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Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields

A reinterpretation of the notion of localization

Andrés J. Kálnay, B. P. Toledo

Published Apr 1, 1967• 43 citations
Publisher
DOI
10.1007/bf02721623

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Most scholars concerned with the foundations of quantum mechanics (QM) think that contextuality and nonlocality (hence nonobjectivity of physical properties) are unavoidable features of QM which follow from the mathematical apparatus of QM. Moreover these features are usually considered as basic in quantum information processing. Nevertheless they raise still unsolved problems, as the objectification problem in the quantum theory of measurement. The extended semantic realism (ESR) model offers a possible way out from these difficulties by embedding the mathematical formalism of QM into a broader mathematical formalism and reinterpreting quantum probabilities as conditional on detection rather than absolute. The embedding allows to recover the formal apparatus of QM within the ESR model, and the reinterpretation of QM allows to construct a noncontextual hidden variables theory which justifies the assumptions introduced in the ESR model and proves its objectivity. According to the ESR model both linear and nonlinear time evolution occur, depending on the physical environment, as in QM. In addition, the ESR model, though objective, implies modified Bell's inequalities that do not conflict with QM, supplies different mathematical representations of proper and improper mixtures, provides a general framework in which the local interpretations of the GHZ experiment obtained by other authors are recovered and explained, and supports an interpretation of quantum logic which avoids the introduction of the problematic notion of quantum truth.
We complete the structural closure of the Historical Attractor Theory (HAT) by analyzing the conditions under which quantum descriptions based on amplitudes and interference remain valid. We introduce the notions of historical density, local saturation, and incompatibility between histories, and show that these concepts impose intrinsic limits on the coexistence of alternative histories. Mass is reinterpreted as an extensive historical cost associated with the accumulation of persistent records. We demonstrate that beyond a critical saturation threshold, interference-based descriptions lose operational meaning independently of environmental decoherence. This work establishes the structural domain of validity of quantum descriptions and prepares the ground for the introduction of effective historical amplitudes.