381 research outputs found
Towards a Neo-Copenhagen Interpretation of Quantum Mechanics
The Copenhagen interpretation is critically considered. A number of
ambiguities, inconsistencies and confusions are discussed. It is argued that it
is possible to purge the interpretation so as to obtain a consistent and
reasonable way to interpret the mathematical formalism of quantum mechanics,
which is in agreement with the way this theory is dealt with in experimental
practice. In particular, the essential role attributed by the Copenhagen
interpretation to measurement is acknowledged. For this reason it is proposed
to refer to it as a neo-Copenhagen interpretation
Preparation and measurement: two independent sources of uncertainty in quantum mechanics
In the Copenhagen interpretation the Heisenberg uncertainty relation is
interpreted as the mathematical expression of the concept of complementarity,
quantifying the mutual disturbance necessarily taking place in a simultaneous
or joint measurement of incompatible observables. This interpretation has
already been criticized by Ballentine a long time ago, and has recently been
challenged in an experimental way. These criticisms can be substantiated by
using the generalized formalism of positive operator-valued measures, from
which a new inequality can be derived, precisely illustrating the Copenhagen
concept of complementarity. The different roles of preparation and measurement
in creating uncertainty in quantum mechanics are discussed.Comment: latex, 18 pages, 4 eps figure
Interpretations of quantum mechanics, and interpretations of violation of Bell's inequality
The discussion of the foundations of quantum mechanics is complicated by the
fact that a number of different issues are closely entangled. Three of these
issues are i) the interpretation of probability, ii) the choice between realist
and empiricist interpretations of the mathematical formalism of quantum
mechanics, iii) the distinction between measurement and preparation. It will be
demonstrated that an interpretation of violation of Bell's inequality by
quantum mechanics as evidence of non-locality of the quantum world is a
consequence of a particular choice between these alternatives. Also a
distinction must be drawn between two forms of realism, viz. a) realist
interpretations of quantum mechanics, b) the possibility of hidden-variables
(sub-quantum) theories.Comment: LATeX, 20 pages, 4 figures, to be published in Proceedings of the
International Conference on Foundations of Probability and Physics, Vaxjo, 27
Nov. -1 Dec. 200
The Haroche-Ramsey experiment as a generalized measurement
A number of atomic beam experiments, related to the Ramsey experiment and a
recent experiment by Brune et al., are studied with respect to the question of
complementarity. Three different procedures for obtaining information on the
state of the incoming atom are compared. Positive operator-valued measures are
explicitly calculated. It is demonstrated that, in principle, it is possible to
choose the experimental arrangement so as to admit an interpretation as a joint
non-ideal measurement yielding interference and ``which-way'' information.
Comparison of the different measurements gives insight into the question of
which information is provided by a (generalized) quantum mechanical
measurement. For this purpose the subspaces of Hilbert-Schmidt space, spanned
by the operators of the POVM, are determined for different measurement
arrangements and different values of the parameters.Comment: REVTeX, 22 pages, 5 figure
From Copenhagen to neo-Copenhagen interpretation
Positive and negative features of the Copenhagen interpretation are
discussed. As positive features can be mentioned its pragmatism and its
awareness of the crucial role of measurement. However, the main part of the
contribution is devoted to the negative features, to wit, its pragmatism (once
again), its confounding of preparation and measurement, its classical account
of measurement, its completeness claims, the ambiguity of its notion of
correspondence, its confused notion of complementarity. It is demonstrated how
confusions and paradoxes stemming from the negative features of the Copenhagen
interpretation can be dealt with in an amended interpretation, to be referred
to as `neo-Copenhagen interpretation', in which the role of the measuring
instrument is taken seriously by recognizing the quantum mechanical character
of its interaction with the microscopic object. The ensuing necessity of
extending the notion of a quantum mechanical observable from the Hermitian
operator of the standard formalism to the positive operator-valued measure of a
generalized formalism is demonstrated to yield a sound mathematical basis for a
transition from the Copenhagen contextualistic-realist interpretation to the
neo-Copenhagen empiricist one. Applications to the uncertainty relations and to
the Bell inequalities are briefly discussed.Comment: To be published in the Proceedings of the Conference: Quantum Theory
- 4, Reconsideration of Foundations, V\"axj\"o, June 11-16, 200
- …