Dear all,
Today I was planning to do a short follow up talk on the discussion about [kinematics and dynamics] vs [causal structure] from two weeks ago, motivated by Rob's paper http://arxiv.org/abs/1209.0023.
If you are interested, there is a conversation about that paper going on the FQXi forum http://www.fqxi.org/community/forum/topic/1558.
Here are a few Q&A resulting from an email exchange with Rob:
1) Your notion of kinematic locality on page 4: \lambda_{AB} = (\lambda_A , \lambda_B). You say that this is the same of separability, but it looks an awful lot like product states.
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. Note 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) Newtonian physics. They all insisted that the kinematics, as they learned it, should be {q_i, \dot{q}_i} (with the velocities), and not just the positions {q_i}.
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 would convince them: 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 one needs to make predictions with the kinematics.
3) Practicability. Is it always clear how to compute the causal-statistical parameters of a theory? For instance, how are they in your two examples (Hamiltonian and Newtonian physics) ? An expansion of the equations of motion?
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) Second page, your methodological principle vs operationalism The definition of operationalism here wasn't super clear to me. After re-reading, I'd guess you take it to mean: " make only claims about the outcomes of experiments, and not about the underlying reality." Is this correct? The Plato Cave example illustrates what you mean by your principle very well, but I was left without understanding what kind of theories would fit operationalism in the example.
I have a guess: The claim "shadows grow in the afternoon" (assume there is a concept of time and they call the hours before the dark "afternoon") respects operationalism. The claim "shadows grow in the afternoon because there is a source of light sinking" does not respect operationalism, because it makes a claim about something (the source of light) that you cannot measure. It would however fit your methodological principle, because it helps explain something empirical.
Is this right? Is that why the 3D shape theory is not operational(ist)?
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 id 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, you talk 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.
You might like to read the first couple of sections of this short paper http://arxiv.org/pdf/1003.5008v1.pdf, which describes the difference between realism and operationalism.
On 17/09/12 15:18, Normand Beaudry wrote:
Dear all,
This Tuesday's group meeting will be at 16:00 in HIT E 41.1. Michael and Lidia will be speaking. Cheers,
Norm
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