Measurement Mechanics

"Measurement Mechanics" (MM) 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. Following Euler (1765), MM identifies that repetitive measurements of an unchanged observable produce measurement result distributions relative to a reference or standard. Such repetitive measurement results (without noise or distortion) appear as a Gaussian distribution of probabilistic measurement result quantities (numerical values and units), not a single numerical value with an error distribution as current representational measurement theory indicates. MM treats these distributions not as errors, but as all the statistically possible sums of a measurement apparatus's interval values relative to a reference or standard. Fig. 1 identifies the frame of reference; Fig. 2 diagrams representational measurement theory; Fig. 3 diagrams how metrology relates to representational theory; and Fig. 4 proposes measurement mechanics. The result of the paper's development (eq. (8) on page 12) identifies that the proposed statistical measurement function converges to the commonly applied metrology measurement function when the numerical value is large. The ramifications to measurement theories and experiments are summarized in the three paragraphs below it.