Once Before Time - Martin Bojowald [65]
COSMIC FORGETFULNESS: FOGGY MEMORIES
What has he with all his grander might
done to lessen our country’s plight?
A kingdom of soldiers he wanted to found,
to kindle and conflagrate all the world’s ground,
to hold everything in his tight-fisted bound.
—FRIEDRICH SCHILLER, Wallenstein
What do theoretical considerations tell us? Independently of observations, theories are sometimes so strict that some possibilities, conceivable otherwise, can be ruled out. Although the equations of quantum gravity remain incomplete—those theories, after all, have not yet been fully formulated—possibilities can be constrained by mathematical consistency conditions. If we knew the present state of the universe precisely, we could calculate back to a time before the big bang, using all mathematically possible equations for quantum cosmology. From different equations one obtains different results, but if they do not differ too much in the whole set of possible equations, one could obtain a good impression of the state of the universe before the big bang. In a way, this resembles what is done by historians, as laid out for instance by Friedrich Schiller in his inaugural lecture11 at the University of Jena:
From the whole of these happenings the universal historian picks out those which have had an essential, unequivocal, and easily followed influence on the current form of the world and the state of generations now alive. The relation of historical data to the current constitution of the world thus is what must be sighted to collect material for world history. World history thus starts from a principle strictly opposite to the beginning of the world. The actual sequence of events descends from the origin of things to their most recent order; the universal historian advances from the newest state of affairs upward toward the origin of everything. When he ascends in thoughts from the current year and century to the preceding ones, and among the events offered by the latter, which contain insight for the next ones—when he has continued this walk step by step to the beginning—not of the world, for thereto leads no landmark—up to the first of statues, then it is up to him to turn back on the ventured way, and to descend unhindered and light along the guideline of the described facts from the first statues to the current age.
The parallel to history should not come as a surprise, for cosmology does investigate a kind of history: that of the universe. Here, one can push backward to much earlier times, perusing entirely new kinds of statues: cosmic background radiation, the distribution of galaxies in the universe, and supernovae (which will be discussed in the next chapter). In cosmology, this approach is known as “top-down”: One starts with knowledge at the top end of the time axis and tries to derive properties at an earlier time at the bottom. Compared to that of Schiller, the view is upside down, because traditionally time in mathematical diagrams is drawn upward (or sometimes to the right). In cosmology, this approach may first have been introduced by Jim Hartle and Stephen Hawking, and was recently formalized by Hawking and Thomas Hertog.12
We do not know the present state very precisely due to the difficulty of observations of the entire universe, and we can never know it arbitrarily precisely due to quantum theoretical uncertainties of the cosmological wave function. The decisive question thus is how much of an influence the ignorance of the present state of the universe has on that before the big bang, obtained by calculating backward. Or: How many statues can we find in the early universe, in addition to the statuesque cosmic background radiation? Ignorance could be roughly constant in time, allowing acceptable precisions in our knowledge of the pre–big bang behavior; compared to the present state, ignorance would be increased only by the imprecisely known quantum cosmological equations.