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arXiv:1406.2217

Measurements of Observables Replaced by "Detections" in Quantum Theory

Nisticò, Giuseppe, Angela Sestito

Published Jun 9, 2014• 0 citations
arXivHTMLPDF

Abstract

In Quantum Physics it is not always possible to directly perform the measurement of an obsevable; in some of these cases, however, its value can be {\sl detected}, i.e. it can be inferred by measuring {\sl another} observable characterized by perfect correlation with the observable of interest. Though a {\sl detection} is often interpreted as a {\sl measurement} of the detected observable, we prove that the two concepts cannot be identified in Quantum Physics. Furthermore, we establish what meaning and role can be ascribed to detections coherently with Quantum Theory.

DOI
10.48550/arxiv.1406.2217

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In Quantum Physics it is not always possible to directly perform the measurement of an obsevable; in some of these cases, however, its value can be {\sl detected}, i.e. it can be inferred by measuring {\sl another} observable characterized by perfect correlation with the observable of interest. Though a {\sl detection} is often interpreted as a {\sl measurement} of the detected observable, we prove that the two concepts cannot be identified in Quantum Physics. Furthermore, we establish what meaning and role can be ascribed to detections coherently with Quantum Theory.
In quantum physics there are circumstances where the direct measurement of particular observables encounters difficulties; in some of these cases, however, its value can be evaluated, i.e. it can be inferred by measuring another observable characterized by perfect correlation with the observable of interest. Though an evaluation is often interpreted as a measurement of the evaluated observable, we prove that the two concepts cannot be identified in quantum physics, because the identification yields contradictions. Then, we establish the conceptual status of evaluations in Quantum Theory and the role can be ascribed to them.
Abstract In rough terms, the quantum measurement problem is the problem of explaining how, when a system in a superposition state is measured, the pointer observable of the measuring apparatus is always found in a definite value. Although quantum mechanics involves several interpretative challenges, the measurement problem has been the main focus of the interest of physicists and philosophers working on the foundations of the theory: most interpretations were designed specifically to solve it. In this chapter, it is shown that the MHI offers a solution to the measurement problem for both ideal and non-ideal measurements, and that, in the non-ideal case, the interpretation distinguishes between reliable and non-reliable measurements. I have also explained how the MHI accounts for consecutive measurements. Finally, it is emphasized that the MHI approach provides a new, more physical understanding of the concept of quantum measurement.
The usual interpretation of quantum theory is clouded by the following points. (1) Invalid classical concepts are ascribed fundamental status. (2) The process of measurement is not describable within the framework of the theory. (3) The subject-object distinction is blurred. (4) The observed system is required to be isolated in order to be defined, yet interacting in order to be observed. These problems are resolved in a straightforward way by the unequivocal acceptance of a thoroughly pragmatic SSS-matrix viewpoint. This interpretation is described, and it is explained how and why the full physical content of quantum theory resides in the SSS matrix.
It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The new approach regards QMS as a statistical samplings (but not as simple detection acts) and their description as a distinct task, independent of actual procedures of quantum mechanics. A QMS is described by means of transformations of probability density and probability current, from intrinsic into recorded readings. The quantum observables appear as random variables, described by usual operators and valuable through probabilistic numerical parameters (mean values, correlations and standard deviations). The values of the respective parameters are not the same in the two mentioned readings. Then the measurement uncertainties (errors) are described by means of the changes in the alluded values. The new QMS approach is illustrated through an one-dimensional example.
A new approach to quantum theory is proposed in this paper. The basis is first taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an actor to assign arbitrarily sharp numerical values to them. In an epistemic process, the accessible variables are just ideal observations connected to an actor or to some communicating actors. Group actions are defined on these variables, and group representation theory is the basis for developing the Hilbert space formalism here. Operators corresponding to accessible theoretical variables are derived, and in the discrete case, it is proved that the possible physical values are the eigenvalues of these operators. The focus of the paper is some mathematical theorems paving the ground for the proposed foundation of quantum theory. It is shown here that the groups and transformations needed in this approach can be constructed explicitly in the case where the accessible variables are finite-dimensional. This simplifies the theory considerably: To reproduce the Hilbert space formulation, it is enough to assume the existence of two complementary variables. To focus only on physical variables rather than mathematical variables, the concept of inaccessible variables is then replaced by the concept of notions, and in this connection, aspects of category theory partly replace group theory. The interpretation inferred from the proposed foundation here may be called a general epistemic interpretation of quantum theory. A special case of this interpretation is QBism; it also has a relationship to several other interpretations.