The Quantum Measurement Problem and Cluster Separability

Abstract

A modified Beltrametti-Cassinelli-Lahti model of measurement apparatus that satisfies both the probability reproducibility condition and the objectification requirement is constructed. Only measurements on microsystems are considered. The cluster separability forms a basis for the first working hypothesis: the current version of quantum mechanics leaves open what happens to systems when they change their separation status. New rules that close this gap can therefore be added without disturbing the logic of quantum mechanics. The second working hypothesis is that registration apparatuses for microsystems must contain detectors and that their readings are signals from detectors. This implies that separation status of a microsystem changes during both preparation and registration. A new rule that specifies what happens at these changes and that guarantees the objectification is formulated and discussed. A part of our result has certain similarity with 'collapse of the wave function'.

Quantum Models of Classical World

“…This is a condition on A inasmuch as there has to be at least one remote state for A. However, Peres does not warn that most operators of quantum theory do not satisfy his condition on A [19]. Indeed, observables of quantum field theory and many-body theories that are constructed from generators of Poincaré or Galilei groups do not satisfy the locality condition.…”

“…A large number of real objects, the so-called classical world, have as yet no satisfactory quantum models. Our own attempts [15] and [19] at constructing such models have lead to some changes in the quantum language. The first part of this review starting here is an attempt at a systematic formulation of this new language.…”

“…As a mathematical operation, (+) p is commutative, associative, and state statistics is invariant with respect to state composition and unitary evolution [19]. Thus, the definitions and assumptions can be generalized to more than two preparations and states (see Rules 12 and 15).…”

“…In our previous work [19,24,34], we have assumed that transformation analogous to that from (65) to (69) result from application of some general alternative dynamical law and that such a law must be postulated. An extended study of all empirical cases that came to mind as yet has shown that a number of specific details must in each case be taken into account so as to make an adequate theoretical description of what happens.…”

“…However, if an indecomposable state of a system is given, no more knowledge on the system can objectively exist than that given by the state. (It follows that a collapse of wave function or analogous processes are not just changes of our information about the system bur genuine physical processes, see Section 5 and [19,34].) Finally, quantum states are non-local: most states of a single particle do not determine its position, but simultaneous registrations by two detectors at different positions will give anti-correlated results (see Section 5).…”