We can take Mott’s solution more seriously. Several points can be made. Situations in which part of a quantum system is in the semiclassical regime, so that Hamilton’s ‘light rays’ are present as latent or even incipient classical histories, are rather common and characteristic. The Heisenberg-Mott work then shows that such latent histories will become entangled with the remaining quantum variables, which must, in some way, reflect and carry information about those histories. What is not clear is whether the histories will exhibit a pronounced sense of direction – an arrow of time. That, above all, is put into the Mott solution by hand.
Also relevant is the mathematically somewhat suspect procedure known as successive approximation used to construct the Mott solution. There is no global arena in which the cloud chamber resides. Its atoms are effectively located in empty Euclidean space, and Mott could keep on adding approximations without worrying about their behaviour far from the cloud chamber. He was not constructing a genuine well-behaved solution, in which one must ensure the behaviour is right everywhere, especially at infinity. Instead, Mott used infinity as a kind of dustbin. This could not be done in a realistic situation, as I would now like to show.
When Planck made the first quantum discovery, he noted an interesting fact. The speed of light, Newton’s gravitational constant, and Planck’s constant clearly reflect fundamental properties of the world. From them it is possible to derive the characteristic mass 
length lplanck and time fplanck with approximate values
On atomic scales the Planck mass is huge, corresponding to about 1019 hydrogen atoms. In contrast, the Planck length and time are far smaller than anything physicists can currently measure.
Much of current cosmology is concerned with the ‘interface’ of quantum gravity and classical physics. The universe around us is described by general relativity. This classical treatment is said to be valid right back into the distant past, very close to the Big Bang. The quantum phase of cosmology is supposed to become important only at extraordinarily small scales, of the order of the Planck length, 10–33 centimetres. Lights travel this distance in 10–43 seconds, and it is argued that quantum gravity ‘comes into its own’ only in this almost incomprehensibly early epoch.
All researchers agree that the nature of reality changes qualitatively in this domain. Different laws must be used. Time ceases to be an appropriate concept: things do not become, they are. In a process often likened to radioactive decay, our classical universe that emerges at the Big Bang is represented as somehow ‘springing’ out of timelessness, or even nothing. A mysterious quantum birth creates the initial conditions that apply at the start of the classical evolution. Our present universe is then the outcome of the conditions created by quantum gravity. The dichotomy between the laws of nature and initial conditions is thus resolved if the quantum creation process can be uniquely determined.
Stephen Hawking has long been working on this problem, and believes it can be solved by his so-called no-boundary proposal, a mechanism which should lead to a unique prediction for the initial conditions. His ‘imaginary-time’ mechanism, described in his A Brief History of Time, seemed to have the potential to do this. However, it has been widely criticized, and there are technical problems. The most serious seems to be that even if the mechanism can be made to work it will not produce unique initial conditions. Where Hawking has led, many have followed, and numerous creation schemes have been proposed.
My difficulty with this approach is the division introduced between the quantum and classical domains. One could almost get the impression that the laws of nature actually change, and I am sure that no theoretical physicist believes that. The approach is adopted because the physical conditions are hugely different in the two domains. In physics it is very common to use quite different schemes if the conditions studied are different. No engineer would use quantum mechanics to describe water flow in pipes, for example. But the much more appropriate hydrodynamic equations are consequences of the deeper quantum equations, and are valid in the appropriate domain.
Cosmology may be different. Most physicists have a deeply rooted notion of causality: explanations for the present must be sought in the past (vertical causality, as I have called it). This instinctive approach will be flawed if the very concept of the past is suspect. If quantum cosmology really is timeless, our notion of causality may have to be changed radically. We cannot look to a past to explain what we find around us. The here and now arises not from a past, but from the totality of things (horizontal causality).
Figure 53. A schematic representation of Platonia. All points in each horizontal section represent configurations of the universe with the same volume but different curvatures and matter distributions in them. According to the ideas of quantum creation, as yet unknown laws of quantum gravity hold near Alpha, and in some rather mysterious way give rise to conditions under which our universe – and with it, time – ‘spring out of Alpha’. The thread shown ascending from Alpha represents the history of our universe that results from the enigmatic quantum creation.
Figure 53, a schematic representation of Platonia, may help. This is the skewed continent, as the cone shape makes clear. The quantum-creation approaches imply that the enigmatic and as yet unknown laws of quantum gravity create at the vertex – Alpha – a ‘spark in eternity’. The spark, in its turn, creates close to Alpha the initial conditions of our actual universe. Time is born at the ‘spark’. Our classical universe is the thread ascending through Platonia to our present location.
Figure 54 shows what is often called the chronology of the universe (the vertical axis is time, and the ‘quantum creation’ at Alpha occurs at the bottom left). Here each horizontal section is one point on the thread through Platonia in Figure 53: it is space at the corresponding time. The characteristic structures in space at the various cosmic epochs are shown: quarks in a soup near Alpha, primordial hydrogen and helium after the first three minutes, incipient galaxies a few thousand years later, and so on, right through to life on Earth at the present. Such is the thread ‘born in the quantum spark’. The Everettian quantum cosmologists believe that the one quantum spark creates many such threads, one of them ours. But is there a ‘spark’ at Alpha? The laws of quantum gravity hold not just near Alpha, but throughout Platonia – they are the conjectured universal and ultimate laws. We have to ask what kind of solutions they can have, and how the solutions are created. How do threads, one or many, emerge?
Figure 54. Chronology of the universe. Redrawn from A Short History of the Universe by Joseph Silk (W. H. Freeman/Scientific American Library, 1994). The vertical axis represents time. Alpha, the ‘quantum creation’, occurs at the bottom left.
Our entire experience tells us that the well-behaved solutions of the stationary Schrödinger equation that describe the characteristic structures of atoms, molecules and solids are determined by the complete structure of the configuration spaces on which they are defined. They exhibit global sensitivity – their behaviour has to be right everywhere. Since the governing equation does not contain the time, this delicate ‘testing out of all possible behaviours’ takes place in timelessness. If the Wheeler-DeWitt equation is like the stationary Schrödinger equation, then Alpha, where time is allegedly born, plays an important role, but it is not the locus at which some all-decisive die is cast. Of course it is singular – Platonia abuts on nothing at Alpha – but there are innumerable other special points scattered all over Platonia. None are quite like Alpha but, together with the overall shape of Platonia, they all have their role to play. Quantum mechanics is nothing if not democratic. Solutions of the Wheeler-DeWitt equation must be produced by a kind of dialogue between every point in Platonia.