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Measurement

Relative measurement theory

Ken Krechmer

Published Nov 9, 2017• 18 citations
Publisher

Abstract

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.

DOI
10.1016/j.measurement.2017.10.053

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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.
In representational measurement theory, the current theory of all measurements, calibration and sampling processes are assumed to be a linear transformation of the coordinate system, of no effect. In this paper calibration and sampling are shown to be independent non-linear processes which do change measurement results. Relational measurement theory is developed to include calibration and sampling. The measurement changes caused by calibration and sampling are proven to be equal to the quantum measurement disturbance described by the universal uncertainty relation which has been verified by experiments. Therefore relational measurement theory explains the measurement disturbance in quantum mechanics.
In many quantum measurement experiments and thought experiments, unexplained results appear. As example, entangled particles appear to interact instantly across distances. A 2018 Measurement paper (Relative Measurement Theory, K. Krechmer, 2018) proposed that the calibration of a measuring apparatus to a reference is required in both quantum measurement models and empirical measurement results. Current quantum measurement models equalize the units but not to a reference. Current empirical measurement indications are equalized to a reference. These two measurements are different. The lack of calibration to a reference in quantum mechanics creates this difference. Including calibration explains the results of the particle spin experiments, quantum teleportation experiments, and Mach-Zehnder interferometer experiments, as well as Mermin's device, Schrödinger's Cat, and other thought experiments.
We show that it is possible to explain the quantum measurement process within the framework of quantum mechanics without any additional postulates. The key concept of the theory is decoherence, which appears as an inherent characteristic of quantum mechanics and results from the uncertainty relation. In contrast to environment-induced decoherence, this decoherence exists prior to a measurement being made. To clarify our idea, we examine three elemental experiments: a Stern-Gerlach-like experiment, the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment, and the double-slit experiment. By considering the first experiment, we explain how the uncertainty relation between position and momentum introduces decoherence prior to measurement. Consideration of the EPR-Bohm experiment leads us to conclude that the correlation of the EPR pair is not a consequence of what is known as the collapse of the wave function. Our theory of decoherence can also be applied to experiments with continuous eigenvalues, such as the double-slit experiment. Consideration of the double-slit experiment leads us to understand how pure quantum mechanics describes the fact that quanta behave as interfering particles.
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.
We show that it is possible to explain the quantum measurement process within the framework of quantum mechanics without any additional postulates. The key concept of the theory is decoherence, which appears as an inherent characteristic of quantum mechanics and results from the uncertainty relation. In contrast to environment-induced decoherence, this decoherence exists prior to a measurement being made. To clarify our idea, we examine three elemental experiments: a Stern-Gerlach-like experiment, the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment, and the double-slit experiment. By considering the first experiment, we explain how the uncertainty relation between position and momentum introduces decoherence prior to measurement. Consideration of the EPR-Bohm experiment leads us to conclude that the correlation of the EPR pair is not a consequence of what is known as the collapse of the wave function. Our theory of decoherence can also be applied to experiments with continuous eigenvalues, such as the double-slit experiment. Consideration of the double-slit experiment leads us to understand how pure quantum mechanics describes the fact that quanta behave as interfering particles.