Once Before Time - Martin Bojowald [68]
Although a quantum theory of gravity can avoid the big bang singularity—already a success—this does not necessarily mean that one can now determine everything in the universe and its exact origin. Doing so would in fact be far from possible: the universe still presents its riddles. In theoretical cosmology one often considers simple model universes in which the history and parameters such as the energy density or temperature at the time of its minimal extension can be calculated precisely. If special properties arising from the simplification are responsible for this high precision, results cannot be considered valid in general.
Even if a whole class of models provides similar statements, one cannot be certain about their generality. One has to be aware of selection effects, as described intuitively in Arthur Eddington’s fishermen parable: Two fishermen chat about their job while their nets are filling with fish. One of them mentions a remarkable observation he has been contemplating: While the fish they catch have different sizes, no fish smaller than about half an inch has ever been seen in the net. The second fisherman does not find this enigmatic at all, for a fish grows in an egg before swimming freely in the sea and possibly being caught in a fishing net. He concludes that all kinds of fish must hatch with a size of about half an inch.
This is an example of an apparently valid but wrong conclusion. Obviously, the fishermen have not taken into account the fixed mesh size of the net, which can contain and pull on board only fish above a certain size. Smaller fish simply fall through the mesh or swim out of the net. Here we are dealing with a selection effect, for the method determines a property of the result. Similarly, there are selection effects in cosmological models whose difficulty in general requires specific properties for a detailed analysis in special cases. It is then difficult to decide whether the requirement of direct tractability itself, for instance by mathematical solutions, already determines at least some part of the result. One can analyze different models, but a large number of characteristic cases is necessary to arrive at a reliable result. In only a few instances is this possible, given the complexity of even the simplest models of quantum cosmology.
Instead, there is a rather more powerful view, which, however, is less popular. Abandoning the focus on positive properties, such as the precise value of a certain quantity, one takes a pessimistic stand, trying to show what limits exist for determining a parameter. In simple models one can compute these limits in much the same way as positive values, but results for limits are often wide and not very constrained. In some cases, however, such as the quantum fluctuations of the universe before the big bang, there are surprising limitations that reveal themselves even in simple models. Such limitations only become stronger in more general situations, and thus can be considered as general properties.
One should not misunderstand this pessimistic viewpoint as giving up. Limits play important roles in science, and they must clearly be recognized. Only then will one see how one can achieve progress within