This paper applies statistical mechanics to reframe representational measurement theory (probabilistic) and metrology (deterministic). This is shown to unify the different measurement theories and correlate the different formulations of measurement result deviation (i.e., uncertainty, standard deviation, variance, precision and accuracy) across the sciences.

Rationale:
• J. C. Maxwell recognized that a numerical value and a quantity are the form of all measurement results.
• The Mach-Zehnder interferometer experiments identify that the numerical value and quantity are independent.
• All measurements are numerical value comparisons which require equal quantities.
• Establishing equal quantities requires equalization by calibration.
• Including calibration explains the Schrödinger’s Cat experiment.

In many quantum measurement experiments and thought experiments, measurement results appear that do not seem to have classic explanations. As example: In quantum particle spin experiments, entangled particles appear to interact instantly across distances; and in interferometer experiments, one measurement result appears to be split over two paths. Currently, these measurement phenomena are treated as unique to quantum mechanics and not understandable in classic physics. Recognizing calibration in theory explains and resolves all the differences that appear to occur between classic and quantum measurements.

The following link for the PDF version: ScienceXSchrodingercat.
In 1935, E. Schrödinger proposed his well-known cat thought experiment suggesting, but not explaining, how a measurement transforms the probable states of an atom into the actual state of a cat (alive or dead). Rather than applying quantum mechanics (the previous approach usually taken), this paper presents an out-of-the-box, logically consistent explanation using metrology (the science of physical measurement).

This short paper identifies that the concept of a local measurement is always violated by a necessary metrological process – calibration. J. S. Bell’s formal development of the same violation demonstrates that the EPR paradox and related discontinuities may be resolved by including the calibration process in a measurement process, as formalized in Measurement, February 2018 “Relative Measurement Theory”.

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.

A previous version,“Relational Measurements and Uncertainty”, was published in Measurement, Vol 93, Nov. 2016, pages 36-40.
Download 2016 PDF Measurement version from this link.

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.