To summarize, the laws of science do not distinguish between the forward and backward directions of time. However, there are at least three arrows of time that do distinguish the past from the future. They are the thermodynamic arrow, the direction of time in which disorder increases; the psychological arrow, the direction of time in which we remember the past and not the future; and the cosmological arrow, the direction of time in which the universe expands rather than contracts. I have shown that the psychological arrow is essentially the same as the thermodynamic arrow, so that the two would always point in the same direction. The no boundary proposal for the universe predicts the existence of a well-defined thermodynamic arrow of time because the universe must start off in a smooth and ordered state. And the reason we observe this thermodynamic arrow to agree with the cosmological arrow is that intelligent beings can exist only in the expanding phase. The contracting phase will be unsuitable because it has no strong thermodynamic arrow of time.
The progress of the human race in understanding the universe has established a small corner of order in an increasingly disordered universe. If you remember every word in this book, your memory will have recorded about two million pieces of information: the order in your brain will have increased by about two million units. However, while you have been reading the book, you will have converted at least a thousand calories of ordered energy, in the form of food, into disordered energy, in the form of heat that you lose to the air around you by convection and sweat. This will increase the disorder of the universe by about twenty million million million million units – or about ten million million million times the increase in order in your brain – and that’s if you remember everything in this book. In the next chapter but one I will try to increase the order in our neck of the woods a little further by explaining how people are trying to fit together the partial theories I have described to form a complete unified theory that would cover everything in the universe.
CHAPTER 10
WORMHOLES AND TIME TRAVEL
The last chapter discussed why we see time go forward: why disorder increases and why we remember the past but not the future. Time was treated as if it were a straight railway line on which one could only go one way or the other.
But what if the railway line had loops and branches so that a train could keep going forward but come back to a station it had already passed? In other words, might it be possible for someone to travel into the future or the past?
H. G. Wells in The Time Machine explored these possibilities as have countless other writers of science fiction. Yet many of the ideas of science fiction, like submarines and travel to the moon, have become matters of science fact. So what are the prospects for time travel?
The first indication that the laws of physics might really allow people to travel in time came in 1949 when Kurt Godel discovered a new space-time allowed by general relativity. Godel was a mathematician who was famous for proving that it is impossible to prove all true statements, even if you limit yourself to trying to prove all the true statements in a subject as apparently cut and dried as arithmetic. Like the uncertainty principle, Godel’s incompleteness theorem may be a fundamental limitation on our ability to understand and predict the universe, but so far at least it hasn’t seemed to be an obstacle in our search for a complete unified theory.
Godel got to know about general relativity when he and Einstein spent their later years at the Institute for Advanced Study in Princeton. His space-time had the curious property that the whole universe was rotating. One might ask: “Rotating with respect to what?” The answer is that distant matter would be rotating with respect to directions that little tops or gyroscopes point in.
This had the side effect that it would be possible for someone to go off in a rocket ship and return to earth before he set out. This property really upset Einstein, who had thought that general relativity wouldn’t allow time travel. However, given Einstein’s record of ill-founded opposition to gravitational collapse and the uncertainty principle, maybe this was an encouraging sign. The solution Godel found doesn’t correspond to the universe we live in because we can show that the universe is not rotating. It also had a non-zero value of the cosmological constant that Einstein introduced when he thought the universe was unchanging. After Hubble discovered the expansion of the universe, there was no need for a cosmological constant and it is now generally believed to be zero. However, other more reasonable space-times that are allowed by general relativity and which permit travel into the past have since been found. One is in the interior of a rotating black hole. Another is a space-time that contains two cosmic strings moving past each other at high speed. As their name suggests, cosmic strings are objects that are like string in that they have length but a tiny cross section. Actually, they are more like rubber bands because they are under enormous tension, something like a million million million million tons. A cosmic string attached to the earth could accelerate it from 0 to 60 mph in 1/30th of a second. Cosmic strings may sound like pure science fiction but there are reasons to believe they could have formed in the early universe as a result of symmetry-breaking of the kind discussed in Chapter 5. Because they would be under enormous tension and could start in any configuration, they might accelerate to very high speeds when they straighten out.