Quantum Mechanical and Classic Measurement Result Quantities are Equal (Even though their Numerical Values are Not)

Abstract

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.