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

We've seen in previous chapters how people's views on the nature of time have changed over time. Until the beginning of the 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 two events. However, the discovery that the speed of light is always the same for any observer in motion led to the theory of relativity; In the theory of relativity, one must abandon the notion that there is a single absolute time. Instead, each observer's clock records his own time measurement – the clock carried by different observers does not necessarily have the same reading. In this way, time becomes a more subjective concept for the observer making the measurement.

When one tries to unify gravity and quantum mechanics, the concept of "imaginary" time must be introduced. Imaginary time is indistinguishable from spatial direction. If a person can go north, he can turn his head and go south; In the same way, if a person can move forward in imaginary time, he should be able to turn around and go backwards. This suggests that there can be no significant difference between forward and backward in imaginary time. On the other hand, when one examines "real" time, as is well known, there is a very large difference between forward and backward directions. Where does this difference between the past and the future come from? Why do we remember the past and not the future?

The laws of science do not distinguish between the past and the future. More precisely, as previously explained, the laws of science are immutable under a combined action (or symmetry) called C, P, and T. (C refers to the substitution of antiparticles for particles; P means to take a mirror, so that left and right are exchanged with each other; T refers to reversing the direction of motion of all particles, i.e., making the motion backwards. Under all normal circumstances, the scientific laws governing the behavior of objects remain unchanged under CP joint symmetry. In other words, for the inhabitants of other planets, if they were our mirror images and made of antimatter instead of matter, life would be exactly the same.

If the scientific laws are invariant under both CP joint symmetry and CPT joint symmetry, they must also be invariant under T-symmetry alone. However, there is a big difference between the forward and backward directions in the real time of everyday life. Imagine a glass of water slipping off a table onto the floor and being shattered. If you record it, you can easily tell if it's going forward or backward. If you pour it back, you'll see the pieces suddenly come together and leave the floor and jump back onto the table to form a complete cup. You can assume that the video is playing backwards, because this kind of behavior has never been seen in everyday life. If this happens, there will be no business in the ceramics industry.

The usual explanation for why we never see broken cups assemble, leave the floor and jump back onto the table is that this violates the second law of thermodynamics, which states that in any closed system, disorder or entropy always increases with time. In other words, it's a form of Murphy's Law: things tend to get worse and worse: a full cup on the table is in a state of high order, while a broken cup on the floor is a state of disorder. It is easy for one to go from a cup on the table earlier to a broken cup on the ground later, not the other way around.

The degree of disorder or entropy increasing with time is an example of what is known as a time arrow. The arrow of time distinguishes the past from the future, giving time a direction. There are at least three different time arrows: the first, the thermodynamic time arrow, which is the disorder or entropy increase in this time direction; Then there is the psychological time arrow, which is the direction in which we feel the passage of time, in which we can remember the past and not the future; Finally, there is the cosmological arrow of time, in which the universe expands, not contracts.

In this chapter, I will argue that the borderless condition of the universe and the principle of anthropicism together explain why all three arrows point in the same direction. Also, why there must be a well-defined arrow of time. I will argue that psychological arrows are determined by thermodynamic arrows, and that both arrows must always point in the same direction. If one assumes the borderless condition 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 have not always pointed in the same direction. I will not, however, that the conditions are suitable for the development of intellectual life that can ask why disorder increases in the temporal direction of the expansion of the universe only if they point to the same thing.

First, I'm going to talk about the thermodynamic time arrow. The fact that there is always a much more disordered state than an ordered state is what makes the second law of thermodynamics exist. For example, consider a box of puzzle toys where there is one and only one arrangement that makes the pieces of paper fit together into a complete picture. On the other hand, there is a huge number of arrangements, at which point the small pieces of paper are disordered and cannot be put together into a painting.

Suppose a system starts from one of these few ordered states. Over time, this system will evolve according to the laws of science, and its state will change. Later, because there is more disorder, it is more likely to be in disorder than in order. Thus, if a system obeys a highly ordered initial condition, the degree of disorder increases over time.

Assuming that the pieces of paper in a puzzle toy box start with an orderly combination that can be arranged into a picture, and if you shake the box, the pieces of paper will take on other combinations, which may be a disordered combination that does not make a proper picture, because there are so many more disordered combinations. Some pieces of paper may still form partial drawings, but the more you shake the box, the more likely they are to be separated, and the pieces of paper will be in a state of complete chaos, in which they will not be able to form any kind of drawing. In this way, if the piece of paper proceeds from the initial condition of a highly ordered state, the disorder of the piece of paper may increase over time.

However, if God decided that whatever state the universe begins in must end in a state of high order, it is possible that the universe would have been in a state of disorder in the early days. This means that the disorder will decrease over time. You will see the broken cups come together and jump back onto the table. However, anyone who observes a cup lives in a universe where disorder decreases with time, and I will conclude that such a person would have a backward psychological time arrow. That is, they will remember future events, not past ones. When a cup is broken, they remember what it was like on the table; But when it's on the table, they don't remember what it was like on the ground.

Since we don't know the details of how the brain works, it is quite difficult to discuss human memory. However, we do know how a computer's memory works. So, I'm going to talk about the psychology of computers time arrows. I think it's reasonable to assume that computers and humans have the same arrows. If not, one could bring down a stock exchange by having a computer that remembers next year's prices.

Basically, a computer's memory is a device that contains elements that can exist in either of two states, and the abacus is a simple example. Its simplest form is made up of many iron bars; Each bar has a rosary on it, and this rosary can stay in one of the two positions. Before the computer memory is stored, its memory is in a disordered state, and the rosary is likely to be in two possible states. (Abacus beads are scattered in a haphazard manner on the iron bars of the abacus). After the interaction between the memory and the system to be remembered, it must be in one state or another depending on the state of the system (each abacus bead will be located to the left or right of the iron bar. In this way, the memory is transformed from an unordered state to an ordered state. However, in order to keep the memory in the correct state, a certain amount of energy is required (e.g., moving an abacus bead or powering a computer). This energy is dissipated in the form of heat, thus increasing the amount of disorder in the universe. One can prove that this disorder increment is always larger than the increment of the order of the memory itself. In this way, the heat expelled by the computer's cooling fan indicates that the total amount of disorder in the universe still increases when the computer records an item in its memory. The direction of the computer's memory of past time is consistent with the direction of increasing disorder.

So, our subjective perception of the direction of time, or the psychological arrow of time, is determined in our mind by the thermodynamic arrow of time. Just like a computer, we have to memorize things in the order in which entropy increases. This almost makes the laws of thermodynamics boring. The increase in disorder over time is due to the fact that we measure time in the direction in which the disorder increases. Take that to bet that you will win.

But why exactly does a thermodynamic time arrow exist? Or in other words, why is the universe in a state of high order at one end of what we call past time? Why isn't it in a state of complete disorder all the time? After all, this seems more likely. And why is the temporal direction of disorder increasing in the same direction as the expansion of the universe?

In classical general relativity, one cannot predict how the universe began because all known scientific laws fail at the Big Bang singularity. The universe can start from a very smooth and orderly state. This leads to a well-defined thermodynamic and cosmological arrow of time, as we have observed. However, it can just as reasonably start with a very undulating state of disorder. In that case, the universe is already in a state of complete disorder, so the degree of disorder does not increase over time. Or it remains constant, in which case there is no well-defined thermodynamic time arrow; Or it decreases, in which case the thermodynamic time arrow will be in the opposite direction to the cosmological time arrow. Any of these possibilities do not correspond to what we have observed. However, as we have seen, classical general relativity predicts its own collapse. When the space-time curvature becomes larger, the quantum gravitational effect becomes important, and classical theories no longer describe the universe well, one must use quantum gravitational theory 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 still has to say how the possible history of the universe behaved in the past space-time boundary. It is only if these histories satisfy the borderless condition that one can avoid the difficulty of having to describe what we do not know and cannot know: they are finite in scale, but have no boundaries, edges, or singularities. In this case, the beginning of time would be a regular, smooth space-time point, and the universe would begin its expansion in a very smooth and orderly state. It cannot be completely homogeneous, otherwise it violates the uncertainty principle of quantum theory. There must be small fluctuations in density and particle velocity, but the absence of boundary conditions means that these fluctuations are as small as possible under conditions consistent with the uncertainty principle.

The universe began with an exponential or "skyrocketing" period, during which its scale increased by a very large multiple. During expansion, the density fluctuation is always small at first, but later it starts to increase. In regions where the density is slightly greater than average, the gravitational attraction of the extra mass slows down the expansion. Eventually, such regions stop expanding and collapse into galaxies, stars, and humans like us. The universe began in a smooth and orderly state, and evolved over time into a state of undulating disorder. This explains the presence of thermodynamic time arrows.

What would happen if the universe stopped expanding and began to contract? Could the thermodynamic arrows be reversed and the disorder begin to decrease over time? This leaves a wide variety of possibilities for science fiction for people who survive from the expansion phase to the contraction phase. Will they see the pieces of the cup come together and leave the floor and jump back onto the table? Will they remember tomorrow's prices and make a fortune on the stock market? Since the universe will have to wait at least another 10 billion years before it begins to shrink, it seems pedantic to worry about what will happen then. But there's a much faster way to find out what's going to happen in the future, and that's to jump into a black hole. The process of star collapse to form a black hole is quite similar to the later phase of the collapse of the universe as a whole; Thus, if the shrinking phase disorder of the universe decreases, it can be expected that it will also decrease in the black hole. Therefore, an astronaut who falls into a black hole may be able to win money by remembering the direction of the ball on the roulette board before making a bet. (Unfortunately, however, it doesn't take long to play before he turns into spaghetti.) Nor can he make us aware of the inversion of the thermodynamic arrow, or even deposit his winnings in the bank, because he is trapped behind the event horizon of the black hole. ）

At first, I believed that disorder would decrease when the universe collapsed. This is because, I think, the universe becomes smaller, it must return to a smooth and orderly state. This suggests that the shrinkage phase is only a time inversion of the expansion phase. People in the contraction phase will live in a regressive way: they die before they are born, and become younger as the universe shrinks.

This notion is appealing because it shows that there is a beautiful symmetry between the expanding and shrinking phases. However, one cannot ignore other ideas about the universe and adopt only this one. The question is: is it implied by a borderless condition or is it incompatible with this condition? As I said, I thought at first that the borderless condition did mean that the disorder would decrease in the shrinking phase. I was misled in part because of the analogy with the Earth's surface. If one corresponds to the beginning of the universe to the North Pole, then the end of the universe should resemble 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 imaginary time. There can be a very big difference between the beginning and the end in real time. I was also misled by my study of a simple model of the universe in which the collapse phase appears to be a time reversal of the expansion phase. However, one of my colleagues, Dang Page of Pennsylvania State University, points out that the no-boundary condition does not require that the shrinkage phase must be the time inversion of the expansion phase. One of my students, Raymond Lovelemon, further discovered that in a slightly more complex model, the collapse and expansion of the universe are very different. I realized that I had made a mistake: the absence of boundary conditions meant that in fact the disorder continued to increase when the phase was contracted. When the universe begins to contract or in a black hole, thermodynamic and psychological time arrows do not reverse.

What do you do when you realize you've made such a mistake? Some people never admit that they are wrong, and continue to find new, often incongruous arguments, to justify themselves – as Eddington did when he opposed the black hole theory. Others are the first to claim that they have never really supported an incorrect view, and if they do, it is only to show that it is incongruous. It seems to me that it would be much better and less confusing if you admitted that you were wrong in the publication. Albert Einstein is a good example of a man who introduced the cosmological constant in his attempt to build a static model of the universe, which he called the biggest mistake of his life.

Going back to the time arrow, the rest of the question is; Why do we observe that thermodynamic and cosmological arrows point in the same direction? Or in other words, why is the temporal direction of disorder increasing the same as the temporal direction of the expansion of the universe? If one believes that the universe expands first and then recontracts, as the no-boundary hypothesis seems to imply, then the question arises as to why we should be in the expansion phase and not in the contraction phase.

One can answer this question on the basis of the principle of anthropic. The conditions of the contraction phase are not suitable for the existence of intelligent humans, and it is they who are able to ask the question of why the temporal direction of disorder increase is the same as the temporal direction of the expansion of the universe. The early explosion of the universe predicted by the borderless hypothesis means that the universe must expand at a critical rate very close to what is needed to avoid collapse, so that it does not collapse for a long time. By that time all the stars will burn out, and the protons and neutrons in them may decay into light particles and radiation. The universe will be in a state of almost complete disorder, and there will be no strong thermodynamic arrow of time. Since the universe is already in a state of almost complete disorder, the degree of disorder will not increase much. However, a strong thermodynamic arrow is necessary for the behavior of intelligent life. In order to survive, human beings must consume food, an ordered form of energy, and convert it into a disordered form of energy, heat, so intelligent life cannot exist in the shrinking phase of the universe. This explains why we observe that the time arrows of thermodynamics and cosmology point to the same point. It is not the expansion of the universe that causes an increase in disorder, but the absence of boundary conditions that causes an increase in disorder, and only in the expanding phase are conditions suitable for intelligent life.

In conclusion, the laws of science do not distinguish between forward and backward directions of time. However, there are at least three time arrows that distinguish the past from the future. They are thermodynamic arrows, which is the temporal direction of the increase in disorder; Psychological arrows, that is, in this direction of time, we can remember the past and not the future; There are also cosmological arrows, that is, the direction in which the universe expands rather than contracts. I pointed out that the psychological arrows should be essentially the same as the thermodynamic arrows. The borderless assumption of the universe predicts a well-defined arrow of thermodynamic time, because the universe must begin in a smooth, ordered state. And we see that the thermodynamic arrows are consistent with the cosmological arrows because intelligent life can only exist in the expanding phase. The shrinkage phase is not suitable for its presence because there is no strong thermodynamic time arrow.

The progress of mankind's understanding of the universe is the establishment of a small and orderly corner of the universe in a universe of increasing disorder. If you memorize every word in the book, your memory records about 2 million units of information – and the order in your mind adds about 2 million units. However, as you read this book, you will be converting at least 1,000 calories of ordered energy in the form of food into disordered energy in the form of heat released into the air around you by convection and sweat. This increases the disorder of the universe by about 2 billion trillion units, or about 1 billion trillion times the increment of order in your head—that's if you remember everything in this book. I'm going to try to add a little more order to our minds in the next chapter, explaining how people can combine some of the theories I've described to form a complete unified theory that will apply to anything in the universe.