The matter-gravity entanglement hypothesis

Bernard Kay (University of York)

We recall our 1998 "matter gravity entanglement hypothesis" according to which the entropy of a closed system (such as a model black hole in a box or a model for the universe) should be identified, not with the system's total von Neumann entropy but rather with its matter-gravity entanglement entropy. Here we assume that (low-energy effective) quantum gravity can be formulated in terms of the traditional Hilbert space approach to quantum mechanics with a total Hilbert space a tensor product of a matter and a gravity Hilbert space and a total density operator, ρ = |Ψ><Ψ|, evolving under a unitary time-evolution.
We recall how this hypothesis offers a resolution to a number of puzzles including puzzles related to quantum black holes. In particular, it offers an objective definition for the entropy of a closed system whose increase is not in conflict with a unitary time-evolution and thereby offers an underpinning to the second law of thermodynamics; it also offers a resolution to the black hole information loss puzzle -- information loss being understood as entropy increase in a special case of the second law.
We also outline some more recent work where: (A) We argue that our hypothesis enables a correction and clarification of the string-theory work on black hole entropy. (B) we argue for a picture of a black hole equilibrium state in a (spherical) box that differs radically from the traditional Hawking-picture (according to which it is a total thermal state). In our picture, the total state is pure. Also, insofar as it can be described by a classical spacetime, that spacetime is just the exterior Schwarzschild spacetime -- the classical describability necessarily breaking down just outside the horizon.
Reference
B.S. Kay. Entropy and quantum gravity. Entropy 17, 8174-8186(2015) [arXiv: 1504.00882]