Approaches to Quantum Gravity

Quantum Gravity phenomenology 431
theory is in principle able to make any definite predictions, since the formalism is
so flexible, so capable of saying anything, that it is feared it will amount basically
to saying nothing.
Usually in physics the demand that a theory be falsifiable is of course the first
and most important requirement, but it is also usually not a tough one: any reasonable,
however naive, concept of theory should give rise to a falsifiable theory.
Two known causes of failure for falsifiability are the lack of logical consistency
(so basically the candidate theory was not a theory after all, since the piece of
mathematics introduced did not combine to produce a logically consistent overall
structure) or the presence of unlimited flexibility, i.e. the scenario feared for string
theory. Of course a theory that in principle is falsifiable but presents us with practically
unsurmountable computational challenges (which might be the case of loop
quantum gravity, if a satisfactory description of the classical limit does not become
available) is for our purposes not falsifiable.
So concerning task two the situation does not look very healthy, but the problem
resides on the theory side, not the phenomenology side. If they give us definite
predictions we will do our best to honour them by killing their theories (which I
still think should be the healthiest attitude to be adopted when doing phenomenology
work). Presently, for most of the fashionable theories, no such honour can be
given.
If indeed, at least for now, we cannot falsify loop quantum gravity and string theory,
can we at least falsify some other theory used in Quantum Gravity research?
I believe it is extremely important for Quantum Gravity phenomenology to find
one such example. If we do find a first example then we can legitimately hope
that the falsifiability of more and more theories will gradually be achieved. And
because of the importance I give to this objective I have invested a lot of effort in
the study of one of the formalisms used in Quantum Gravity research, that of the
κ-Minkowski noncommutative spacetime. I do not necessarily “favour” this formalism,
but I have the intuition that it should be falsifiable. This intuition must,
however, still find full support in the analysis. The logical consistency of theories
in κ-Minkowski has still not really been shown, at least not to the level desired
by physicists, and we are presently unable to do many computations in this framework,
which may be a manifestation of a serious unsurmountable challenge for
computations; but at present it is still legitimate to hope (in my view rather reasonable
to expect) that we will soon be able to do these computations. There have,
for many years, been results on κ-Minkowski providing weak links (the usual
weak links from theory to effects in Quantum Gravity research) to effects such
as deformed dispersion relations, deformed energy-momentum-conservation laws,
and deformed boost transformations. Some of these links have become gradually
somewhat more robust. I expect that progress in this direction will accelerate thanks