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

Ken Krechmer

Published Aug 16, 2023• 0 citations
Publisher

Abstract

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.

DOI
10.32388/aoxtc5.3

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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.
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.
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.
The discontinuous, non-causal and instantaneous changes due to a measurement that appear in quantum mechanics (QM) theory are not consistent with a classical understanding of physical reality, but are completely confirmed by experiments. Relative measurement theory explains why. This paper presents the first formal development of an experimental measurement which includes the uncertainty due to calibration and resolution. The uncertainty due to calibration and resolution, previously considered experimental artifacts, is shown to be equal to the uncertainty that appears in QM theory and experiment. When the calibration to a reference and resolution effects are considered, all the QM measurement discontinuities are consistent with classical explanations.
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.
The discontinuous, non-causal and instantaneous changes due to a measurement that appear in quantum mechanics (QM) theory are not consistent with a classical understanding of physical reality, but are completely confirmed by experiments. Relative measurement theory explains why. This paper presents the first formal development of an experimental measurement which includes the uncertainty due to calibration and resolution. The uncertainty due to calibration and resolution, previously considered experimental artifacts, is shown to be equal to the uncertainty that appears in QM theory and experiment. When the calibration to a reference and resolution effects are considered, all the QM measurement discontinuities are consistent with classical explanations.