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The correlation of classic and experimental measurement results with quantum measurement theory

Ken Krechmer

Published Jul 31, 2023• 0 citations
Publisher

Abstract

In classic measurement theory each measurement result has a precision which becomes infinitesimal as noise and distortion approach zero. I. e., exact repetitive measurement results are theoretically possible. This classic measurement theory is not well correlated with experimental measurement results. Because, when noise and distortion are minimized, repetitive experimental measurement results display a Gaussian distribution. This paper first correlates classic and experimental measurements by developing a new measurement function and related definitions. Then this new measurement function is shown to correlate with quantum measurement theory and resolve existing quantum measurement perplexities.

DOI
10.32388/aoxtc5.2

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In classic measurement theory each measurement result has a precision which becomes infinitesimal as noise and distortion approach zero. I. e., exact repetitive measurement results are theoretically possible. This classic measurement theory is not well correlated with experimental measurement results. Because, when noise and distortion are minimized, repetitive experimental measurement results display a Gaussian distribution. This paper first correlates classic and experimental measurements by developing a new measurement function and related definitions. Then this new measurement function is shown to correlate with quantum measurement theory and resolve existing quantum measurement perplexities.
In classic measurement theory each physical measurement result has a precision which becomes infinitesimal as noise and distortion approach zero, i. e., exact repetitive measurement results (± a Planck) are theoretically possible. This classic measurement theory is not well correlated with experimental measurement results. When noise and distortion are minimized, repetitive experimental measurement results display a Gaussian distribution. This paper addresses experimental measurements by first developing a formal measurement function and related definitions, which identify that a classic measurement result is not possible in theory as well as in experiments. This new measurement function is then correlated with quantum measurement theory. This correlation explains existing quantum measurement perplexities.
In classic measurement theory each physical measurement result has a precision which becomes infinitesimal as noise and distortion approach zero, i. e., exact repetitive measurement results (± a Planck) are theoretically possible. This classic measurement theory is not well correlated with experimental measurement results. When noise and distortion are minimized, repetitive experimental measurement results always display a Gaussian distribution. This paper first addresses experimental measurements by developing a formal measurement function and related definitions. The formal measurement function identifies that an exact repetitive classic measurement result is not possible in theory as well as in experiments. This new measurement function is then shown to explain the existing quantum measurement problems.
A classic (i.e., physical) measurement result is a quantity (e.g., 6.9 seconds, 13 metres, 0.17 grams, etc.). A quantity is the product of two terms: a numerical value and a unit. The unit when calibrated to a standard has a +/- precision. In quantum mechanics (QM) a wave function produces a distribution of eigenvalues of unity eigenvectors. Each product of one eigenvalue of eigenvectors also represents one measurement result quantity. In a QM measurement process this distribution of quantities appears to collapse into one classic measurement result quantity (one numerical value and a unit). In classic measurement result quantities, (without noise or distortion) the numerical value of an observable appears fixed over repetitive measurements and the units have a precision relative to a standard. However in a QM measurement result quantity, the eigenvalues have Heisenberg's uncertainty and the eigenvectors are unity. This paper formally develops and verifies that both the QM and classic measurement result quantities are equal products and the classic unit precision is equal to the QM eigenvalue uncertainty.
Abstract This paper is a response to the EPR paper titled: "Can quantum-mechanical description of physical reality be considered complete?", published in Physical Review in 1935. A quantum-mechanical (QM) measure function describes a distribution of local results, while each experimental measurement process produces one result as exact as allowed by a measuring apparatus calibrated to a non-local unit standard. Repeating experimental measurements produces a Gaussian distribution of measurement results. These QM and experimental measurement result distributions can be compared. To compare a QM measure function describing a distribution of eigenvectors to a distribution of repetitive experimental measurement results, it is necessary to determine, by calibration, the precision of the eigenvectors to the same standard as the experimental results, because each eigenvector evidences uncertainty relative to a standard. When the calibration process is recognized as formal as well as empirical, QM measure function and experimental measurement process results are unified.
Heisenberg's uncertainty principle has been understood to set a limitation on measurements, whereas the long standing mathematical formulation does not allow such an interpretation. Recently, a new relation was found by the present author to give a universally valid relation between noise and disturbance in general quantum measurements, and it has become clear that the new relation plays a role of the first principle to derive various quantum limits on measurement and information processing. Here, we discuss the state-dependent notion of precise measurements of a given observable, and consider a perfect distance such that zero distance implies the perfect correlation. Then, we shall show that even in the perfect error notions both the position measuring noise and the momentum disturbance can be arbitrarily small. We also show that it is possible to generalize the new noise-disturbance uncertainty relation to perfect error distances.
A misunderstanding of entangled states has spawned decades of concern about quantum measurements and a plethora of quantum interpretations. The "measurement state" or "Schrodinger's cat state" of a superposed quantum system and its detector is nonlocally entangled, suggesting that we turn to nonlocality experiments for insight into measurements. By studying the full range of superposition phases, these experiments show precisely what the measurement state does and does not superpose. These experiments reveal that the measurement state is not, as had been supposed, a paradoxical superposition of detector states. It is instead a nonparadoxical superposition of two correlations between detector states and system states. In this way, the experimental results resolve the problem of definite outcomes ("Schrodinger's cat"), leading to a resolution of the measurement problem. However, this argument does not yet resolve the measurement problem because it is based on the results of experiments, while measurement is a theoretical problem: How can standard quantum theory explain the definite outcomes seen experimentally? Thus, we summarize the nonlocality experiments' supporting theory, which rigorously predicts the experimental results directly from optical paths. Several previous theoretical analyses of the measurement problem have relied on the reduced density operators derived from the measurement state, but these solutions have been rejected due to criticism of reduced density operators. Because it avoids reduced density operators, the optical-path analysis is immune to such criticism.