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European Journal for Philosophy of Science

Histories in quantum mechanics: distinguishing between formalism and interpretation

Marcelo Losada, Olímpia Lombardi

Published Jan 16, 2018• 3 citations
Publisher
DOI
10.1007/s13194-017-0197-x

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This chapter discusses the main points and thought sources of the quantum histories interpretation. Section 3.1 introduces its core concepts, theoretical assumptions, and basic formalism first, as well as how probability calculations and propositional reasoning are performed here, and shows how this interpretation depicts the process by which (quasi-)classicality is derived from quantum histories. Section 3.2 sorts out the five important thought sources from which it emerges: the Copenhagen interpretation, Feynman’s sum-over-histories formulation of quantum mechanics, Wigner’s measurement theory, Everett’s relative state interpretation or many-worlds interpretation, and the mechanism of decoherence. Their respective correlations, similarities, and differences with the quantum histories interpretation are briefly analyzed. In the appendix to this chapter, three notorious paradoxes showing intractable aspects of quantum mechanics, namely the Einstein-Podolsky-Rosen (EPR) paradox, Wheeler’s delayed choice gedankenexperiment, and Frauchiger–Renner paradox, are formulated via history chain operator analysis in the quantum histories formalism.

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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.

Journal of Physics Conference Series•Jun 10, 2013•0 citations
This chapter discusses the main points and thought sources of the quantum histories interpretation. Section 3.1 introduces its core concepts, theoretical assumptions, and basic formalism first, as well as how probability calculations and propositional reasoning are performed here, and shows how this interpretation depicts the process by which (quasi-)classicality is derived from quantum histories. Section 3.2 sorts out the five important thought sources from which it emerges: the Copenhagen interpretation, Feynman’s sum-over-histories formulation of quantum mechanics, Wigner’s measurement theory, Everett’s relative state interpretation or many-worlds interpretation, and the mechanism of decoherence. Their respective correlations, similarities, and differences with the quantum histories interpretation are briefly analyzed. In the appendix to this chapter, three notorious paradoxes showing intractable aspects of quantum mechanics, namely the Einstein-Podolsky-Rosen (EPR) paradox, Wheeler’s delayed choice gedankenexperiment, and Frauchiger–Renner paradox, are formulated via history chain operator analysis in the quantum histories formalism.
To revisit and analyze the histories formalism of quantum mechanics, this chapter will refer to the basic idea of the nomological interpretation of the quantum wave function as described in the previous chapter. The quantum wave functions can be interpreted as nomological and non-ontological elements of Bohmian mechanics. This inspires us that, in quantum histories formalism, the multiple conditions/criteria of determining the possible families of histories, whose validity can be examined by reasonable tests regarding the properties of subsystems, can be argued as lawful or nomological, while the quantum histories can be argued as the fundamental physical reality. We will specifically focus on this novel depiction of the formalism concerning quantum reality, which enables us to reconsider the numerous objections to the histories interpretation that were raised in previous chapters and re-examine/resolve from the nomological perspective the several aforementioned ontological and logical issues of quantum histories interpretation. However, there still remain challenging issues in the understanding of quantum histories.
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.