Lecture 18: Resolution to the naive Information Paradox
The naive information paradox is easy to resolve. We can show that expectation values of an operator in a typical pure state are exponentially close to expectation values in a mixed state. So, unless we can measure correlators to an accuracy of e^{-S/2}, we cannot differentiate between a pure final state and a mixed final state. This means that Hawking's computation is not precise enough to lead to a paradox.
Furthermore, the relevant coupling constant when we take the back-reaction of Hawking radiation into account is 1/S. So, unless we account for non-perturbative effects we cannot refine Hawking's original computation to produce a paradox.
We will need cleverer arguments to refine the information paradox.
