The Interpretation of Quantum Mechanics and the Measurement Process

Abstract

The main theme of this book is the idea that quantum mechanics is valid not only for microscopic objects but also for the macroscopic apparatus used for quantum mechanical measurements. The author demonstrates the intimate relations that exist between quantum mechanics and its interpretation which are induced by the quantum mechanical measurement process. Consequently, the book is concerned both with the philosophical, metatheoretical problems of interpretations and with the more formal problems of quantum object theory. The consequences of this approach turn out to be partly very promising and partly rather disappointing. On the one hand, it is possible to give a rigorous justification of some important parts of interpretation, such as probability, by means of object theory. On the other hand, the problem of the objectification of measurement results leads to inconsistencies which cannot be resolved in an obvious way. This open problem has far-reaching consequences for the possibility of recognising an objective reality in physics.

Unsharp Quantum Reality

“…Moreover, adapting arguments initially developed in the context of the relative-state interpretation of Quantum Mechanics, Peter Mittelstaedt has shown that the quantum mechanical probability emerges as an approximately definite property of a large ensemble of identically prepared systems represented by the same state [13]. The quantum mechanical probability postulate is thus found to be deducible from the probability-free eigenvalue-eigenstate rule, which specifies the definite properties of a quantum system in any given state.…”

“…What is at stake here is the semantic consistency of the theory-an issue of great concern in Mittelstaedt's work [13] which is called into question by the problem of objectification (see Sec. 3).…”

Hidden variables in quantum mechanics: Generic models, set-theoretic forcing, and the appearance of probability

“…The rationale for this choice seems to be that since any proposition has a definite value for any pseudoclassical state, we may filter an ensemble by a proposition without changing the (states of the) elements of the ensemble. Without going into an analysis of the theory of measurement in a hidden-variables model [2,11,5], it seems quite plausible that subjecting a pseudoclassical state F to an interaction with an observer O that may be regarded as a measurement of a proposition P , and then filtering on the basis of that measurement, which amounts to "collapsing the wave packet", will yield a result from which the answer to 'Q ∈ F ? ', for Q not commuting with P , cannot be inferred.…”

“…11 We call programmable procedures in this sense effective or recursive procedures. We will consider two types of recursive procedure in this discussion.…”

100 Jahre Quantenphysik: Universell und inkonsistent?: Quantenmechanik am Ende des 20. Jahrhunderts

“…Neben vielen wertvollen Einsichten in den Messvorgang führen diese Untersuchungen aber auch auf ein bis heute ungelöstes Problem: Wenn nach dem dynamischen Teil des quantenmechanischen Messvorgangs das Objekt S und Messgerät M voneinander getrennt werden (Abb. 1), dann befindet sich der Zeiger des Messgerätes in einem Gemischzustand W' M , der keine Ignoranzinterpretation erlaubt [21]. Das bedeutet, dass es nicht erlaubt ist anzunehmen, dass der Zeiger objektiv einen festen Wert hat, den nur der Beobachter subjektiv nicht kennt.…”