On the implications of the Bekenstein bound for black hole evaporation

Abstract

We provide general arguments regarding the connection between low-energy theories (gravity and quantum field theory) and a hypothetical fundamental theory of quantum gravity, under the assumptions of (i) validity of the holographic bound and (ii) preservation of unitary evolution at the level of the fundamental theory. In particular, the appeal to the holographic bound imposed on generic physical systems by the Bekenstein-Hawking entropy implies that both classical geometry and quantum fields propagating on it should be regarded as phenomena emergent from the dynamics of the fundamental theory. The reshuffling of the fundamental degrees of freedom during the unitary evolution then leads to an entanglement between geometry and quantum fields. The consequences of such scenario are considered in the context of black hole evaporation and the related information-loss issue: we provide a simplistic toy model in which an average loss of information is obtained as a consequence of the geometry-field entanglement.Comment: 10 pages, 2 figure

Two arguments for more fundamental building blocks

“…microscopic configurations of the Xons giving raise to the same emergent geometry, but to different/non-equivalent field configurations. Let us now summarize a possible way to formalize the above, for more details see [1]. If H indicates the fundamental Hilbert space of the Xons, what discussed above means that there is some mapping, P G : H → H G , which assigns to a microscopic state in H the corresponding "classical geometry".…”

“…The actual analytic computations of the entanglement entropy are a heavy tall, so in [1] we proceed with easier (but not trivial...) numerical computations. The case we want to report here is for the following choice of N G = 30, N T = 2, and R i F = 1, for each topology.…”

“…In Section 2 we explain why the Bekenstein bound could mean that Xons exist, we present the quasiparticle picture stemming from this, and we show that it could be the key to the solution of the information-loss puzzle. In Section 3 we discuss how the above scenario could be realized in analogs, then we face the issue of analogs in general, and we close that Section by reflecting on Feynman's conclusions on why analogs do work, leading him to evoke Xons, as the ultimate elementary constituents of matter 1 . That striking argument is simply based on the observation of what we daily have around.…”

“…Here we elaborate on the work of [1], where it is proposed that, at our energies, the fields and spacetimes they live in are entangled. This entanglement is there because both, matter and space, emerge from the dynamics of the same more fundamental objects, whose existence can be inferred from the celebrated upper bound on the entropy of any system, conjectured by Bekenstein [2,3].…”

“…The most noticeable result of [1] is that the evaporation of a black hole (BH) can only lead to an information loss, in the sense that, in general, there is a nonzero entanglement entropy associated to the final products of the evaporation. In what follows, we recollect that result, next to suggestions on how to realize the model on certain analog systems.…”