“The Direction Of Time” – By Stephen Hawking
In his book, The Go-Between, L. P. Hartley wrote, “The past is a foreign country. They do things differently there—but why is the past so different from the future? Why do we remember the past, but not the future?”
In other words, why does time move forward? Is it connected to the fact that the universe is expanding?
The laws of physics do not differentiate between the past and the future. More precisely, the laws of physics are unchanged under a combination of operations known as C, P, and T. (C means changing particles to antiparticles. P means taking the mirror image so that left and right are swapped for each other. And T means reversing the direction of motion of all particles – in fact, reversing motion drive towards.)
The laws of physics that govern the behavior of matter under all normal conditions remain unchanged under the operation of C and P. In other words, life would be the same for the inhabitants of another planet that were mirror images of us and which were made of antimatter.
If you meet someone from another planet and he holds his left hand, don’t shake it. It may be made of antimatter. The two of you will disappear in an overwhelming blaze of light.
If the laws of physics are unchanged by the combination of operations C and P, as well as by the combination of C, P, and T, then they must also be unchanged under operation T alone. Yet in normal life, there is a great difference between the forward and backward directions of time.
Imagine a cup of water falling from the table and breaking into pieces on the floor. If you film it, you can easily tell whether it is being driven forward or backward. If you play it backward, you’ll see the pieces suddenly gather together off the floor and jump back to form a full cup on the table.
You can tell that the film is being pushed back because this kind of behavior is never seen in ordinary life. If that were the case, crockery manufacturers would be out of business.
The Arrow of Time
The explanation that is commonly given as to why we do not see broken cups jumping back on the table is prohibited by the second law of thermodynamics. It says that disorder or entropy always increases with time.
In other words, it’s Murphy’s Law – things get worse. An intact cup is in a higher-order position on the table, but a broken cup on the floor is in a disordered state. So the whole cup on the table in the past can lead to a broken cup on the floor in the future, but not vice versa.
An example of this is the increase of disorder or entropy over time called the arrow of time, something that gives direction to time and separates the past from the future. 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. Second, there is the psychological arrow of time. This is the direction in which we feel that time is passing – the direction of time in which we remember the past, but not the future.
Third, there is the cosmological arrow of time. This is the direction of time in which the universe is expanding instead of shrinking. I would argue that the psychological arrow is determined by the thermodynamic arrow and that these two arrows always point in the same direction.
If one assumes no boundaries for the universe, then they are related by the cosmological arrow of time, although they may not point in the same direction.
However, I would argue that when they agree with the cosmological arrow there will be intelligent beings who may ask the question: why does disorder increase in the same direction of time in which the universe expands?
The Thermodynamic Arrow
I’ll talk about the thermodynamic arrow of time first. The second law of thermodynamics is based on the fact that there are many more disordered states than ordered states.
For example, consider the pieces of a jigsaw in a box. There is one and only one arrangement in which the pieces make up the complete picture.
On the other hand, there are a very large number of arrangements in which the pieces are disorganized and do not take a picture.
Suppose a system starts in one of a small number of ordered states. With the passage of time, the system will evolve according to the laws of physics and its state will change. At a later time, there is a high probability that it will be in a more disordered state, simply because there are a lot more disordered states.
Thus, if the system obeys a higher-order initial state, the disorder will increase with time.
Suppose the pieces of the jigsaw begin in the orderly arrangement in which they form a picture. If you shake the box, the pieces will make another arrangement.
It would probably be a chaotic arrangement in which the pieces do not form a proper picture, simply because there are too many chaotic arrangements. Some groups of pieces may still be part of the picture, but the more you move the box, the more likely these groups are to break.
The pieces will be in a completely disordered state in that they do not form any kind of picture. Thus, the disorder of the pieces will probably increase over time if they follow the initial position they start in a higher-order position.
Suppose, however, that God decreed that the universe must end late in a state of higher order, no matter in which state it began. Clutter will reduce over time
You must have broken the cups by gathering yourself together and jumping back on the table. However, any human looking at the cups must be living in a universe in which disorder has diminished over time.
I would argue that such beings would have had a psychological arrow of time that went backward. That is, they remember from there late and do not remember from there early.
The Psychological Arrow
It is difficult to talk about human memory because we do not know in detail how the brain works. However, we all know how computer memories work. That’s why I’ll discuss the psychological arrow of time for computers.
I think it’s fair to assume that arrows to computers are what it is to humans. If it didn’t, having a computer that remembers yesterday’s prices could be killing the stock exchange.
Computer memory is basically some device that can be in either of two states. An example would be a superconducting loop of wire. If current flows through the loop, it will continue to flow because there is no resistance.
On the other hand, if there is no current, the loop will continue to run without current. One can label the two states of memory “one” and “zero”. Before an item is entered in to memory, the memory is in a disordered state with equal probabilities for one and zero. After interacting with the system to be remembered by the memory, it will definitely be in some state according to the state of the system.
Thus, memory goes from a disordered state to an ordered state. However, a certain amount of energy must be used to ensure that the memory is in the correct state. This energy is dissipated as heat and increases the amount of disorder in the universe.
One can show that this progression of the disorder is more than an increase in the order of memory. Thus, when a computer records an object into memory, the total amount of clutter in the universe increases.
The direction in which the computer remembers the past is in the same direction in which the disorder progresses. This means that the direction of time, our subjective sense of the psychological arrow of time, is determined by the thermodynamic arrow of time.
This makes the second law of thermodynamics almost trivial. Disorder increases with time because we measure time in the direction in which disorder increases. You can’t have a safer bet than this.
The Boundary Condition of the Universe
But why must the universe be in a state of higher order at one end of time, the end we call the past? Why wasn’t it in a state of complete disarray all the time? After all, it may seem more probable. And why is time in the same direction as the direction in which the chaos grows?
One possible answer is that God simply chose that the universe should be in a smooth and orderly state at the beginning of the expansion phase.
We should not try to understand why or question the reasons for it because the beginning of the universe was the work of God. But the entire history of the universe can be said to be an act of God. The universe appears to evolve according to well-defined laws.
These rules may or may not be set by God, but we seem to be able to discover and understand them. Therefore, is it unreasonable to expect that the beginning of the universe may have had the same or even similar laws?
In the classical theory of general relativity, the beginning of the universe must be a singularity of infinite density in the space-time curvature. Under such circumstances, all known laws of physics would be broken. Thus, one cannot use them to predict how the universe will begin.
The universe could have started in a very smooth and orderly state. As we see, this would have led to the well-defined thermodynamic and cosmological arrows of time. But it equally well could have started in a very lumpy and disorganized state.
In this case, the universe would already be in a state of complete disorder, so the disorder could not increase over time. It would either remain constant, in which case there would be no well-defined thermodynamic arrow of time, or it would decrease, in which case the thermodynamic arrow of time would point in the opposite direction to the cosmic arrow.
None of these would likely agree with what we’ve seen. As I mentioned, the classical theory of general relativity predicts that the universe must begin with a singularity where the curvature of space-time is infinite. In effect, this means that classical general relativity predicts its own collapse.
When the curvature of space-time becomes large, the quantum gravitational effect will become significant and the classical theory will no longer be a good description of the universe. The quantum theory of gravity has to be used to understand how the universe began. In the quantum theory of gravity, all possible histories of the universe are considered.
Associated with each history, there are some numbers. One represents the shape of the wave and the other represents the face of the wave, i.e. the wave is at a peak or trough. The probability that the universe has a particular property is given by adding up the waves for all history with that property.
History will be curved spaces that represent the evolution of the universe in time. One still has to say how the possible histories of the universe would have behaved at the space-time boundary in the past. We do not and cannot know the boundary conditions of the universe in the past.
However, this difficulty can be avoided if the boundary condition of the universe is that it has no boundaries. In other words, all possible histories are limited in range but have no limit, edge, or singularity. They are like the surface of the Earth, but with two more dimensions.
In that case, the beginning of time would be a regular smooth point of space-time. This means that the universe must have started its expansion in a very smooth and orderly state. It could not be completely uniform because it would violate the uncertainty principle of quantum theory.
There should have been small fluctuations in the density and velocity of the particles. However, the condition of no limit would imply that these fluctuations were as small as could be consistent with the uncertainty principle. The universe may have started with a period of exponential or “inflationary” expansion.
In this, it would have increased its size by a very large factor. The density fluctuations during this expansion may have been small at first but would have started increasing later. In regions where the density was slightly above average, their expansion would have been slowed by the gravitational attraction of the extra mass.
Eventually, such regions would stop expanding and collapse to form galaxies, stars, and creatures like us. The universe would have started in a smooth and orderly state and would become lumpy and disordered as time went on.
This would explain the existence of the thermodynamic arrow of time. The universe would begin in a higher-order state and become more disordered over time. As I showed earlier, the psychological arrow of time points in the same direction as the thermodynamic arrow.
So our subjective sense of time would be the one in which the universe is expanding, not the opposite direction in which it would be shrinking.
Does The Arrow of Time Reverse
But what if and when the universe stops expanding and begins to contract again? Will the thermodynamic arrow reverse and the disorder start to decrease over time?
This would lead to all kinds of science-fiction-like possibilities for those who survived the expansion contract stage. Will they watch the broken cups gather together from the floor and jump back to the table? Will they be able to remember yesterday’s prices and make a fortune in the stock market?
It may seem a bit academic to worry about what will happen when the universe collapses again, as it will not begin to contract until at least ten thousand million years. But there’s a faster way to find out what will happen: jump into the black hole. The breakup of a star to form a black hole is like the later stages of the collapse of the entire universe.
Thus, if disorder were to decrease in the contraction phase of the universe, one might also expect it to decrease inside a black hole. So perhaps an astronaut who fell into a black hole would be able to make money in roulette by remembering where the ball had gone before he placed his bet.
Unfortunately, though, it didn’t take long for them to come into play before they were turned into spaghetti by very strong gravitational fields. Nor would he be able to tell us about the reversal of the thermodynamic arrow, or even bank his victory, as he would be trapped behind the black hole’s event horizon.
At first, I believed that the disorder would subside when the universe collapsed again. This was because I thought the universe would have to return to a smooth and orderly state when it got smaller again.
This would mean that the contract phase was like timing as opposed to the expansion phase. In the contract phase, people will lead a backward life. They will die before they are born and they will get smaller as the universe shrinks. The idea is attractive because it would mean a good symmetry between the expansion and contract phases.
However, independent of other ideas about the universe, one cannot adopt it on its own. The question is, is it implied by the limitless condition or is it inconsistent with that condition?
As I mentioned, I previously thought that no boundary condition would actually imply that the disorder would decrease in the contraction phase. It was based on work on a simple model of the universe in which the collapsing phase resembled time as opposed to the expansion phase.
However, a colleague of mine, Don Page, pointed out that the no-limit condition does not require a contract phase, necessarily timing the opposite of an extension phase. Furthermore, one of my students, Raymond Laflamme, found that in a slightly more complex model, the collapse of the universe was very different from the expansion.
I realized that I made a mistake. In fact, the no boundary condition means that the disorder will continue to increase during contraction.
The thermodynamic and psychological arrows of time will not reverse when the universe begins to shrink again or is inside a black hole. What should you do when you feel that you have made such a mistake?
Some people, like Eddington, never admit they are wrong. They keep finding new, and often mutually incompatible, arguments to support their case. Others claim that they never supported the wrong view in the first place or, if they did, it was simply to show that it was inconsistent.
I can give many examples of this, but I will not because it would make me very unpopular. It sounds a lot better and less confusing to me if you admit in print that you were wrong.
A good example of this was Einstein, who said that the cosmological constant, which he introduced when trying to build a stable model of the universe, was the biggest mistake of his life.
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