Abstract
Consistency between quantum mechanical and general relativistic views of the world is a longstanding problem, which becomes particularly prominent in black hole physics. We develop a coherent picture addressing this issue by studying the quantum mechanics of an evolving black hole. After interpreting the Bekenstein-Hawking entropy as the entropy representing the degrees of freedom that are coarse-grained to obtain a semiclassical description from the microscopic theory of quantum gravity, we discuss the properties these degrees of freedom exhibit when viewed from the semiclassical standpoint. We are led to the conclusion that they show features which we call extreme relativeness and spacetime-matter duality---a nontrivial reference frame dependence of their spacetime distribution and the dual roles they play as the "constituents" of spacetime and as thermal radiation. We describe black hole formation and evaporation processes in distant and infalling reference frames, showing that these two properties allow us to avoid the arguments for firewalls and to make the existence of the black hole interior consistent with unitary evolution in the sense of complementarity. Our analysis provides a concrete answer to how information can be preserved at the quantum level throughout the evolution of a black hole, and gives a basic picture of how general coordinate transformations may work at the level of full quantum gravity beyond the approximation of semiclassical theory.
Highlights
In the early 90’s, a remarkable suggestion to avoid this difficulty — called complementarity — was made [5]: the apparent cloning of the information occurring in black hole physics implies that the internal spacetime and horizon/Hawking radiation degrees of freedom appearing in different, i.e. infalling and distant, descriptions are not independent
Our analysis provides a concrete answer to how information can be preserved at the quantum level throughout the evolution of a black hole, and gives a basic picture of how general coordinate transformations may work at the level of full quantum gravity beyond the approximation of semiclassical theory
This picture is consonant with the fact that in quantum mechanics, having a well-defined geometry of spacetime, e.g. a black hole in a well-defined spacetime location, requires taking a superposition of an enormous number of energy-momentum eigenstates, so we expect that there are many different ways to arrive at the same background for the semiclassical theory within the precision allowed by quantum mechanics
Summary
As described in the introduction, semiclassical theory applied to an entire global spacetime leads to overcounting of the true degrees of freedom at the quantum level. For a single description allowing a semiclassical interpretation of the system, the spacetime region represented is restricted to the causal patch associated with a single worldline With this restriction, the description can be local in the sense that any physical correlations between low energy field theoretic degrees of freedom respect causality in spacetime (beyond some microscopic quantum gravitational distance l∗, meaning that possible nonlocal corrections are exponentially suppressed ∼ e−r/l∗). (Excited string degrees of freedom will require the corresponding operators.) In general, the procedure of electing coordinates (t, x), which we need to define states and operators, must be given independently of the background spacetime, since we do not know it a priori (and states may even represent superpositions of very different semiclassical geometries); an example of such procedures is described in ref. We do not expect difficulty in extending it to more general cases
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