Auteur: Tineke Ridderbos
Vakgroep: Wetenschapsfilosofie, Logica en Kentheorie
Physics and the infinite.
In modern physics, phenomena are described in mathematical language. Sometimes infinities occur in these descriptions. At first sight this seems strange; the physical systems we want to describe are almost by definition finite (the one possible exception being the universe as a whole, although most physicists seem to be convinced that the observable universe has a finite extent in both space and time). By a system being finite we mean finite in the sense of having a finite spatial extent, consisting of finitely many particles, having a finite amount of energy, a finite mass, etc.
As a result, when the mathematical description of a physical system uses infinities, we are confronted with an interpretation problem; what exactly do we mean when our mathematical description uses for example infinite systems, or when it seems to tell us that the mass of a particle is infinite?
In this thesis I consider two theories, viz. statistical mechanics and quantum field theory, in detail. I will look at the role the infinite plays in these theories and the interpretational problems this causes.
Consequently, a proposal of Paul Teller for an interpretation of the infinities in quantum field theory which renders them less problematic will be studied. In this interpretation infinite quantities are considered to be 'ideal elements', understandable only in terms of the limiting processes leading to them. I will evaluate these ideas and extend them to statistical mechanics. Finally this interpretation in terms of ideal elements will be compared to David Hilbert's finitistic ideas on the philosophy of mathematics.
From this thesis we may conclude that for working physicists, truth is not good enough. They must have calculability. Indeed, if a choice must be made, often physicists must abandon truth and seek calculable theories which provide adequate approximations. In the case of quantum field theories, a complete theory, integrating both electromagnetic forces and gravity, i.e. a theory of reach. In the meanwhile quantum field theories, though using infinities, provide one of the best agreements between experiment and theory that exists anywhere in physics.
|Laatst gewijzigd:||30 mei 2016 12:14|