Introduction
As I mentioned, I thought at first that the no boundary condition did indeed imply that disorder would decrease in the contracting phase. This was based on work on a simple model of the Universe in which the collapsing phase looked like the time reverse of the expanding phase. However, a colleague of mine, Don page, Pointed out that the no boundary condition did not require the contracting phase necessarily to be the time reverse of the expanding phase. Further, one of my students, Raymond Laflamme, found that in a slightly more complicated model, the collapse of the universe was very different from the expansion. I realised that disorder would continue to increase during the contraction. The thermodynamic and psychological arrows of the time would not reverse when the universe begins to re contract or inside black holes.
What should you do when you find you have made a mistake like that? Some people, Like Eddigton, never admit that they are wrong. They continue to find new, often mutually inconsistent, argument to support their case. Others claim to have never really supported the incorrect view in the first place or, if they did, it was only to show that it was only to show that it was inconsistent. I could give a large number of examples of this, but I won't because it would make me too unpopular. It seems to me much better and less confusing 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 he was trying to make a static model of the Universe, was the biggest mistake of his life.
The laws of Physics do not distinguish between the past and the future. More precisely, the law of physics are unchanged under the combination of operations known as C, P, and T. C means changing particles for anti-particles. P means taking the mirror image so left and right are swapped for each other and T means reversing the direction of motion of all particles- in effect, running the motion backward. The laws of physics that govern the behavior of matter under all normal situations are unchanged under the operations C and P on their own. In other word, life would be just the same for the inhabitants of another planet who were our mirror images and who were made of antimatter .
If you meet someone from another planet and he holds out his hands, don't shake it. He might be made of antimatter. You would both disappear in a tremendous flash of light of operations C, P and also by the combinations C,P and T they must also be unchanged under the operation T alone. Yet there is a big difference between forward and backward directions of the time in ordinary life. Imagine a cup of water falling off a table and breaking in pieces on the floor. If you take a film of this, you can easily tell whether it is being run forward or backward. If you run it backward, you will see the pieces suddenly gather themselves together off the floor and jump back to form a whole cup on the table . You can tell that film is being run backward because this kind of behavior is never observed in ordinary life. If it were, the crockery manufactures woul go out the business.
The Arrow Of Time
The explanation that is usually given as to why we don't see broken cups jumping back onto the table is that is forbidden by the second law of thermodynamics. This says that disorder or entropy always increase with the time. In other word's, it is Murphy's law-thing get worse. An intact cup on the table is a state of high disorder, but a broken cup on the floor is a disordered state. One can therefore go from the whole cup on the table in the past to the broken cup on the floor in the future, but not the other way around.
The increase of disorder or entropy with the time is one of the example with the time is one of the example of what is called The Arrow Of The Time, some thing that gives a direction to the time and distinguish the past from the future the future. There are at least three different arrows of time. First there is the arrow of Thermodynamics Arrow Of Time. Second there is the Psychological Arrow Of Time. This is the direction in which we remember the past, but not the future of time in which the universe is expanding, rather than contracting.
I shall argue the psychological arrow is determined by the Thermodynamic arrow and that these two arrows always point in the same direction. If one makes the no boundary assumption for the universe, they are related to the cosmological arrow that there will be intelligent beings who can ask the question: Why does disorder increase in the same direction of time as that in which the universe expands?
Does the Time Arrow Reversed
But what would happen if and when the universe stopped expanding and began to contract again? Would the thermodynamic arrow reverse and disorder begin to decrease with time? This would lead to all sorts of science fiction like possibilities for the people who survived from expanding to the contracting phase. Would they see broken cups gathering themselves together off the floor and jumping back on the table? Would they able to remember tomorrow's prices and make a fortune on the stock market?
It might seem a bit academic to worry about what should happen when the universe collapse again, as it will not start to contract again for at least another ten thousand million years. But there is a quicker way to find out what will happen: Jump into a black hole. The collapse of a star to form a black hole is rather like the later stages of the collapse of the whole universe, one might also except it to decrease inside a black hole. So perhaps an astronaut who fell into a black hole would be able to make money at roulette by remembering where the ball went before he placed his bet. Unfortunately, however, he would have long to play before he was turned to spaghetti by very strong gravitational fields. Nor would be able let us know about the reversal of the thermodynamic arrow, or even bank his wining, because he would be trapped behind the event horizon of the black hole.
At first, I believed that disorder would decrease when the universe re collapsed. This was because I thought that the universe had to return to a smooth and ordered state when it became small again. This would have meant that the contracting phase would live their lives backward. They would die before they were born and would get younger as the universe contracted. This idea is attractive because it would mean a nice symmetry between expanding and contracting phases. However, one cannot adopt it on its own, independent of other ideas about the Universe. The question is: Is it implied by the no boundary condition or is it incontinent with that condition?
If you meet someone from another planet and he holds out his hands, don't shake it. He might be made of antimatter. You would both disappear in a tremendous flash of light of operations C, P and also by the combinations C,P and T they must also be unchanged under the operation T alone. Yet there is a big difference between forward and backward directions of the time in ordinary life. Imagine a cup of water falling off a table and breaking in pieces on the floor. If you take a film of this, you can easily tell whether it is being run forward or backward. If you run it backward, you will see the pieces suddenly gather themselves together off the floor and jump back to form a whole cup on the table . You can tell that film is being run backward because this kind of behavior is never observed in ordinary life. If it were, the crockery manufactures woul go out the business.
The Arrow Of Time
The explanation that is usually given as to why we don't see broken cups jumping back onto the table is that is forbidden by the second law of thermodynamics. This says that disorder or entropy always increase with the time. In other word's, it is Murphy's law-thing get worse. An intact cup on the table is a state of high disorder, but a broken cup on the floor is a disordered state. One can therefore go from the whole cup on the table in the past to the broken cup on the floor in the future, but not the other way around.
The increase of disorder or entropy with the time is one of the example with the time is one of the example of what is called The Arrow Of The Time, some thing that gives a direction to the time and distinguish the past from the future the future. There are at least three different arrows of time. First there is the arrow of Thermodynamics Arrow Of Time. Second there is the Psychological Arrow Of Time. This is the direction in which we remember the past, but not the future of time in which the universe is expanding, rather than contracting.
I shall argue the psychological arrow is determined by the Thermodynamic arrow and that these two arrows always point in the same direction. If one makes the no boundary assumption for the universe, they are related to the cosmological arrow that there will be intelligent beings who can ask the question: Why does disorder increase in the same direction of time as that in which the universe expands?
Does the Time Arrow Reversed
But what would happen if and when the universe stopped expanding and began to contract again? Would the thermodynamic arrow reverse and disorder begin to decrease with time? This would lead to all sorts of science fiction like possibilities for the people who survived from expanding to the contracting phase. Would they see broken cups gathering themselves together off the floor and jumping back on the table? Would they able to remember tomorrow's prices and make a fortune on the stock market?
It might seem a bit academic to worry about what should happen when the universe collapse again, as it will not start to contract again for at least another ten thousand million years. But there is a quicker way to find out what will happen: Jump into a black hole. The collapse of a star to form a black hole is rather like the later stages of the collapse of the whole universe, one might also except it to decrease inside a black hole. So perhaps an astronaut who fell into a black hole would be able to make money at roulette by remembering where the ball went before he placed his bet. Unfortunately, however, he would have long to play before he was turned to spaghetti by very strong gravitational fields. Nor would be able let us know about the reversal of the thermodynamic arrow, or even bank his wining, because he would be trapped behind the event horizon of the black hole.
At first, I believed that disorder would decrease when the universe re collapsed. This was because I thought that the universe had to return to a smooth and ordered state when it became small again. This would have meant that the contracting phase would live their lives backward. They would die before they were born and would get younger as the universe contracted. This idea is attractive because it would mean a nice symmetry between expanding and contracting phases. However, one cannot adopt it on its own, independent of other ideas about the Universe. The question is: Is it implied by the no boundary condition or is it incontinent with that condition?
As I mentioned, I thought at first that the no boundary condition did indeed imply that disorder would decrease in the contracting phase. This was based on work on a simple model of the Universe in which the collapsing phase looked like the time reverse of the expanding phase. However, a colleague of mine, Don page, Pointed out that the no boundary condition did not require the contracting phase necessarily to be the time reverse of the expanding phase. Further, one of my students, Raymond Laflamme, found that in a slightly more complicated model, the collapse of the universe was very different from the expansion. I realised that disorder would continue to increase during the contraction. The thermodynamic and psychological arrows of the time would not reverse when the universe begins to re contract or inside black holes.
What should you do when you find you have made a mistake like that? Some people, Like Eddigton, never admit that they are wrong. They continue to find new, often mutually inconsistent, argument to support their case. Others claim to have never really supported the incorrect view in the first place or, if they did, it was only to show that it was only to show that it was inconsistent. I could give a large number of examples of this, but I won't because it would make me too unpopular. It seems to me much better and less confusing 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 he was trying to make a static model of the Universe, was the biggest mistake of his life.
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