Thirdly, it is thought that on a sub-microscopic scale quantum effects again warp and tear the fabric of spacetime, and that closed loops of time — in effect, tiny time machines — exist on that scale. As we shall see in the next chapter, this sort of breakdown of the sequence of time is also physically possible on a large scale, and it is an open question whether it occurs near such objects as rotating black holes.
Thus, although we cannot yet detect any of these effects, our best theories already tell us that spacetime physics is never an exact description of reality. However good an approximation it is, time in reality must be fundamentally different from the linear sequence which common sense supposes. Nevertheless, everything in the multiverse is determined just as rigidly as in classical spacetime. Remove one snapshot, and the remaining ones determine it exactly. Remove most snapshots, and the few remaining ones may still determine everything that was removed, just as they do in spacetime. The difference is only that, unlike spacetime, the multiverse does not consist of the mutually determining layers I have called super-snapshots, which could serve as ‘moments’ of the multiverse. It is a complex, multi-dimensional jigsaw puzzle.
In this jigsaw-puzzle multiverse, which neither consists of a sequence of moments nor permits a flow of time, the common-sense concept of cause and effect makes perfect sense. The problem that we found with causation in spacetime was that it is a property of variants of the causes and effects, as well as of the causes and effects themselves. Since those variants existed only in our imagination, and not in spacetime, we ran up against the physical meaning-lessness of drawing substantive conclusions from the imagined properties of non-existent (‘counter-factual’) physical processes. But in the multiverse variants do exist, in different proportions, and they obey definite, deterministic laws. Given these laws, it is an objective fact which events make a difference to the occurrence of which other events. Suppose that there is a group of snapshots, not necessarily identical, but all sharing the property X. Suppose that, given the existence of this group, the laws of physics determine that there exists another group of snapshots with property Y. One of the conditions for X to be a cause of Y has then been met. The other condition has to do with variants. Consider the variants of the first group that do not have the property X. If, from the existence of these, the existence of some of the Y snapshots is still determined, then X was not a cause of Y: for Y would have happened even without X. But if, from the group of non-X variants, only the existence of non-Y variants is determined, then X was a cause of Y.
There is nothing in this definition of cause and effect that logically requires causes to precede their effects, and it could be that in very exotic situations, such as very close to the Big Bang or inside black holes, they do not. In everyday experience, however, causes always precede their effects, and this is because — at least in our vicinity in the multiverse — the number of distinct types of snapshot tends to increase rapidly with time, and hardly ever decreases. This property is related to the second law of thermodynamics, which states that ordered energy, such as chemical or gravitational potential energy, may be converted entirely into disordered energy, i.e. heat, but never vice versa. Heat is microscopically random motion. In multiverse terms, this means many microscopically different states of motion in different universes. For example, in successive snapshots of the coin at ordinary magnifications, it seems that the setting-down process converts a group of identical ‘predictably heads’ snapshots into a group of identical ‘heads’ snapshots. But during that process the energy of the coin’s motion is converted into heat, so at magnifications large enough to see individual molecules the latter group of snapshots are not identical at all. They all agree that the coin is in the ‘heads’ position, but they show its molecules, and those of the surrounding air and of the surface on which it lands, in many different configurations. Admittedly, the initial ‘predictably heads’ snapshots are not microscopically identical either, because some heat is present there too, but the production of heat in the process means that these snapshots are very much less diverse than the later ones. So each homogeneous group of ‘predictably heads’ snapshots determines the existence of — and therefore causes — vast numbers of microscopically different ‘heads’ snapshots. But no single ‘heads’ snapshot by itself determines the existence of any ‘predictably heads’ snapshots, and so is not a cause of them.
The conversion, relative to any observer, of possibilities into actualities — of an open future into a fixed past — also makes sense in this framework. Consider the coin-tossing example again. Before the coin toss, the future is open from the point of view of an observer, in the sense that it is still possible that either outcome, ‘heads’ or ‘tails’, will be observed by that observer. From that observer’s point of view both outcomes are possibilities, even though objectively they are both actualities. After the coin has settled, the copies of the observer have differentiated into two groups. Each observer has observed, and remembers, only one outcome of the coin toss. Thus the outcome, once it is in the past of any observer, has become single-valued and actual for every copy of the observer, even though from the multiverse point of view it is just as two-valued as ever.
Let me sum up the elements of the quantum concept of time. Time is not a sequence of moments, nor does it flow. Yet our intuitions about the properties of time are broadly true. Certain events are indeed causes and effects of one another. Relative to an observer, the future is indeed open and the past fixed, and possibilities do indeed become actualities. The reason why our traditional theories of time are nonsense is that they try to express these true intuitions within the framework of a false classical physics. In quantum physics they make sense, because time was a quantum concept all along. We exist in multiple versions, in universes called ‘moments’. Each version of us is not directly aware of the others, but has evidence of their existence because physical laws link the contents of different universes. It is tempting to suppose that the moment of which we are aware is the only real one, or is at least a little more real than the others. But that is just solipsism. All moments are physically real. The whole of the multiverse is physically real. Nothing else is.
flow of time The supposed motion of the present moment in the future direction, or the supposed motion of our consciousness from one moment to another. (This is nonsense!)
spacetime Space and time, considered together as a static four-dimensional entity.
spacetime physics Theories, such as relativity, in which reality is considered to be a spacetime. Because reality is a multiverse, such theories can at best be approximations.
free will The capacity to affect future events in any one of several possible ways, and to choose which shall occur.
counter-factual conditional A conditional statement whose premise is false (such as ‘Faraday had died in 1830, then X would have happened’).
snapshot (terminology for this chapter only) A universe at a particular time.
Time does not flow. Other times are just special cases of other universes.
Time travel may or may not be feasible. But we already have reasonably good theoretical understanding of what it would be like if it were, an understanding that involves all four strands.