How to introduce physical quantities physically

Abstract

The centuries-long practice of the teaching turned mechanics into an academic construct detached from its underlying science, the physics of macroscopic bodies. In particular, the regularities that delineate the scope of validity of Newtonian mechanics was never used as premises in that construct. Instead, its logical structure has been built with the only purpose to ease the presentation of mechanics as an application of calculus and algebra. This leaves no room for the explicit physical description of the fundamental notions of the construct, such as the ability of (a system of) physical bodies to keep a spatial form, symbolized by a rigid measuring rod, and the possibility to count out even temporal intervals, symbolized by a standard clock, let alone the origin of the basic mechanical quantities. The comparison between (states of) physical objects is possible as far as the natural regularities enable a researcher to define an equivalence relation in a set of these objects. The class of macroscopic (or macroscopically perceived) objects is that one where certain composition rules hold so that constituents of any object are macroscopic, too. Then the properties of compositions of macroscopic objects, being in conjunction with the equivalence relations between them, yield a numerical characterization of each macroscopic object, i.e. a basic physical quantity. The technique of logically arranged feasible/thought experiments is used to formulate the logically impeccable, induction-based definitions for two quantities: the length of a line segment as an instructive toy example and the mass of a macroscopic body as an example applicable to the real world.