vanhees71 said:
It's typical that one can only say what "physical reality" is not, but there seems to be no clear definition of it. If it's not the sum of (at least in principle possible) objective observations of phenomena, what is it then?
I would suggest to compare realism with the Lagrange formalism.
Theories with a Lagrange formalism have a certain structure. It consists of some configuration space, a parameter named time, and the Lagrangian, a function which defines some action S for a given continuous trajectory. And there is a formula which defines the Euler-Lagrange equations as the evolution equations of the theory, a formula derived from some (quite metaphysical) minimum principle.
Is there some "clear definition of the Lagrangian"? No, not in general. Is the Lagrangian observable? Not at all. Is it useful to have a Lagrange formalism? Certainly.
The situation with realism is quite similar. It is the particular realist theory which defines what, according to this theory, really exists. This is its ontology. In classical theories with a Lagrange formalism, this ontology is simply defined by the configuration space of that theory.
So, a realistic theory is a theory with some additional structure, and such an additional structure is useful. This is quite typical for fundamental principles like realism, causality, minimum principle, Hamilton formalism and so on: They require some additional restrictive structure.
vanhees71 said:
There's no determinism in QT, i.e., observables do not need to take certain values independent of the state the system is in, but that doesn't mean that there's anything incomplete in our description, because the randomness of the outcome of measurements is an observed fact, and the prediction of QT concerning the probabilities are consistent with the observations to a high confidence level.
There cannot be such an observable fact like randomness. There are well-known deterministic theories which, because of our inability to specify the initial values with sufficient accuracy, show random results for all observations. The question if this randomness is some genuine, fundamental one or simply deterministic chaos is nothing one can decide by looking only at the outcome of experiments.
In this sense QT covers all known observable stuff, no matter whether it's observed or not.