From the Bookshelf of 2025 Reading Challenge…

Given an event P, one can divide the other events in the universe into three classes. Those events that can be reached from the event P by a particle or wave traveling at or below the speed of light are said to be in the future of P. They will lie within or on the expanding sphere of light emitted from the event P. Thus they will lie within or on the future light cone of P in the space-tim

Given an event P, one can divide the other events in the universe into three classes. Those events that can be reached from the event P by a particle or wave traveling at or below the speed of light are said to be in the future of P. They will lie within or on the expanding sphere of light emitted from the event P. Thus they will lie within or on the future light cone of P in the space-time diagram. Only events in the future of P can be affected by what happens at P because nothing can travel faster than light.

Similarly, the past of P can be defined as the set of all events from which it is possible to reach the event P traveling at or below the speed of light. It is thus the set of events that can affect what happens at P. The events that do not lie in the future or past of P are said to lie in the elsewhere of P.

Science seems to have uncovered a set of laws that, within the limits set by the uncertainty principle, tell us how the universe will develop with time, if we know its state at any one time. These laws may have originally been decreed by God, but it appears that he has since left the universe to evolve according to them and does not now intervene in it. But how did he choose the initial state or configuration of the universe? What were the “boundary conditions” at the beginning of time? One possible answer is to say that God chose the initial configuration of the universe for reasons that we cannot hope to understand.

The increase of disorder or entropy with time is one example of what is called an arrow of time, something that distinguishes the past from the future, giving a direction to time. There are at least three different arrows of time. First, there is the thermodynamic arrow of time, the direction of time in which disorder or entropy increases. Then, there is the psychological arrow of time. This is the direction in which we feel time passes, the direction in which we remember the past but not the future. Finally, there is the cosmological arrow of time. This is the direction of time in which the universe is expanding rather than contracting.

...Suppose, however, that God decided that the universe should finish up in a state of high order but that it didn’t matter what state it started in. At early times the universe would probably be in a disordered state. This would mean that disorder would decrease with time. You would see broken cups gathering themselves together and jumping back onto the table. However, any human beings who were observing the cups would be living in a universe in which disorder decreased with time. I shall argue that such beings would have a psychological arrow of time that was backward. That is, they would remember events in the future, and not remember events in their past. When the cup was broken, they would remember it being on the table, but when it was on the table, they would not remember it being on the floor.

It is rather difficult to talk about human memory because we don’t know how the brain works in detail. We do, however, know all about how computer memories work. I shall therefore discuss the psychological arrow of time for computers. I think it is reasonable to assume that the arrow for computers is the same as that for humans. If it were not, one could make a killing on the stock exchange by having a computer that would remember tomorrow’s prices!

...Before an item is recorded in a computer’s memory, the memory is in a disordered state, with equal probabilities for the two possible states. (The abacus beads are scattered randomly on the wires of the abacus.) After the memory interacts with the system to be remembered, it will definitely be in one state or the other, according to the state of the system. (Each abacus bead will be at either the left or the right of the abacus wire.) So the memory has passed from a disordered state to an ordered one. However, in order to make sure that the memory is in the right state, it is necessary to use a certain amount of energy (to move the bead or to power the computer, for example). This energy is dissipated as heat, and increases the amount of disorder in the universe. One can show that this increase in disorder is always greater than the increase in the order of the memory itself. Thus the heat expelled by the computer’s cooling fan means that when a computer records an item in memory, the total amount of disorder in the universe still goes up. The direction of time in which a computer remembers the past is the same as that in which disorder increases.

Our subjective sense of the direction of time, the psychological arrow of time, is therefore determined within our brain by the thermodynamic arrow of time.

...But why should the thermodynamic arrow of time exist at all? Or, in other words, why should the universe be in a state of high order at one end of time, the end that we call the past? Why is it not in a state of complete disorder at all times? After all, this might seem more probable. And why is the direction of time in which disorder increases the same as that in which the universe expands?

...The universe would have started off with a period of exponential or “inflationary” expansion in which it would have increased its size by a very large factor. During this expansion, the density fluctuations would have remained small at first, but later would have started to grow. Regions in which the density was slightly higher than average would have had their expansion slowed down by the gravitational attraction of the extra mass. Eventually, such regions would stop expanding and collapse to form galaxies, stars, and beings like us. The universe would have started in a smooth and ordered state, and would become lumpy and disordered as time went on. This would explain the existence of the thermodynamic arrow of time.

...However, a strong thermodynamic arrow is necessary for intelligent life to operate. In order to survive, human beings have to consume food, which is an ordered form of energy, and convert it into heat, which is a disordered form of energy. Thus intelligent life could not exist in the contracting phase of the universe. This is the explanation of why we observe that the thermodynamic and cosmological arrows of time point in the same direction. It is not that the expansion of the universe causes disorder to increase. Rather, it is that the no boundary condition causes disorder to increase and the conditions to be suitable for intelligent life only in the expanding phase.