size the curvature outside the horizons will be everywhere small compared to the Planck
scale. This means the approximation I have made of ignoring cubic and higher terms in
the perturbations should be good. Thus the conclusion that information can be lost in
black holes should be reliable.
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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 fluctuations 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 fields, 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 final state after the black holes have disappeared will be what is called a mixed quantum state. This can be regarded as an ensemble of
different 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 final 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 scientific determinism that we could predict
the future with certainty. It seems God still has a few tricks up his sleeve.
A
A A
A
A A
AA
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3. Quantum Cosmology
S. W. Hawking
In my third lecture I shall turn to cosmology. Cosmology used to be considered a
pseudo-science and the preserve of physicists who may have done useful work in their
earlier years but who had gone mystic in their dotage. There were two reasons for this.
The first was that there was an almost total absence of reliable observations. Indeed,
until the 1920s about the only important cosmological observation was that the sky at
night is dark. But people didn’t appreciate the significance of this. However, in recent
years the range and quality of cosmological observations has improved enormously with
developments in technology. So this objection against regarding cosmology as a science,
that it doesn’t have an observational basis is no longer valid.
There is, however, a second and more serious objection. Cosmology can not predict
anything about the universe unless it makes some assumption about the initial conditions.
Without such an assumption, all one can say is that things are as they are now because
they were as they were at an earlier stage. Yet many people believe that science should be
concerned only with the local laws which govern how the universe evolves in time. They
would feel that the boundary conditions for the universe that determine how the universe
began were a question for metaphysics or religion rather than science.
The situation was made worse by the theorems that Roger and I proved. These
showed that according to general relativity there should be a singularity in our past. At
this singularity the field equations could not be defined. Thus classical general relativity
brings about its own downfall: it predicts that it can’t predict the universe.
Although many people welcomed this conclusion, it has always profoundly disturbed
me. If the laws of physics could break down at the begining of the universe, why couldn’t
they break down any where. In quantum theory it is a principle that anything can happen if
it is not absolutely forbidden. Once one allows that singular histories could take part in the path integral they could occur any where and predictability would disappear completely.
If the laws of physics break down at singularities, they could break down any where.
The only way to have a scientific theory is if the laws of physics hold everywhere