Classical Versus Quantum Ontology
This is an essay review of the book by D. Home: "Conceptual Foundations of Quantum Physics: An Overview from Modern Perspectives" (New York: Plenum Press, 1997), xvii+386 pp., ISBN 0-306-45660-5.
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arXiv subjects
P. Busch
Publications and source records attributed to P. Busch.
Geometrical and Operational Aspects of Irreversibility
In the statistical description of dynamical systems, an indication of the irreversibility of a given state change is given geometrically by means of a (pre-)ordering of state pairs. Reversible state changes of classical and quantum systems are shown to be represented by isometric state transformations. An operational distinction between reversible and irreversible dynamics is given and related to the geometric characterisation of the associated state transformations.
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Orthogonality and Disjointness in Spaces of Measures
The convex and metric structures underlying probabilistic physical theories are generally described in terms of base normed vector spaces. According to a recent proposal, the purely geometrical features of these spaces are appropriately represented in terms of the notion of `measure cone' and the `mixing distance' [1], a specification of the novel concept of `direction distance' [2]. It turns out that the base norm is one member of a whole characteristic family of `mc-norms' from which it can be singled out by virtue of a certain orthogonality relation. The latter is seen to be closely related to the concept of minimal decomposition. These connections suggest a simple geometric interpretation of the familiar notion of the disjointness of (probability) measures and the Hahn-Jordan decomposition of measures which has been addressed briefly in [1] and will be elaborated here. The results obtained give an indication of the extent to which a general measure cone admits measure theoretic interpretations. [1] P. Busch, E. Ruch: The Measure Cone -- Irreversibility as a Geometrical Phenomenon, Int. J. Quant. Chem. 41 (1992) 163-185. [2] E. Ruch: Der Richtungsabstand}, Acta Applic. Math. 30 (1992) 67-93.
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Can `unsharp objectification' solve the quantum measurement problem?
The quantum measurement problem is formulated in the form of an insolubility theorem that states the impossibility of obtaining, for all available object preparations, a mixture of states of the compound object and apparatus system that would represent definite pointer positions. A proof is given that comprises arbitrary object observables, whether sharp or unsharp, and besides sharp pointer observables a certain class of unsharp pointers, namely, those allowing for the property of pointer value definiteness. A recent result of H. Stein is applied to allow for the possibility that a given measurement may not be applicable to all possible object states but only to a subset of them. The question is raised whether the statement of the insolubility theorem remains true for genuinely unsharp observables. This gives rise to a precise notion of unsharp objectification.
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Remarks on unsharp quantum observables, objectification, and modal interpretations
This paper addresses the question whether a variant of a modal interpretation is conceivable that could accommodate property ascriptions associated with nonorthogonal resolutions of the unity and nonorthogonal families of relative states as they occur in imperfect or genuinely unsharp measurements. I will review a recent formulation of the quantum measurement problem in the form of an insolubility theorem that incorporates the case of unsharp object observables as well as certain types of unsharp pointers. In addition to demonstrating the necessity for some modification of quantum mechanics, this allows me to specify the logical position of the modal interpretations as a resolution to the measurement problem and to indicate why I think their current versions are not yet capable of dealing adequately with unsharp quantum observables. The technical tools that will have been explained along this line of reasoning will finally serve to make precise the notion of (unsharp) value ascription that I would find desirable for a modal interpretation to ascertain.
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Is the quantum state (an) observable?
We explore the sense in which the state of a physical system may or may not be regarded (an) observable in quantum mechanics. Simple and general arguments from various lines of approach are reviewed which demonstrate the following no-go claims: (1) the structure of quantum mechanics precludes the determination of the state of a single system by means of measurements performed on that system only; (2) there is no way of using entangled two-particle states to transmit superluminal signals. Employing the representation of observables as general positive operator valued measures, our analysis allows one to indicate whether optimal separation of different states is achieved by means of sharp or unsharp observables.
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Insolubility of the Quantum Measurement Problem for Unsharp Observables
The quantum mechanical measurement problem is the difficulty of dealing with the indefiniteness of the pointer observable at the conclusion of a measurement process governed by unitary quantum dynamics. There has been hope to solve this problem by eliminating idealizations from the characterization of measurement. We state and prove two `insolubility theorems' that disappoint this hope. In both the initial state of the apparatus is taken to be mixed rather than pure, and the correlation of the object observable and the pointer observable is allowed to be imperfect. In the {\it insolubility theorem for sharp observables}, which is only a modest extension of previous results, the object observable is taken to be an arbitrary projection valued measure. In the {\it insolubility theorem for unsharp observables}, which is essentially new, the object observable is taken to be a positive operator v alued measure. Both theorems show that the measurement problem is not the consequence of neglecting the ever-present imperfections of actual measurements.
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