Harald Markum (Vienna):

On the Mass in Fundamental and Effective Theories of Physics and Its Measurement

Abstract:

In Classical Newtonian Mechanics the Hamiltonian function consists of a sum of kinetic and potential energy, where the mass of a body enters as a parameter. Within gravity one does not distinguish between gravitational mass in the attraction of bodies in contrast to the inertial mass of objects in empty space; experimentally no difference can be found. In Special Theory of Relativity there appears the energy-momentum relation, where the value of the mass depends on the velocity; the rest mass is the same parameter as in Classical Mechanics. In Quantum Mechanics the mass stays as a parameter in the Hamiltonian; excited states in the Hydrogen atom are proportional to the rest masse. In Quantum Field Theory the mass becomes a (divergent) parameter, which has to be fixed to the experimental value via a renormalisation procedure. In the Standard Model of Particle Physics the masses depend on the vacuum expectation value of the Higgs Field. The fermions are additionally influenced from a Yukawa Coupling, being an open parameter.

In the Three Body Problem the mass of the interacting particles plays a decisive role. In general such systems are chaotic. A stability criterion is given by the Kolmogorow-Arnold-Moser Theorem. Approximate solutions can be derived if one mass of the bodies is small. It is also exactly solvable if the two heavy bodies are in equilibrium with respect to gravity. There exists an analytic solution for the special case of identical masses of the three bodies travelling on a special loop. We give an overview of the different definitions and measurements.