Does God Play Dice? (3 page)

With black holes, however, the situation is rather different. One will end up with the same state outside the hole, whatever one threw in, provided it has the same mass. Thus there is not a one to one correspondence between the initial state, and the final state outside the black hole. There will be a one to one correspondence between the initial state, and the final state both outside, and inside, the black hole. But the important point is that the emission of particles, and radiation by the black hole, will cause the hole to lose mass, and get smaller. Eventually, it seems the black hole will get down to zero mass, and will disappear altogether. What then will happen to all the objects that fell into the hole, and all the people that either jumped in, or were pushed? They can't come out again, because there isn't enough mass or energy left in the black hole, to send them out again. They may pass into another universe, but that is not something that will make any difference, to those of us prudent enough not to jump into a black hole. Even the information, about what fell into the hole, could not come out again when the hole finally disappears. Information can not be carried free, as those of you with phone bills will know. Information requires energy to carry it, and there won't be enough energy left when the black hole disappears.

What all this means is, that information will be lost from our region of the universe, when black holes are formed, and then evaporate. This loss of information will mean that we can predict even less than we thought, on the basis of quantum theory. In quantum theory, one may not be able to predict with certainty, both the position, and the speed of a particle. But there is still one combination of position and speed that can be predicted. In the case of a black hole, this definite prediction involves both members of a particle pair. But we can measure only the particle that comes out. There's no way even in principle that we can measure the particle that falls into the hole. So, for all we can tell, it could be in any state. This means we can not make any definite prediction, about the particle that escapes from the hole. We can calculate the probability that the particle has this or that position, or speed. But there's no combination of the position and speed of just one particle that we can definitely predict, because the speed and position will depend on the other particle, which we don't observe. Thus it seems Einstein was doubly wrong when he said, God does not play dice. Not only does God definitely play dice, but He sometimes confuses us by throwing them where they can't be seen.

Many scientists are like Einstein, in that they have a deep emotional attachment to determinism. Unlike Einstein, they have accepted the reduction in our ability to predict, that quantum theory brought about. But that was far enough. They didn't like the further reduction, which black holes seemed to imply. They have therefore claimed that information is not really lost down black holes. But they have not managed to find any mechanism that would return the information. It is just a pious hope that the universe is deterministic, in the way that Laplace thought. I feel these scientists have not learnt the lesson of history. The universe does not behave according to our pre-conceived ideas. It continues to surprise us.

One might not think it mattered very much, if determinism broke down near black holes. We are almost certainly at least a few light years, from a black hole of any size. But, the Uncertainty Principle implies that every region of space should be full of tiny virtual black holes, which appear and disappear again. One would think that particles and information could fall into these black holes, and be lost. Because these virtual black holes are so small, a hundred billion billion times smaller than the nucleus of an atom, the rate at which information would be lost would be very low. That is why the laws of science appear deterministic, to a very good approximation. But in extreme conditions, like in the early universe, or in high energy particle collisions, there could be significant loss of information. This would lead to unpredictability, in the evolution of the universe.

To sum up, what I have been talking about, is whether the universe evolves in an arbitrary way, or whether it is deterministic. The classical view, put forward by Laplace, was that the future motion of particles was completely determined, if one knew their positions and speeds at one time. This view had to be modified, when Heisenberg put forward his Uncertainty Principle, which said that one could not know both the position, and the speed, accurately. However, it was still possible to predict one combination of position and speed. But even this limited predictability disappeared, when the effects of black holes were taken into account. The loss of particles and information down black holes meant that the particles that came out were random. One could calculate probabilities, but one could not make any definite predictions. Thus, the future of the universe is not completely determined by the laws of science, and its present state, as Laplace thought. God still has a few tricks up his sleeve.

That is all I have to say for the moment. Thank you for listening.

Stephen W. Hawking