Page 39 - Nature Of Space And Time

If information is lost in macroscopic black holes it should also be lost in processes
in which microscopic, virtual black holes appear because of quantum
uctuations of the
metric. One could imagine that particles and information could fall into these holes and
get lost. Maybe that is where all those odd socks went. Quantities like energy and electric
charge, that are coupled to gauge elds, would be conserved but other information and

global charge would be lost. This would have far reaching implications for quantum theory.
It is normally assumed that a system in a pure quantum state evolves in a unitary way
through a succession of pure quantum states. But if there is loss of information through the
appearance and disappearance of black holes there can't be a unitary evolution. Instead

the loss of information will mean that the nal state after the black holes have disappeared
will be what is called a mixed quantum state. This can be regarded as an ensemble of
di erent pure quantum states each with its own probability. But because it is not with
certainty in any one state one can not reduce the probability of the nal state to zero

by interfering with any quantum state. This means that gravity introduces a new level
of unpredictability into physics over and above the uncertainty usually associated with
quantum theory. I shall show in the next lecture we may have already observed this extra
uncertainty. It means an end to the hope of scienti c determinism that we could predict

the future with certainty. It seems God still has a few tricks up his sleeve.

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