Losing Information Outside the Horizon

Abstract

Suppose we allow a system to fall freely from infinity to a point near (but not beyond) the horizon of a black hole. We note that in a sense the information in the system is already lost to an observer at infinity. Once the system is too close to the horizon it does not have enough energy to send its information back because the information carrying quanta would get redshifted to a point where they get confused with Hawking radiation. If one attempts to turn the infalling system around and bring it back to infinity for observation then it will experience Unruh radiation from the required acceleration. This radiation can excite the bits in the system carrying the information, thus reducing the fidelity of this information. We find the radius where the information is essentially lost in this way, noting that this radius depends on the energy gap (and coupling) of the system. We look for some universality by using the highly degenerate BPS ground states of a quantum gravity theory (string theory) as our information storage device. For such systems one finds that the critical distance to the horizon set by Unruh radiation is the geometric mean of the black hole radius and the radius of the extremal hole with quantum numbers of the BPS bound state. Overall, the results suggest that information in gravity theories should be regarded not as a quantity contained in a system, but in terms of how much of this information is accessible to another observer.

Arrow of Time, Entropy, and Protein Folding: Holistic View on Biochirality

“…The first and second laws of thermodynamics, complemented by Noether’s Theorem, operating with the concepts of space, time and entropy, allow a unifying, non-contradicting interpretation of a wide variety of phenomena, ranging from Black Hole irradiation [ 15 , 16 ] to photon chirality [ 17 , 18 ], protein synthesis [ 19 ], and even to the evolution of brain function [ 20 ]. For more information regarding space-time integrity and the link between the entropy and time direction, see [ 21 , 22 , 23 , 24 ]. Following the idea of Schrödinger, pointing to the non-trivial behavior of entropy in the living system [ 25 ], the interdisciplinary discussion of the non-equilibrium (NE) thermodynamics of biological systems revealed the inherent link between the concept of entropy, chirality, and spontaneous racemization, linked to the evolution of life, and biological aging ( Figure 1 d) [ 26 , 27 , 28 ].…”