The End of Time: The Next Revolution in Physics

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.

The picture suggested by such arguments is this. Platonia as a whole determines how the static wave function ‘beds down’ on its landscape. There will be regions of semiclassical behaviour with respect to a large set of macroscopic quantities in which latent classical histories are defined. Just as the latent alpha-particle tracks get correlated through the wave function with the chamber electrons, ‘nudging’ the wave function onto time capsules, the same thing can happen in Platonia.

VISION OF A TIMELESS UNIVERSE

Let me now give you my vision of quantum cosmology, contrasting it with the chronology of the universe (Figure 54), that temporal representation of the ‘thread’ in Figure 53. Every instant of time you can conceive of is somewhere in Platonia. But the instants of time can themselves be richly structured beyond imagination. All things we see around us now in the universe are just parts of instants of time. All over Platonia there exist instants of time in which Wagner is composing Tristan and Isolde, astronauts are repairing the Hubble Space Telescope, birds are building nests and I am baking bread. The wave function of the universe finds its way to very few of them. The structure of the wave function and the form of the laws of nature – in which the tendency of gravity to clump matter is surely vital – forces the blue mist to seek out the most special instants, strung out along delicate threads. I think it is wrong of cosmologists to call Figure 54 a chronology of the universe. It is the map of a footpath in Platonia. The blue mist shines at instants containing time capsules, all of which, in their different ways, tell stories of a journey from Alpha along a fine thread of ‘history’ – a path winding through Platonia. Time is in such instants since they reflect the story of the path and, since the structure of Platonia in its totality forces the universal wave function to ‘light up’ the paths, there is a sense in which these instants reflect everything that is.

However, whereas alpha particles create, through their tracks, a literal image of history, the time capsules of the real universe embody their stories in a much subtler manner. This is inevitable given the grandeur of the story – cosmology in its entirety. Consider, for example, the Sun. Quantum mechanically, it will need to be represented in a configuration space of, say, 10⁶⁰ dimensions, but vast stretches of it will be virtually devoid of wave function. The mere fact that the Sun is roughly spherical and can be well modelled by the laws of stellar structure sweeps most of the configuration space clean of wave function. The particular abundances of the chemical elements within the Sun have the same effect, drastically limiting the region of the solar configuration space in which the blue mist is concentrated.

One configuration at which the blue mist does shine brightly will be a characteristic distribution of all the particles in the Sun. To an experienced astrophysicist, this distribution tells an immensely rich story stretching back to the first three minutes (in the standard picture) when the primordial hydrogen and helium abundances were established. The whole story of the cosmos that we call our own is written in the distribution of the Sun’s particles: the formation of galaxies and the earliest generations of stars; the supernova explosion that triggered the formation of the Sun and the solar system, and left the radioactivity that still powers so much tectonic and volcanic activity on the Earth; and the Sun’s steady burning of its nuclear fuel.