The Model in Physics

Abstract

It must have been in an unthinking moment that I promised to speak about 'the' model in physics. For even in physics models of quite different types are used for quite different purposes. Rather than talk about 'the' model, I will take a few examples of some types of models in physics. The catalogue of types will by no means be exhaustive. Two extreme types are the model as a more or less exemplary ideal and the model as a more or less poor substitute. In various types the ideal meaning and the substitute meaning appear intermixed. A sharp classification of types seems unworkable. And I know of no model of a model. I. REPRESENTATIVE MODEL Representative models may be built for demonstration or for experimental investigation. In a planetarium the planetary motion is imitated by a mechanism with entirely different equations of motion. In 1780 such a planetarium was built in Franeker by Eise Eisinga in order to demonstrate that a planetary conjunction would not result in a catastrophic collision. More direct are small scale models, e.g. hydrodynamic models of ships or tidal currents, for manageable experimental investigation. The equations of motion and the boundary conditions are roughly the same as in the original system, but some details may be changed by the scale transformation, e.g. the tidal current deviation by Coriolis forces. For our present topic a still more interesting type of representative model is the analogue model. Its equations of motion are, apart from scale constants, formally similar to those of the original system, but the mechanism may be entirely different. In this way e.g. the motion of single electrons in an electronic tube may be imitated with small balls rolling on a rubber sheet. The sheet is braced over models of electrodes at heights proportional to the potentials of their originals. In a similar way the motion of radio signals in the ionosphere may be imitated with balls Yfolling on a curved surface. The height of the surface is now proportional 98 H. Freudenthal, The Concept and the Role of the Model in Mathematics and Natural and Social Sciences