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arXiv:quant-ph/0310135 · Physics Essays

Conceptual Analysis of Quantum History Theory

Giuseppe Nisticò

Published Mar 1, 2003• 0 citations
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Abstract

We give formal content to some concepts, naturally stemming from consistent history approach (CHA), which are not formalized in the standard formulation of the theory. The outcoming (extended) conceptual basis is used to perform a formal, conceptually transparent analysis of some debated questions in CHA. As results, the problems raised by contrary inferences of Kent are ruled out, whereas some prescriptions of the theory cannot be mantained.

DOI
10.4006/1.3025560

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ABSTRACT. We give formal content to some concepts, naturally stemming from consistent history approach (CHA), which are not formalized in the standard formulation of the theory. The outcoming (extended) conceptual basis is used to perform a formal, conceptually transparent analysis of some debated questions in CHA. As results, the problems raised by contrary inferences of Kent are ruled out, whereas some prescriptions of the theory cannot be mantained. RESUMÉ. Nous fournissons contenu formel à quelques concepts, sortant naturellement de la théorie des histoires consistantes (CHA), qui ne sont pas formalizés dans la formulation usuel. La base conceptuelle (extendue) qui en sort est usée pour effectuer une analyse formel conceptuelment transparente de quelques problèmes débattus dans CHA. Nous avons comme resultat que le problèmes soulevés par les inferences contraires de Kent sont résolus; toutefois, des prescriptions de la théorie ne peuvent pas étre maintenues. Key words: Foundations of quantum theory, Consistent history approach, contrary inferences2

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We give formal content to some concepts, naturally stemming from consistent history approach (CHA), which are not formalized in the standard formulation of the theory. The outcoming (extended) conceptual basis is used to perform a formal, conceptually transparent analysis of some debated questions in CHA. As results, the problems raised by contrary inferences of Kent are ruled out, whereas some prescriptions of the theory cannot be mantained.
ABSTRACT. We give formal content to some concepts, naturally stemming from consistent history approach (CHA), which are not formalized in the standard formulation of the theory. The outcoming (extended) conceptual basis is used to perform a formal, conceptually transparent analysis of some debated questions in CHA. As results, the problems raised by contrary inferences of Kent are ruled out, whereas some prescriptions of the theory cannot be mantained. RESUMÉ. Nous fournissons contenu formel à quelques concepts, sortant naturellement de la théorie des histoires consistantes (CHA), qui ne sont pas formalizés dans la formulation usuel. La base conceptuelle (extendue) qui en sort est usée pour effectuer une analyse formel conceptuelment transparente de quelques problèmes débattus dans CHA. Nous avons comme resultat que le problèmes soulevés par les inferences contraires de Kent sont résolus; toutefois, des prescriptions de la théorie ne peuvent pas étre maintenues. Key words: Foundations of quantum theory, Consistent history approach, contrary inferences2
We introduce quantum history states and their mathematical framework, thereby reinterpreting and extending the consistent histories approach to quantum theory. Through thought experiments, we demonstrate that our formalism allows us to analyze a quantum version of history in which we reconstruct the past by observations. In particular, we can pass from measurements to inferences about what happened in a way that is sensible and free of paradox. Our framework allows for a richer understanding of the temporal structure of quantum theory, and we construct history states that embody peculiar, non-classical correlations in time.
We critically evaluate the treatment of the notion of measurement in the Consistent Histories approach to quantum mechanics. We find such a treatment unsatisfactory because it relies, often implicitly, on elements external to those provided by the formalism. In particular, we note that, in order for the formalism to be informative when dealing with measurement scenarios, one needs to assume that the appropriate choice of framework is such that apparatuses are always in states of well defined pointer positions after measurements. The problem is that there is nothing in the formalism to justify this assumption. We conclude that the Consistent Histories approach, contrary to what is claimed by its proponents, fails to provide a truly satisfactory resolution for the measurement problem in quantum theory.
The Consistent Histories (CH) formalism attempts to construct a quantum framework which can be used without the need to introduce observers external to the studied system. The prime motivation in mind is the application of the formalism to the universe as a whole. In order to achieve this, CH maintains that a formulation of quantum mechanics should allow for the assignment of probabilities to alternative histories of a system. Therefore, it provides an observer-independent criterion to decide which sets of histories can be given probabilities and states rules to determine them. The framework establishes that each realm, that is, each set of histories to which probabilities can be assigned, provides a valid quantum-mechanical account of a system. Furthermore, the version of CH first presented in [1, 2] proposes an "evolutionary" explanation of our existence in the universe and of our preference for quasiclassical descriptions of nature. The present work critically evaluates claims to the effect that the formalism offered in [1, 2] solves many interpretational problems in quantum mechanics. In particular, it is pointed out that the interpretation of the proposed framework leaves vague two crucial points, namely, whether realms are fixed or chosen and the link between measurements and histories. The claim of this work is that by doing so, CH overlooks the main interpretational problems of quantum mechanics. Furthermore, we challenge the evolutionary explanation offered and we critically examine the proposed notion of a realm-dependent reality.
We introduce quantum history states and their mathematical framework, thereby reinterpreting and extending the consistent histories approach to quantum theory. Through thought experiments, we demonstrate that our formalism allows us to analyze a quantum version of history in which we reconstruct the past by observations. In particular, we can pass from measurements to inferences about ‘what happened’ in a way that is sensible and free of paradox. Our framework allows for a richer understanding of the temporal structure of quantum theory, and we construct history states that embody peculiar, non-classical correlations in time.