Keyhole: Equal signs as bridges between the phenomenological and theoretical dimensions

If one aims at understanding what physics is about, recognise how experimental measurements and mathematical reasoning are intertwined is essential. In this work we exemplify such entanglement by analysing three case studies.

In the first one, the explanation of the Hall effect underlines how we indirectly penetrate into the microscopic structure of a wire and manage to evaluate the number of charged particles per unit volume inside it from a set of macroscopic measurements. The second case shows how our reasoning allows us to determine the radius of a hydrogen atom from the experimental measure of the atom's binding energy. The third example comes from kinetic gas theory and illustrates how it is possible to estimate the number of gas particles per unit volume from the experimental values of pressure and temperature.