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 energymomentum 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 KolmogorowArnoldMoser
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.
