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Measurement Mechanics — Resolves QM Measurement Discrepancies

Ken Krechmer

Published Aug 5, 2024• 0 citations
Publisher

Abstract

Measurement Mechanics proposes a major modification to the current understanding of measurement. This modification adds a unit standard as axiomatic to measurement theory. Currently, measurement theory (representational) defines the result of a measurement comparison to be a ratio of quantities (numerical value and unit) where the unit terms are equal and cancel. When the units cancel such a ratio is local to one measurement system, i.e., probabilistic. Thus all QM measurement results, based upon current measurement theory are local, as J. S. Bell confirmed. However, the units of each metrology measurement result are correlated by calibration to an independent unit standard. Then measurement result comparisons are a ratio of quantities each correlated to a common unit standard, which allows independent measurement result comparisons that are non-local and deterministic. When unit standards are included in measurement theory all the apparent discrepancies between QM and classic measurements are resolved.

DOI
10.32388/efjp80.2

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Measurement Mechanics proposes a major modification to the current understanding of measurement. This modification adds a unit standard as axiomatic to measurement theory. Currently, measurement theory (representational) defines the result of a measurement comparison to be a ratio of quantities (numerical value and unit) where the unit terms are equal and cancel. When the units cancel such a ratio is local to one measurement system, i.e., probabilistic. Thus all QM measurement results, based upon current measurement theory are local, as J. S. Bell confirmed. However, the units of each metrology measurement result are correlated by calibration to an independent unit standard. Then measurement result comparisons are a ratio of quantities each correlated to a common unit standard, which allows independent measurement result comparisons that are non-local and deterministic. When unit standards are included in measurement theory all the apparent discrepancies between QM and classic measurements are resolved.
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.
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) measurement function describes a distribution of local results and each empirical measurement process produces one result as exact as allowed by a measuring instrument calibrated to a non-local unit standard. Repeating these empirical measurements produces a bell shaped distribution of measurement results. Each of these distributions can be compared to the other. To precisely compare a QM measurement function describing a distribution of eigenvectors to a distribution of repetitive empirical measurement results, it is necessary to determine, by calibration, the precision of the eigenvectors to the same standard as the empirical results, because each eigenvector evidences uncertainty relative to a standard. When the calibration process is recognized as formal as well as empirical, QM measurement function results and metrology 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.
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.
Superposition is a quantum mechanical concept currently without a recognized equivalent in metrology measurements. Relative Measurement Theory (RMT) developed the significance of unit standards to metrology measurements. This paper introduces a limit into Cantor's Transfinite Set Theory (CTST) and develops how it relates to a unit standard. Recognizing CTST also describes a superposition, this paper develops how a transfinite superposition transforms into a normal distribution of metrology measurement results, when measurement results include calibration to a unit standard. Then a superposition has an equivalent set of metrology measurements.