Illustrated Theory of Everything: The Origin and Fate of the Universe by Stephen Hawking Page A

quantum theory of gravity, one considers all possible histories of theuniverse. Associated with each history, there are a couple of numbers. Onerepresents the size of a wave and the other the face of the wave, that is,whether the wave is at a crest or a trough. The probability of the universehaving a particular property is given by adding up the waves for all the histo-ries with that property. The histories would be curved spaces that wouldrepresent the evolution of the universe in time. One would still have to sayhow the possible histories of the universe would behave at the boundary ofspace-time in the past. We do not and cannot know the boundary conditionsof the universe in the past. However, one could avoid this difficulty if theboundary condition of the universe is that it has no boundary. In other words,all the possible histories are finite in extent but have no boundaries, edges, orsingularities. They are like the surface of the Earth, but with two more dimen-sions. In that case, the beginning of time would be a regular smooth point ofspace-time. This means that the universe would have begun its expansion ina very smooth and ordered state. It could not have been completely uniformbecause that would violate the uncertainty principle of quantum theory. Therehad to be small fluctuations in the density and velocities of particles. The noboundary condition, however, would imply that these fluctuations were assmall as they could be, consistent with the uncertainty principle.
The universe would have started off with a period of exponential or “inflation-ary” expansion. In this, it would have increased its size by a very large factor.During this expansion, the density fluctuations would have remained small atfirst, but later would have started to grow. Regions in which the density wasslightly higher than average would have had their expansion slowed down bythe gravitational attraction of the extra mass. Eventually, such regions wouldstop expanding, and would collapse to form galaxies, stars, and beings like us.The universe would have started in a smooth and ordered state and wouldbecome lumpy and disordered as time went on. This would explain the exis-tence of the thermodynamic arrow of time. The universe would start in a stateof high order and would become more disordered with time. As I showed ear-lier, the psychological arrow of time points in the same direction as the ther-modynamic arrow. Our subjective sense of time would therefore be that inwhich the universe is expanding, rather than the opposite direction, in whichit would be contracting.
DOES THE ARROW OF TIME REVERSE?
But what would happen if and when the universe stopped expanding andbegan to contract again? Would the thermodynamic arrow reverse anddisorder begin to decrease with time? This would lead to all sorts ofscience-fiction-like possibilities for people who survived from the expandingto the contracting phase. Would they see broken cups gathering themselvestogether off the floor and jumping back on the table? Would they be able toremember tomorrow’s prices and make a fortune on the stock market?It might seem a bit academic to worry about what would happen when the uni-verse collapses again, as it will not start to contract for at least another tenthousand million years. But there is a quicker way to find out what will hap-pen: Jump into a black hole. The collapse of a star to form a black hole is ratherlike the later stages of the collapse of the whole universe. Thus, if disorder wereto decrease in the contracting phase of the universe, one might also expect itto decrease inside a black hole. So perhaps an astronaut who fell into a blackhole would be able to make money at roulette by remembering where the ballwent before he placed his bet. Unfortunately, however, he would not have longto play before he was turned to spaghetti by the very strong gravitational fields.Nor would he be able to let us know about the reversal of the thermodynamicarrow, or even