Kiefer C. Quantum gravity

324 INTERPRETATION
classical turning point, which would then constitute the ‘end’ of evolution. This
would be analogous to the quantum region at the onset of inflation discussed
in Section 10.1.2. Quantum gravity would thus in principle be able to provide a
foundation for the origin of irreversibility—a remarkable achievement.
10.3 Outlook
Where do we stand? We have not yet achieved the final goal of having constructed
a consistent quantum theory of gravity checked by experiments. It seems, however,
clear what the main problems are. They are both of a conceptual and a
mathematical nature. On the conceptual side, the most important task is to get
rid of an external background space–time. This is drastically different from ordinary
quantum field theory which heavily relies on Minkowski space (and its
Poincaré symmetry) or a given curved space–time. An expression of this issue is
the ‘problem of time’ with its connected problems of Hilbert space and the role
of the probability interpretation. On the mathematical side, the main task is to
construct a non-perturbative, anomaly-free framework from which definite and
testable predictions can be made. An example would be the prediction for the
final evaporation stage of black holes.
In this book I have presented two main approaches—quantum GR (in both
covariant and canonical versions) and string theory. Both rely on the linear structure
of quantum theory, that is, the general validity of the superposition principle.
In this sense also string theory is a rather conservative approach, in spite of its
‘exotic’ features such as higher dimensions. This has to be contrasted with the
belief of some of the founders of quantum mechanics (especially Heisenberg) that
quantum theory has already to be superseded by going from the level of atoms
to the level of nuclei.
What are the predictions of quantum gravity? Can it, for example, predict
low-energy coupling constants and masses? As is well known, only a fine-tuned
combination of the low-energy constants leads to a universe like ours in which
human beings can exist. It would thus appear strange if a fundamental theory
possessed just the right constants to achieve this. Hogan (2000) has argued that
grand unified theories constrain relations among parameters, but leave enough
freedom for a selection. In particular, he suggests that one coupling constant and
two light fermion masses are not fixed by the symmetries of the fundamental theory.
5 One could then determine this remaining free constants only by the (weak
form of the) anthropic principle: they have values such that a universe like ours
is possible. The cosmological constant, for example, must not be much bigger
than the presently observed value, because otherwise the universe would expand
much too fast to allow the formation of galaxies. The universe is, however, too
special to be explainable on purely anthropic grounds. In Section 10.2, we have
mentioned that the maximal entropy would be reached if all the matter in the
5 String theory contains only one fundamental dimensionful parameter, the string length.
The connection to low energies may nonetheless be non-unique due to the existence of many
different possible ‘vacua’.