The matter-gravity entanglement hypothesis.

I outline some of my work (some dating back to 1998, some more recent) on my matter-gravity entanglement hypothesis, according to which the entropy of a closed quantum gravitational system is equal to the system's matter-gravity entanglement entropy. The main arguments presented are: (1) this hypothesis is capable of resolving the second-law puzzle, i.e. the puzzle as to how the entropy increase of a closed system can be reconciled with the asssumption of unitary time-evolution; (2) the black hole information loss puzzle may be regarded as a special case of this second law puzzle and therefore the same resolution applies to it; (3) the black hole thermal atmosphere puzzle (which I recall) can be resolved by adopting a radically different-from-usual description of quantum black hole equilibrium states, according to which they are total pure states, entangled between matter and gravity so that the partial states of matter and gravity are each approximately thermal equilibrium states (at the Hawking temperature); (4) the Susskind-Horowitz-Polchinski string-theoretic understanding of black hole entropy as the logarithm of the degeneracy of a long string (which is the weak string coupling limit of a black hole) cannot be correct but should be replaced by a modified understanding according to which it is the entanglement entropy between a long string and its stringy atmosphere, when in a total pure equilibrium state in a suitable box, which (in line with (3)) goes over, at strong-coupling, to a black hole in equilibrium with its thermal atmosphere. The modified understanding in (4) is based on a general result, which I describe, about the likely state of a quantum system weakly coupled to an energy-bath when the total state is a random pure state with given energy. This result generalizes Goldstein et al.'s 'canonical typicality' result to systems which are not necessarily small.