FIGURE 11.7 A region of the multiverse containing a spinning coin. Each point in the diagram represents one snapshot.
The determinism of quantum theory, just like that of classical physics, works both forwards and backwards in time. From the state of the combined collection of ‘heads’ and ‘tails’ snapshots at the later time in Figure 11.7, the ‘spinning’ state at an earlier time is completely determined, and vice versa. Nevertheless, from the point of view of any observer, information is lost in the coin-tossing process. For whereas the initial, ‘spinning’ state of the coin may be experienced by an observer, the final combined ‘heads’ and ‘tails’ state does not correspond to any possible experience of the observer. Therefore an observer at the earlier time may observe the coin and predict its future state, and the consequent subjective probabilities. But none of the later copies of the observer can possibly observe the information necessary to retrodict the ‘spinning’ state, for that information is by then distributed across two different types of universe, and that makes retrodiction from the final state of the coin impossible. For example, if all we know is that the coin is showing ‘heads’, the state a few seconds earlier might have been the state I called ‘spinning’, or the coin might have been spinning in the opposite direction, or it might have been showing ‘heads’ all the time. There is no possibility of retrodiction here, even probabilistic retrodiction. The earlier state of the coin is simply not determined by the later state of the ‘heads’ snapshots, but only by the joint state of the ‘heads’ and the ‘tails’ snapshots. Any horizontal line across Figure 11.7 passes through a sequence of snapshots with increasing clock readings. We might be tempted to think of such a line — such as the one shown in Figure 11.8 — as a spacetime, and of the whole diagram as a stack of spacetimes, one for each such line. We can read off from Figure 11.8 what happens in the ‘spacetime’ defined by the horizontal line. For a period, it contains a spinning coin. Then, for a further period, it contains the coin moving in a way that will predictably result in ‘heads’. But later, in contradiction to that, it contains the coin moving in a way that will predictably result in ‘tails’, and eventually it does show ‘tails’. But this is merely a deficiency of the diagram, as I pointed out in Chapter 9 (see Figure 9.4, p. 212). In this case the laws of quantum mechanics predict that no observer who remembers seeing the coin in the ‘predictably heads’ state can see it in the ‘tails’ state: that is the justification for calling that state ‘predictably heads’ in the first place. Therefore no observer in the multiverse would recognize events as they occur in the ‘spacetime’ defined by the line. All this goes to confirm that we cannot glue the snapshots together in an arbitrary fashion, but only in a way that reflects the relationships between them that are determined by the laws of physics. The snapshots along the line in Figure 11.8 are not sufficiently interrelated to justify their being grouped together in a single universe. Admittedly they appear in order of increasing clock readings which, in spacetime, would be ‘time stamps’ which would be sufficient for the spacetime to be reassembled. But in the multiverse there are far too many snapshots for clock readings alone to locate a snapshot relative to the others. To do that, we need to consider the intricate detail of which snapshots determine which others.
FIGURE 11.8 A sequence of snapshots with increasing clock readings is not necessarily a spacetime.
In spacetime physics, any snapshot is determined by any other. As I have said, in the multiverse that is in general not so. Typically, the state of one group of identical snapshots (such as the ones in which the coin is ‘spinning’) determines the state of an equal number of differing snapshots (such as the ‘heads’ and ‘tails’ ones). Because of the time-reversibility property of the laws of quantum physics, the overall, multi-valued state of the latter group also determines the state of the former. However, in some regions of the multiverse, and in some places in space, the snapshots of some physical objects do fall, for a period, into chains, each of whose members determines all the others to a good approximation. Successive snapshots of the solar system would be the standard example. In such regions, classical physical laws are a good approximation to the quantum ones. In those regions and places, the multiverse does indeed look as in Figure 11.6, a collection of spacetimes, and at that level of approximation the quantum concept of time reduces to the classical one. One can distinguish approximately between ‘different times’ and ‘different universes’, and time is approximately a sequence of moments. But that approximation always breaks down if one examines the snapshots in more detail, or looks far forwards or backwards in time, or far afield in the multiverse.
All experimental results currently available to us are compatible with the approximation that time is a sequence of moments. We do not expect that approximation to break down in any foreseeable terrestrial experiment, but theory tells us that it must break down badly in certain types of physical process. The first is the beginning of the universe, the Big Bang. According to classical physics, time began at a moment when space was infinitely dense and occupied only a single point, and before that there were no moments. According to quantum physics (as best we can tell), the snapshots very near the Big Bang are not in any particular order. The sequential property of time does not begin at the Big Bang, but at some later time. In the nature of things, it does not make sense to ask how much later. But we can say that the earliest moments which are, to a good approximation, sequential occur roughly when classical physics would extrapolate that the Big Bang had happened 10–43 seconds (the Planck time) earlier.
A second and similar sort of breakdown of the sequence of time is thought to occur in the interiors of black holes, and at the final recollapse of the universe (the ‘Big Crunch’), if there is one. In both cases matter is compressed to infinite density according to classical physics, just as at the Big Bang, and the resulting gravitational forces tear the fabric of spacetime apart.
By the way, if you have ever wondered what happened before the Big Bang, or what will happen after the Big Crunch, you can stop wondering now. Why is it hard to accept that there are no moments before the Big Bang or after the Big Crunch, so that nothing happens, or exists, there? Because it is hard to imagine time coming to a halt, or starting up. But then, time does not have to come to a halt or start up, for it does not move at all. The multiverse does not ‘come into existence’ or ‘cease to exist’; those terms presuppose the flow of time. It is only imagining the flow of time that makes us wonder what happened ‘before’ or ‘after’ the whole of reality.