System parameters and measurement instrument parameters are not separately observable: Relational mass is observable while absolute mass is not

Abstract

A brief summary of the objections to the relational nature of inertial mass, gravitational mass and electric charge is presented. The objections are refuted by showing that the measurement process of comparing an instrument reference clock and a reference rod both obeying the laws of physics to a system obeying the same laws of physics results in relational quantities: inertial mass, gravitational mass and electric charge appear only as ratios. This means that scaling of the absolute inertial mass of every object in the universe by the same factor is unobservable (likewise for gravitational mass and electric charge). It is shown that the measurement process does not separate the instrument parameters from the system parameters. Instead a measurement produces functions of fundamental, dimensionless parameters such as the fine structure constant, electron-proton mass ratio and the proton gyro-magnetic factor. It is shown that the measurement of Planck's constant also results in such a function of these dimensionless parameters. Application of this analysis to the "absolute" Planck units shows that they too are functions only of relational quantities. Analysis focuses initially on non-relativistic systems for the sake of clarity and simplicity. The results are then extended to relativistic systems described by the Dirac equation and the Einstein field equations of general relativity. The results support the assertion that instrument parameters cannot be separated from system parameters even in classical mechanics.