Slide 20 of 24
The problem can be described heuristically as follows. Suppose I take my computer and throw it into a black hole (a tempting prospect at times). Once the computer passes the event horizon, the information stored on the hard disc is irrevocably lost to the outside world,
according the Einstein's gravity theory. This is a nuisance, but not a fundamental problem, since if I get desperate enough I can recover the information by jumping into the black hole after the computer. So the information is still accessible, in principle.
But now Hawking tells us that this black hole evaporates due to microscopic processes that occur just outside the event horizon. If Einstein is right, this means that the radiation emitted by the black hole can't carry any information about what fell into the
black hole previously, since for information to escape from the black hole it would have to travel faster than the speed of light. Moreover, we believe that energy must be conserved (can't be created or destroyed), so as the black hole evaporates, its mass must decrease (the energy in the radiation must come from somewhere).
The second picture shows the black hole in the middle
of its evaporation process. It is smaller because its mass has decreased, and the Universe (represented by the box) contains radiation emitted by the hole. However, all the information that was on the hard disc is still hidden behind the event horizon of the black hole.
The final picture takes this process to its logical conclusion. The Universe is filled with radiation emitted by the black hole. For reasons given above, this radiation still carries no information about what fell into the black hole. Now however, the black hole has completely evaporated, so there is no event horizon for the information to hide behind. The information seems to have irrevocably vanished from the Universe for ever.
In physics, such information loss is unacceptable: it means among other things, that the future cannot be predicted by knowing the past. There is no apparent correlation between the final state of the Universe (in the last picture), and its initial state (i.e. the hard
disc and all its information) in the first picture. This is a big problem for a discipline whose main task is to predict the outcome of experiments.
Let me emphasize that this is fundamentally different from just throwing the computer into a fire, for example. In this case, the information on the hard disk is lost only in practice, but not in principle. The light and heat given off by the fire is caused by
chemical reactions that do keep track of everything that fell into the fire, so in principle it is possible to recover the information by looking at the light emitted by the fire. In the black hole case, the light originates from just outside the horizon so it cannot contain the required information, even in principle.