|19 November (Wednesday)
|László E. Szabó
|Department of Logic, Institute of Philosophy
Eötvös University, Budapest
|Operationalist Approach to Quantum Theory: Two Representation Theorems
we formulate a general framework in operationalist terms describing a
typical experimental scenario in physics: one can perform different
measurement operations on a physical system, each of which may have
different possible outcomes. Empirical data are the observed relative
frequencies of how many times different measurement operations are
performed and how many times different outcome events occur, including
the joint performances of two or more measurements and the conjunctions
of their outcomes.
Then we show that these empirical data always admit a classical
probabilistic description in a suitable Kolmogorovian probability space,
no matter whether the phenomena in question belong to classical or
quantum physics. In other words, we give a proof of the Kolmogorovian
Censorship Hypothesis within our general operationalist framework.
The frequencies with which the measurement operations are
performed constitute the “soft” part of the empirical data, as they may
depend on circumstances outside of the physical system under
consideration; for example, on the free choice of a human. Therefore we
treat them as free parameters. Under some plausible---and
empirically easily verifiable---conditions, we isolate a notion in the
Kolmogorovian probabilistic model, which is independent from these free
parameters and describes the state of the system, in the sense that it
characterizes the system's future probabilistic behavior against all
possible measurement operations.
Thus, the first representation theorem says that whatever
the physical system in question is---traditionally categorized as
classical or quantum---everything that can be described in
empirical/operational terms can be described within the classical
Kolmogorovian probability theory.
At the same time, in a second representation theorem, we
show that everything that can be described in empirical/operational
terms can also be represented in the Hilbert space quantum mechanical
formalism. There always exists a suitable Hilbert space such that the
outcomes of each measurement can be represented by orthogonal
projectors, the states of the system can be represented by suitable
density operators, and the probabilities of the measurement outcomes can
be reproduced by the usual trace formula of quantum mechanics.
Moreover, if the measurement outcomes are “labeled” by real numbers,
that is, the measurements correspond real-valued physical quantities,
then each quantity can be associated with a suitable self-adjoint
operator, and the expectation value can be reproduced by the usual trace
formula applied to the self-adjoint operator.
The second representation theorem can be interpreted that
the basic premises of quantum theory are in fact analytic statements.
They do not tell us anything new about a physical system, beyond the
fact that the system can be described in empirical/operational terms.
|26 November (Wednesday)
|Is philosophy an American discipline?
psychologist colleagues currently began to seriously worry about a kind
of cultural bias pervading the science of psychology. Psychology likes
to identify itself as a science of human mind as such, but recent
surveys demonstrate that, at least in leading American professional
(APA) journals, the representation of our species is rather confined to
people of the well-developed (WEIRD: Western, educated, industrialized,
rich, democratic) countries and especially to a particular segment of
the American population. This strong cultural bias might badly distort
our overall picture of the mental functioning of the humankind and so
undermine the original objective of scientific psychology. In my
presentation, I want to suggest some analogous problems with philosophy
as we mainly know it today. I will provide my own research data about
leading international philosophy journals. As these data reveal, the
vast majority (75%) of the authors in these journals are American, which
can be a source of a cultural bias and the narrowness of the whole
discipline. My research suggests that philosophy is even more American
today than psychology, which was declared the most American of all the
scientific fields. Especially if we accept the basic role of culturally
molded intuitions in philosophy (experimental philosophers just try to
convince us about it), we must be aware of this cultural bias and make
steps to balance it in order to make world philosophy a more diverse and