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Calibration Completes the Quantum-Mechanical Description of Physical Reality

Ken Krechmer

Published Jan 4, 2023• 1 citation
Publisher

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) 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.

DOI
10.20944/preprints202301.0059.v1

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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.
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.
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.
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.
This is the introduction to the section on Quantum Mechanics in the centennial collection of noteworthy articles appearing in The Physical Review and Physical Review Letters through 1983, since it all began in 1893. The selections for this section are "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" by Einstein, Podolsky and Rosen; Bohr's response, with the same title; Bohm's first hidden variables paper: "A Suggested Interpretation of the Quantum Theory in Terms of `Hidden' Variables. I"; Aharonov and Bohm's "Significance of Electromagnetic Potentials in the Quantum Theory"; and "Experimental Test of Bell's Inequalities Using Time-Varying Analyzers" by Aspect, Dalibard and Roger.