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.
If you are interested, there is a conversation about that paper
going on the
FQXi forum.
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,
which describes the difference between realism and operationalism.
On 17/09/12 15:18, Normand Beaudry wrote: