In this article we try to take some further steps on this road. In
particular, we pay attention to a number of \textit{prima facie} implausible
and counter-intuitive aspects of realist interpretations of unitary quantum
mechanics. We shall argue that from a realist viewpoint, quantum contextuality
naturally leads to ``perspectivalism'' with respect to properties of spatially
extended quantum systems, and that this perspectivalism is important for making
relativistic covariance possible.
