44 research outputs found
A Gelfand triple approach to Wigner and Husimi representations
The notion of Gelfand triples is applied to interpret mathematically a family of phase-space representations of quantum mechanics interpolating between the Wigner and Husimi representations. Gelfand triples of operators on Hilbert space, and Gelfand triples of functions on phase-space are introduced in order to get isomorphic correspondences between operators and their phase-space representations. The phasespace Gelfand triples are characterized by means of growth conditions on the analytic continuation of the functions. We give integral expressions for the sesquilinear forms belonging to the phase-space Gelfand triples. This provides mathematically rigorous phase-space analogues for quantum mechanical expectation values of bounded operators. 1
POVMs: a small but important step beyond standard quantum mechanics
It is the purpose of the present contribution to demonstrate that the
generalization of the concept of a quantum mechanical observable from the
Hermitian operator of standard quantum mechanics to a positive operator-valued
measure is not a peripheral issue, allegedly to be understood in terms of a
trivial nonideality of practical measurement procedures, but that this
generalization touches the very core of quantum mechanics, viz. complementarity
and violation of the Bell inequalities.Comment: Contribution to Proceedings of the Workshop `Beyond the quantum',
Leiden, May/June 200
Quantum Locality
It is argued that while quantum mechanics contains nonlocal or entangled
states, the instantaneous or nonlocal influences sometimes thought to be
present due to violations of Bell inequalities in fact arise from mistaken
attempts to apply classical concepts and introduce probabilities in a manner
inconsistent with the Hilbert space structure of standard quantum mechanics.
Instead, Einstein locality is a valid quantum principle: objective properties
of individual quantum systems do not change when something is done to another
noninteracting system. There is no reason to suspect any conflict between
quantum theory and special relativity.Comment: Introduction has been revised, references added, minor corrections
elsewhere. To appear in Foundations of Physic
Detection model based on representation of quantum particles by classical random fields: Born's rule and beyond
Recently a new attempt to go beyond quantum mechanics (QM) was presented in
the form of so called prequantum classical statistical field theory (PCSFT).
Its main experimental prediction is violation of Born's rule which provides
only an approximative description of real probabilities. We expect that it will
be possible to design numerous experiments demonstrating violation of Born's
rule. Moreover, recently the first experimental evidence of violation was found
in the triple slits interference experiment, see \cite{WWW}. Although this
experimental test was motivated by another prequantum model, it can be
definitely considered as at least preliminary confirmation of the main
prediction of PCSFT. In our approach quantum particles are just symbolic
representations of "prequantum random fields," e.g., "electron-field" or
"neutron-field"; photon is associated with classical random electromagnetic
field. Such prequantum fields fluctuate on time and space scales which are
essentially finer than scales of QM, cf. `t Hooft's attempt to go beyond QM
\cite{H1}--\cite{TH2}. In this paper we elaborate a detection model in the
PCSFT-framework. In this model classical random fields (corresponding to
"quantum particles") interact with detectors inducing probabilities which match
with Born's rule only approximately. Thus QM arises from PCSFT as an
approximative theory. New tests of violation of Born's rule are proposed.Comment: Relation with recent experiment on violation of Born's rule in the
triple slit experiment is discussed; new experimental test which might
confirm violation of Born's rule are presented (double stochsticity test and
interference magnitude test); the problem of "double clicks" is discusse
POVMs: a small but important step beyond standard quantum mechanics
It is the purpose of the present contribution to demonstrate that the generalization of the concept of a quantum mechanical oservable from the Hermitian operator of standard quantum mechanics to a positive operator-valued measure is not a peripheral issue, allegedly to be understood in terms of a trivial nonideality of practical measurement procedures, but that this generalization touches the very core of quantum mechanics, viz. complementarity and violation of the Bell inequalities
Lezer-excitaties : Antwoord op F.A. Muller's reactie "Schijn en werkelijkheid"
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