Once Before Time - Martin Bojowald [66]
Chaos does play a role also in cosmology, but we can ignore it for the main questions of interest here. In the simplest models of general relativity, the total volume changes in a way that does not show chaos. Hope thus remains to venture backward successfully, at least in thoughts, but we still have to see whether the equations of quantum cosmology themselves might not add more uncertainty compared to those of general relativity.
Of particular interest is the question of what kind of quantum uncertainty could have prevailed before the big bang. Repulsive forces of quantum gravity prevent the singularity, save space-time from its demise, and make possible a world before the big bang. But as a quantum theory, quantum gravity also shows such typical properties as fluctuations and uncertainty. To some degree, the behavior can remain prevalent even at a distance from the big bang. One normally envisions a nonsingular space-time at the big bang as a so-called “bounce” where the universe reaches its minimal volume. But in reality one is talking about a quantum version of space-time, for without quantum theory there would be the singularity.13 This must lead to fluctuations, alien to the classical world. Quantum forces are welcome, but they bring along unclassical jumpiness. Does the quantum world then keep space-time in fluctuating turmoil after having prevented the singularity—like an army of mercenaries that, long after repelling a dangerous aggressor, marauds through and plunders the ravaged lands?
In a precise analysis of currently available models one sees that many properties of the universe can be computed backward quite precisely. Many, but not all. There are physical quantities, important for some of the interesting questions, whose values before the big bang have such a weak influence on what is happening afterward that they are irrelevant for the present state. In such a case, the values before the big bang cannot be restricted by conditions one would obtain by extrapolating backward from the present values.
The universe, as it were, forgets which precise value such a property had taken before the big bang. Even though the value might in principle still have an effect on the behavior of the universe, the influence is so imperceptibly small that the value is irrelevant. No other phenomenon would still register it—it is forgotten. The main example of such forgetful properties is the degree of quantum uncertainty. Thanks to repulsive forces of quantum gravity, the big bang is no longer singular as in general relativity, yet it remains a rather special place. The value characterizing quantum fluctuations for a long time before the big bang suddenly becomes relatively unimportant after the big bang; quantum fluctuations are then determined by a new parameter, in general independent of the old one. Although the old value still influences what happens in a very minute way, by realistic observations it can no longer be recovered.
17. Illustration of a wave function for a nonsingular universe. Contour lines show the values of the wave function depending on the volume (vertical) and time (horizontal). The bottom axis, corresponding to vanishing volume, is never reached, and neither is the singularity. Quantum fluctuations, represented by the width of the ridge, may have been different before minimal volume was reached than they are afterward. This is the basis of cosmic forgetfulness, for the strength of quantum fluctuations before the big bang cannot easily be reconstructed after the big bang.
In other words, the state of the universe