Quantum Gravity : Mathematical Models and Experimental Bounds

16 Claus Lämmerzahl
compared with the standard results. Therefore, one trivial answer to the above
questionsisthatany experiment is also an experiment searching for QG effects.
However, from general considerations one may extract some kind of strategy of
where it is preferable to look for such effects, that is, in which situations QG
effects are expected to show up more pronounced than in other situations. This is
one issue addressed in this contribution.
Another aspect is the present status of experimental test of the validity of
the standard theories. The validity of a theory relies on the experimental verification
of the basic principles or foundations of the theory under consideration. This
experimental exploration defines the ”landscape” of the experimentally explored
regime which then is covered by standard theories. QG effects can be present only
outside this explored domains.
These remarks define the outline of this paper: At first we recall the basic
principles present day standard physics relies on. This is the Einstein Equivalence
Principle which essentially determines the structure of all equations of motion. This
is followed by a compact review of most of the experiments aimed at testing the
Einstein Equivalence Principle. Then we come to open problems (“dark clouds”)
of present physics which found no explanation so far. This leads us to the issue of
how we could search for QG effects. We discuss the expected magnitude of these
effects and also where we might expect QG effects and how we should search for
these effects. That is, we discuss some strategy for the search for QG effects. We
close this contribution by outlining which experimental progress we can we expect
in the future.
2. The basic principles of standard physics
The basic principle of standard physics is the Einstein Equivalence Principle which
consists of three parts
The Universality of Free Fall (UFF): This principle states that in a gravitational
field all kinds of structureless matter fall in the same way. In principle,
this is an amazing fact; gravity is the only interaction with this property. In
the frame of elementary particle theory this just means that all elementary
particles fall in the gravitational field in the same way. Therefore one carries
through experiments with various macroscopic species of materials with
different proton to neutron ratio.
The Universality of the Gravitational Redshift (UGR): This universality means
that all clocks based on non-gravitational physics behave in the same way
when moved together in gravitational fields. This again is an amazing fact
and means that in addition to all particles also all (non-gravitational) interactions
(also represented by particles) couple to the gravitational field in the
same way. Again, one has to test this for all kinds of clocks and to analyze
the results in terms of the coupling of elementary particles to gravity.