[also adapted from our email exchange]
Hi Lydia,
Nice to hear for you, and thanks for the comments.
1) This is a confusion of terminology, which I'm sorry I didn't clarify in the paper. The term "separability" is used by quantum information theorists to describe quantum states that are convex combinations of product states. In quantum foundations, the same term is sometimes used to describe an assumption about ontological models, namely that the ontic state space satisfies kinematical locality. You're right that lambda_AB is just the ontic state for AB. The consequences of kinematical locality on the epistemic states is just that we can write P(lambda_AB) = P(lambda_A,lambda_B) and we can therefore talk about whether lambda_A and lambda_B are correlated or uncorrelated, etcetera. Kinematical locality does not imply the quantum information theorists' notion of separability.
2) The information that needs to be specified to make predictions is certainly the positions and the velocities, but I don't think one should consider the velocities to be part of the kinematics. Maybe this argument will clarify why I think so: in a variational approach to classical mechanics, one could specify the initial position and the final position and deduce the trajectory followed by the particle in the intervening time. But one would not thereby conclude that the kinematics included the initial and final positions (at least, that's not how people usually talk about kinematics). So one shouldn't, I think, identify the variables used for boundary conditions with the kinematics.
3) The bit where I present the causal diagrams for Hamiltonian and Newtonian mechanics shows that one can easily translate a theory from the kinematical-dynamical paradigm into the causal paradigm. Deterministic dynamics is represented by a conditional probability distribution which is a point distribution on the conditioned variable for every value of the conditioning variable. For instance, in the Hamiltonian scheme, the conditional probability P(p2|q1,p1) is just delta(p2,f(q1,p1)) where delta(.,.) is the Kronecker delta and f(q1,p1) is just the function that defines p2 in terms of the earlier phase space point. That being said, these causal diagrams don't yet capture all and only the nonconventional bits. I'm not exactly sure what mathematical formalism does this. People in machine learning have introduced the notion of an equivalence class of causal diagrams, and this strikes me as promising.
4) As I see it, an operationalist is a kind of empiricist. Empiricism in the philosophy of science is the idea that the goal of science is simply to "reproduce the phenomena", for instance, to provide an account of what we experience. We should not ask "why", according to the empiricist, only "how". Empiricists were motivated to build knowledge on top of statements about experience because they thought that in this way it would be immune from error. This motivation was later convincingly shown to be misguided by people like Popper and Quine but in physics we still have a strong empiricist streak in our attitude towards quantum theory. The operational brand of empiricism is that the primitives in terms of which experience is described are experimental operations.
So, yes, "not about the underlying reality" is a good description of operationalism. If you look at any of the recent work on operational axioms for quantum theory, you'll get a feeling for the operational interpretation. Basically, an operationlist talks about preparations, transformations and measurements of systems, not about properties of systems or evolution of those properties. Your example of shadow growth is spot on.
The first couple of sections of this short paper that I wrote with Lucien Hardy describes in more detail the difference between realism and operationalism.
