"Time Arrow" - Excerpted from "A Brief History of Time"

We have seen in the previous chapters how people's views on the nature of time have changed for a long time. Until the beginning of this century, people believed in absolute time. That is, each event can be marked in a unique way by a number called "time", and all good clocks are consistent in measuring the time interval between the two events. However, the discovery that the speed of light is always the same for any moving observer, leading to relativity; in relativity, one must abandon the idea of ​​a unique absolute time. Instead, each observer carries his own time measurement—the clock carried by different observers does not need to read. In this way, time becomes a more subjective concept for the observer making the measurement.

When people try to unify gravity and quantum mechanics, the concept of "virtual" time must be introduced. Virtual time cannot be distinguished from the direction of space. If a person can go north, he can turn his head and walk south; similarly, if a person can go forward in virtual time, he should be able to go backward and walk backward. This shows that there is no important difference between forward and backward in virtual time. On the other hand, when people examine "real" time, as we all know, there is a huge difference in the direction of forward and backward. Where does this difference between the past and the future come from? Why do we remember the past instead of the future?

The laws of science do not distinguish between the past and the future. To be more precise, as explained above, the laws of science remain unchanged under the combined action (or symmetry) of c, p and t. (c means replacing antiparticles with particles; p means taking a mirror image, so that the left and right exchange each other; t means reversing the direction of movement of all particles, that is, reversing the motion.) Under all normal circumstances, the laws of science that restrict the behavior of objects remain unchanged under the joint symmetry of CP. In other words, for the residents of other planets, if they are our mirror image and are composed of antimatter rather than matter, life will be exactly the same.

If the laws of science remain unchanged in the CP joint symmetry and the CP joint symmetry, they must also remain unchanged in the separate t symmetry. However, in real time of daily life, there is still a big difference between the direction of forward and backward. Imagine a glass of water sliding from the table to the floor and being broken. If you record it, you can easily tell whether it is moving forward or backward. If you pour it back, you will see the fragments suddenly gather together and jump back to the table to form a complete cup. You can conclude that the video is being played backwards, because this behavior has never been seen in daily life. If such a thing happens, the ceramic industry will have no business to do.

Why we never see broken cups gathering, leaving the ground and jumping back to the table, the usual explanation is that this violates the second law of thermodynamics as stated in any closed system of disorder or entropy always increases over time. In other words, it is a form of Mufi's law: things always tend to get worse: a complete cup on the table is a highly ordered state, while a broken cup on the floor is a disordered state. It is easy for one to go from a cup on the earlier table to a broken cup on the ground later than the other way around.

Disorder degree or entropy increases with time is an example of the so-called time arrow. The time arrow distinguishes the past and the future, giving time a direction. There are at least three different time arrows: the first is the thermodynamic time arrow, that is, the disorder degree or entropy increase in this time direction; then the psychological time arrow, which is the direction in which we feel the passage of time, in which we can remember the past rather than the future; finally, the cosmological time arrow, in which the universe is expanding, not contracting.

I will argue in this chapter that the boundless conditions of the universe and the principle of weak anthropology can explain why all three arrows point in the same direction. Moreover, why there must be a well-defined time arrow. I will argue that the psychological arrow is determined by thermodynamic arrows, and that both arrows must always point in the same direction. If one assumes the boundless conditions of the universe, we will see that there must be well-defined thermodynamic and cosmological time arrows. But for the entire history of the universe, they do not always point in the same direction. However, I will point out that only when they point to the same direction, are appropriate conditions for the development of intellectual life that can ask why disorder increases in the time direction of the universe's expansion.

First, I want to discuss the thermodynamic time arrow. The fact that there are always many more disordered states than ordered states is the reason why the second law of thermodynamics exists. For example, considering a box of toys, there is one and only one that makes these small pieces of paper into an arrangement of a complete picture. On the other hand, there is a huge number of arrangements, and at this time the small pieces of paper are disordered and cannot be organized into a painting.

Suppose a system starts from one of these few ordered states. As time goes by, the system will evolve according to the laws of science, and its state will change. Later, because there are more disordered states, the possibility of it being in disordered state is greater than that in an ordered state. In this way, if a system obeys a highly ordered initial condition, the degree of disorder will increase with time.

Assume that the sheets of paper in the toy box start with an orderly combination that can be arranged into a picture, if you shake the box, the sheets will adopt other combinations, which may be a disorder that cannot form a suitable picture because there are so many disorderly combinations. Some pieces of paper may still form part of the picture, but the more you shake the box, the more likely these pieces will be separated, and the pieces will be in a completely chaotic state in which they cannot form any kind of picture. In this way, if the sheets start from the initial conditions of a highly ordered state, the disorder of the sheets will likely increase over time.

However, assuming that God decides that no matter where the universe starts, it must end in a highly ordered state, then in the early days the universe may be in a disordered state. This means that the disorder will decrease over time. You will see broken cups gathered together and jump back to the table. However, anyone who observes the cup lives in a universe where the disorder decreases over time, I will argue that such people will have a reverse psychological time arrow. That is to say, they will remember future events, not past events. When the cup is broken, they will remember its situation on the table; but when it is on the table, they will not remember its situation on the ground.

Since we don't know the details of the brain's work, it's quite difficult to discuss human memory. However, we do know how computer memory works. So, I'll discuss computer psychology time arrows. I think it's reasonable to assume that computers and humans have the same arrows. If that's not the case, people might have caused the stock exchange to collapse because they have a computer that remembers the price next year.

Generally speaking, a computer memory is a device that contains components that can exist in either of two states. The abacus is a simple example. Its simplest form is composed of many iron bars; each iron bar has a rosary, and the rosary can stay in one of two positions. Before the computer memory is stored, its memory is in disorder, and the rosary, etc. is likely to be in two possible states. (Abacus beads are scattered on the iron bars of the abacus). After the memory interacts with the system to be memorized, it is definitely in one or another state according to the state of the system (each abacus bead will be located in the iron bars).

Left or right.) In this way, the memory changes from disorder to order. However, in order to ensure that the memory is in the correct state, a certain amount of energy is needed (for example, moving abacus beads or turning on the computer power). This energy is dissipated in the form of heat, thereby increasing the amount of disorder in the universe. One can prove that this disorder increment is always greater than the increment of order in the memory itself. In this way, the heat discharged by the computer cooling fan indicates that when the computer records an item in its memory, the total amount of disorder in the universe still increases. The computer memory's past time direction and the direction of increase in disorder are consistent.

Therefore, our subjective sense of the direction of time or psychological time arrows are determined in our minds by the thermodynamic time arrows. Just like a computer, we must remember things in the order of increasing entropy. This almost turns the laws of thermodynamics into boring things. The increase in disorder over time is because we measure time in the direction of increasing disorder. Take this bet, and you will win.

But exactly why do thermodynamic time arrows have to exist? Or in other words, at one end of what we call past time, why is the universe in a highly ordered state? Why is it not in a completely disordered state at all times? After all, this seems more likely. And why is the time direction of the increase in disorder and the direction of the expansion of the universe?

In classic general theory of relativity, because all known scientific laws fail at the Big Bang singularity, one cannot predict how the universe begins. The universe can start with a very smooth and ordered state. This leads to, as we have observed, time arrows that define well-defined thermodynamics and cosmology. However, it can equally reasonably start with a very undulating disordered state. In that case, the universe is already in a completely disordered state, so the degree of disorder does not increase over time. Or

It remains constant, and at this time there is no good thermodynamic time arrow defined; or it will decrease, and the thermodynamic time arrow will be opposite to the cosmological time arrow. Any of these possibilities do not match what we have observed. However, as we have seen, classical general relativity predicts its own collapse. When the curvature of space-time becomes larger, quantum gravity becomes important, and classical theory can no longer describe the universe well, people must use quantum gravity to understand how the universe began.

As we saw in the previous chapter, in quantum gravity theory, in order to specify the state of the universe, one must still explain how the possible history of the universe at the boundary of space-time in the past was behaving. Only if these histories meet the boundless conditions can one avoid this difficulty that we have to describe what we do not know and cannot know: they are limited in scale, but have no boundaries, edges or singularities. In this case, the beginning of time will be regular, smooth space-time points, and the universe begins its expansion in a very smooth and orderly state. It cannot be completely uniform, otherwise it violates the uncertainty principle of quantum theory. There must be small fluctuations in density and particle velocity, but boundless conditions mean that these fluctuations are as small as possible under conditions consistent with the principle of uncertainty.

At the beginning of the universe there was an exponential or "surge" period, during which its scale increased by a very large multiple. During expansion, the density fluctuations were small at first, but then they began to grow larger. In areas with a slightly larger density than the average, the gravity attraction of the extra mass slowed down the expansion. Eventually, such regions stopped expanding and collapsed to form galaxies, stars, and humans like us. The universe began in a smooth and orderly state, which evolved into a undulating and unordered state over time. This explained the existence of thermodynamic time arrows.

What happens if the universe stops expanding and begins to contract? Will the thermodynamic arrows turn backwards and disorder begin to decrease over time? This leaves a variety of science fiction possibilities for people who survive from expansion to contraction phase. Will they see pieces of cups gather together and jump back to the table? Will they remember tomorrow's price and get rich in the stock market? Since the universe will have to wait at least another 10 billion years before it begins to shrink, worrying about what will happen then seems a bit pedantic. But there is a faster way to find out what will happen in the future

So, jump into the black hole. The process of star collapse forming a black hole is quite similar to the later stage of the collapse of the entire universe; in this way, if the disorder of the contraction phase of the universe decreases, it can be expected that it will also decrease in the black hole. Therefore, an astronaut who falls into the black hole can probably win money by remembering the direction of the ball on the round-the-rock plate before making a bet. (However, unfortunately, he will become spaghetti after playing for a long time. He cannot make us know the inversion of thermodynamic arrows, or even deposit his winning money in the bank because he is trapped behind the event horizon of the black hole.)

At first, I believe that disorder will decrease when the universe collapses. This is because, I think that the universe becomes smaller again, it must return to a smooth and orderly state. This shows that the contracted phase is merely a time inversion of the expansion phase. People in the contracted phase will live in a backward way: they are dead before birth and become younger as the universe contracts.

This concept is attractive because it shows that there is a beautiful symmetry between the expansion phase and the contracting phase. However, one cannot ignore other ideas about the universe and adopt only this concept. The question is: is it implicit by the boundless condition or is it inconsistent with this condition? As I said, I initially thought that the boundless condition does mean that disorder will decrease in the contracting phase. I am misled in part because of an analogy with the surface of the earth. If one corresponds to the beginning of the universe to the North Pole, the end of the universe should be similar to its beginning, just as the South Pole is similar to the North Pole. However, the North and South Poles correspond to the beginning and end of the universe in virtual time.

There can be a very large difference between the beginning and end of real time. I was also misled by a simple study of the universe model I had in which the collapsed phase appears to be a time inversion of the expansion phase. However, one of my colleagues, D. Page of Penn State University, pointed out that the boundless condition does not require that the contracted phase must be a time inversion of the expansion phase. One of my students, Raymond Laflemon, further found that in a slightly complex model, the collapse and expansion of the universe are very different. I realized that I made a mistake: the boundless condition means that the disorder continues to increase in the actual degree of disorder as the shrinking phase is converged. When the universe begins to contract or in black holes, the thermodynamic and psychological time arrows do not reverse.

What should you do when you find yourself making such a mistake? Some people never admit that they are wrong, but continue to find new arguments that are often inconsistent with each other - just as Eddington did when he opposed black hole theory. Others first declared that they never really supported an incorrect view, and if they did, they just wanted to show that it was inconsistent. In my opinion, if you admit that you were wrong in publications, it would be much better and less confusing. Einstein was a good example, introducing cosmic constants in his attempt to build a static model of the universe, which he called the biggest mistake in his life.

Let’s talk about the time arrows, the remaining question is; why do we observe that thermodynamics and cosmological arrows point in the same direction? Or in other words, why is the time direction of the increase in disorder the time direction of the universe expanding? If one believes that as the boundless hypothesis seems to imply that the universe expands first and then contracts again, then why should we be in the expansion phase rather than in the contracting phase, this becomes a problem.

People can answer this question based on the principle of weak anthropology. The conditions of the contraction phase are not suitable for the existence of intelligent humans, but they are able to raise the question of why the time direction of disorder increases and the time direction of the universe expanding. The boundaryless assumption that the prophetic universe's surge in early stages means that the universe must expand at a critical rate that is very close to avoid collapse so that it will not collapse for a long time. By then all stars will burn out, and the protons and neutrons in it may decay into light particles and radiation. The universe will be in an almost completely disordered state, and there will be no strong thermodynamic time arrows.

Since the universe is already in an almost complete disorder, the degree of disorder will not increase much. However, for the behavior of intelligent life, a strong thermodynamic arrow is necessary. In order to survive, humans must consume an ordered form of energy - food and convert it into a disordered form of energy - calories, so intelligent life cannot exist in the contracting phase of the universe. This explains why we observe that the time arrows of thermodynamics and cosmology are consistent. It is not that the expansion of the universe leads to an increase in disorder, but that the boundless conditions cause the increase in disorder, and only in the expansion phase are there suitable conditions for intelligent life.

In short, scientific laws cannot distinguish the direction of time for advancement and retreat. However, there are at least three time arrows that distinguish the past and the future. They are thermodynamic arrows, which are the time direction of the increase in disorder; psychological arrows, that is, in this time direction, we can remember the past rather than the future; cosmological arrows, that is, the direction of the expansion rather than the contraction of the universe. I pointed out that psychological arrows should essentially be the same as thermodynamic arrows. The boundless assumption of the universe predicts well-defined thermodynamic time arrows, because the universe must start from a smooth, ordered state. And we see that the consistency between thermodynamic arrows and cosmological arrows is because intelligent life can only exist in the expansion phase. The contracting phase is not suitable for its existence, because there are no strong thermodynamic time arrows there.
Chapter completed!