Scientific modeling: round trips to many destinations

To understand modern science we cannot talk merely about theories. We must recognize the indispensable role of models. By theories we mean basic theories in physics, as described in scientific textbooks. Each basic theory describes a separate aspect of physical reality: movement under forces, gravity, electricity and magnetism, heat phenomena, and the like. Interactions described by basic theories are universal, that is, they apply to every element of physical reality. Every two elements of mass attract each other with the force described by the theory of gravity. However small is that force, however small or remote are the masses, the theory assigns that force some value, even if it is non-measurably small. Empirical verification of statements about individual interactions between concrete objects is difficult not only because the effects caused by a particular interaction may be non-measurable, but also because we cannot measure a selected interaction, but rather a resultant of many interactions, some of them we may not even know. Physical systems are usually too complex to be effectively described by application of a single theory. In most cases the observed behavior can be only explained when we consider many interactions by combining different theories, applying them jointly to a complex structure. Even if basic theories are universal, they are difficult to discover from complex interactions. Fortunately, scientists notice or create very simple systems, that lead to discovery of individual interactions. The history of science demonstrates on numerous cases that theories have been developed in result of empirical investigation of simple, one-sided systems, in which the phenomena transcending a given theory were practically insignificant. In the majority of physical situations, however, several theories must be applied simultaneously. For those situations the scientists construct models. We will describe model construction in the next sections. Here we only briefly indicate that a model consists primarily of (1) an idealized structure representing spatiotemporal objects, interactions and processes, and (2) a system of equations that represent quantitative reintions in the system and phenomenon being modeled. Each component of the idealized system has its counterpart in one or few terms that occur as pieces of equations. The mapping between the idealized physical system and the physical world tells which physical entities (bodies, waves, fields) we decided to consider and how we decided to represent them (material points, rigid spheres, and the like), and what objects, interactions and processes we believe are relevant to the modeled phenomenon. To further contrast theories with models, let us compare the scopes of application and empirical verification of basic theories and models. A good model of O is empirically confirmed by direct measurements of O, when it captures all the important interactions. A basic theory can rarely be directly verified because it describes only one type of interactions while neglecting all other, no matter how significant they axe in given situation. In different sense, however, each basic theory applies universally, because for each object it describes a particular interaction. We are unable to demonstrate this universal claim by a direct empirical verification, but it is confirmed indirectly in each model in which we use given theory to describe that particular interaction.