Lecture 8

In lecture 8, we considered the "old information paradox". This is the paradox, that appears to arise because Hawking radiation is thermal, and so this suggests that if we start with a pure state, that collapses to form a black hole, the process of Hawking radiation will convert it into a mixed state. Such evolution, from a pure to a mixed state would, of course, violate unitarity.

But this is not really a paradox, because in large statistical systems, generic pure states look almost exactly like thermal states. So, by determining low-point correlators (which is what Hawking's calculation does), one cannot determine whether the state is pure or thermal. So, Hawking's calculation is not precise enough to lead to a paradox.