Unique transition probabilities in the modal interpretation

doi:10.1016/1355-2198(95)00004-6

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

Volume 27, Issue 2, June 1996, Pages 133-159

https://doi.org/10.1016/1355-2198(95)00004-6 Get rights and content

Abstract

The modal interpretation of quantum theory ascribes at each instant physical magnitudes with definite values to quantum systems. Starting from certain natural requirements, I determine unique solutions for the evolution of these possessed magnitudes in free systems and in special cases of interacting systems. The evolution is given in terms of transition probabilities that relate the values of the possessed magnitudes at one instant to the values at a second instant. I also determine a joint property ascription to a composite system and its separate subsystems. Finally, I give a proof that the predictions of the modal interpretation with respect to measurement outcomes agree with the predictions of the standard interpretation.

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A modal-Hamiltonian interpretation of quantum mechanics
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Citation Excerpt :
This means that actualization is a phenomenon that repeatedly occurs at each instant. This interpretational position leads to the need of accounting for the dynamics of actual properties (see Vermaas, 1996). In our interpretation, on the contrary, this step is unnecessary since the dynamics of actual properties is trivial.
The aim of this paper is to introduce a new member of the family of the modal interpretations of quantum mechanics. In this modal-Hamiltonian interpretation, the Hamiltonian of the quantum system plays a decisive role in the property-ascription rule that selects the definite-valued observables whose possible values become actual. We show that this interpretation is effective for solving the measurement problem, both in its ideal and its non-ideal versions, and we argue for the physical relevance of the property-ascription rule by applying it to well-known physical situations. Moreover, we explain how this interpretation supplies a description of the elemental categories of the ontology referred to by the theory, where quantum systems turn out to be bundles of possible properties.
Dynamical reduction models
2003, Physics Reports
The report presents an exhaustive review of the recent attempt to overcome the difficulties that standard quantum mechanics meets in accounting for the measurement (or macro-objectification) problem, an attempt based on the consideration of nonlinear and stochastic modifications of the Schrödinger equation. The proposed new dynamics is characterized by the feature of not contradicting any known fact about microsystems and of accounting, on the basis of a unique, universal dynamical principle, for wavepacket reduction and for the classical behavior of macroscopic systems. We recall the motivations for the new approach and we briefly review the other proposals to circumvent the above mentioned difficulties which appeared in the literature. In this way we make clear the conceptual and historical context characterizing the new approach. After having reviewed the mathematical techniques (stochastic differential calculus) which are essential for the rigorous and precise formulation of the new dynamics, we discuss in great detail its implications and we stress its relevant conceptual achievements. The new proposal requires also to work out an appropriate interpretation; a procedure which leads us to a reconsideration of many important issues about the conceptual status of theories based on a genuinely Hilbert space description of natural processes. Attention is also paid to many problems which are naturally raised by the dynamical reduction program. In particular we discuss the possibility and the problems one meets in trying to develop an analogous formalism for the relativistic case. Finally we discuss the experimental implications of the new dynamics for various physical processes which should allow, in principle, to test it against quantum mechanics. The review covers the work which has been done in the last 15 years by various scientists and the lively debate which has accompanied the elaboration of the new proposal.
The modal interpretation of algebraic quantum field theory
2000, Physics Letters, Section A: General, Atomic and Solid State Physics
We show that Dieks' recent proposal for extending the modal interpretation to algebraic quantum field theory fails to yield a well-defined prescription for which observables in a local spacetime region possess definite values. On the other hand, we demonstrate that there is a well-defined and unique extension of the modal interpretation to the local algebras of quantum field theory (which may, however, face a serious difficulty in connection with ergodic field states).
Two no-go theorems for modal interpretations of quantum mechanics
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Modal interpretations take quantum mechanics as a theory which assigns at all times definite values to magnitudes of quantum systems. In the case of single systems, modal interpretations manage to do so without falling prey to the Kochen and Specker no-go theorem, because they assign values only to a limited set of magnitudes. In this paper I present two further no-go theorems which prove that two modal interpretations become nevertheless problematic when applied to more than one system. The first theorem proves that the modal interpretation proposed by Kochen and by Dieks cannot correlate the values simultaneously assigned to three systems. The second and new theorem proves that the atomic modal interpretation proposed by Bacciagaluppi and Dickson and by Dieks cannot correlate the values simultaneously and sequentially assigned to two systems if one assumes that these correlations are uniquely related to the dynamics of the state of the systems.
Modal interpretations, decoherence and measurements
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We address Albert and Loewer's criticism of non-ideal measurements in the modal interpretation, by examining the implications of the theory of decoherence for the modal interpretation. In the models originally considered by Albert and Loewer, the inclusion of decoherence provides an answer to their criticism. New problems seem to arise in different models and in situations more general than measurements.
A uniqueness theorem for 'no collapse' interpretations of quantum mechanics
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We prove a uniqueness theorem showing that, subject to certain natural constraints, all ‘no collapse’ interpretations of quantum mechanics can be uniquely characterized and reduced to the choice of a particular preferred observable as determinate (definite, sharp). We show how certain versions of the modal interpretation, Bohm's ‘causal’ interpretation, Bohr's complementarity interpretation, and the orthodox (Dirac-von Neumann) interpretation without the projection postulate can be recovered from the theorem. Bohr's complementarity and Einstein's realism appear as two quite different proposals for selecting the preferred determinate observable—either settled pragmatically by what we choose to observe, or fixed once and for all, as the Einsteinian realist would require, in which case the preferred observable is a ‘beable’ in Bell's sense, as in Bohm's interpretation (where the preferred observable is position in configuration space).

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ArticleUnique transition probabilities in the modal interpretation

Abstract

Wanted Dead or Alive: Two Attempts to Solve Schrödinger's Paradox

Continuity and Discontinuity of Definite Properties in the Modal Interpretation

Helvetica Phyica Acta

Modal Interpretations, Decoherence and Measurement

Studies in History and Philosophy of Modern Physics

Schrödinger's Cat and Other Entanglements of Quantum Mechanics

The Quantum Theory of Measurement

The Formalism of Quantum Theory: An Objective Description of Reality?

Annalen der Physik

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Unique transition probabilities in the modal interpretation