The black hole information paradox arises from an apparent conflict between the Hawk-ing black hole radiation and the fact that time evolution in quantum mechanics is unitary. The trouble is that while the former suggests that information of a system falling into a black hole disappears, the latter implies that information must be con-served. In this work we discuss the current divergence in views regarding the paradox, we evaluate the role that objective collapse theories could play in its resolution and we propose a link between spontaneous collapse events and microscopic virtual black holes. 1
The black hole information paradox arises from an apparent conflict between the Hawk-ing black hole radiation and the fact that time evolution in quantum mechanics is unitary. The trouble is that while the former suggests that information of a system falling into a black hole disappears, the latter implies that information must be con-served. In this work we discuss the current divergence in views regarding the paradox, we evaluate the role that objective collapse theories could play in its resolution and we propose a link between spontaneous collapse events and microscopic virtual black holes. 1
Abstract The black hole information paradox (Hawking, 19741976) poses a fundamental conict: quantum mechanics requires unitary evolution (information is preserved), while black hole evaporation via Hawking radiation appears to destroy information (the radiation is thermal, carrying no information about the in-fallen state). After fty years of debate, the paradox remains unresolvedHawking conceded it in 2004 [3] but no complete mechanism has been identied. ˆ We resolve the paradox by identifying its source: confusing Ω with Πext[Ω]. Information is never destroyed. Ω-conservation (Noether, P2) guarantees this. What is destroyed at the event horizon is not the information but the exterior ˆ observer's projection operator : Πext becomes inapplicable inside the horizon. The ˆ ˆ information encoded in the in-fallen matter passes from Πext[Ω] to Πint[Ω]two projections of the same Ω = 1 that agree in total but disagree in local accessibility. Hawking radiation is the κ→0 leakage of Ω-entanglement across the projection boundary. The Page curve [4]entanglement entropy rising and then falling as the black hole evaporatesfollows directly from Ω-conservation without invoking island formulas [8, 9] or specic stringy mechanisms. The paradox is not a paradox. It is a projection error.
Can quantum-information theory shed light on black-hole evaporation? By entangling the in-fallen matter with an external system we show that the black-hole information paradox becomes more severe, even for cosmologically sized black holes. We rule out the possibility that the information about the in-fallen matter might hide in correlations between the Hawking radiation and the internal states of the black hole. As a consequence, either unitarity or Hawking's semiclassical predictions must break down. Any resolution of the black-hole information crisis must elucidate one of these possibilities.
The black hole information paradox remains one of modern physics’ most persistent conceptual fractures. Hawking’s original formulation suggested that black hole evaporation yields thermal radiation, apparently severing the relation between the initial state and the final emitted state. Quantum theory, however, requires unitary evolution and therefore forbids true information destruction. This paper proposes that the paradox may be more fruitfully interpreted not as a flat binary contradiction between preservation and loss, but as an unresolved boundary-state problem. To clarify that claim, the paper introduces the 101 Phase State as a symbolic formalism for intermediate informational resolution. In this model, +1 denotes preserved or recoverable informational order, -1 denotes apparent loss or thermal unreadability, and 0 denotes the boundary interface at which observational contradiction becomes structurally legible but not yet fully resolved.
We consider the black hole information problem within the context of collapse theories in a scheme that allows the incorporation of the backreaction to the Hawking radiation. We explore the issue in a setting of the two dimensional version of black hole evaporation known as the Russo-Susskind-Thorlacius model. We summarize the general ideas based on the semiclassical version of Einstein’s equations and then discuss specific modifications that are required in the context of collapse theories when applied to this model.
Thirty years ago, John Preskill concluded "that the information loss paradox may well presage a revolution in fundamental physics" and mused that "Conceivably, the puzzle of black hole evaporation portends a scientific revolution as sweeping as that that led to the formulation of quantum theory in the early 20th century." Many still agree with this assessment. On the other hand, it seems to me the "paradox" has little to do with the physical world but rather, at best, simply points out the possible inconsistency of two, already disparate, theories (mathematical models) of nature, general relativity and quantum mechanics, with virtually no conceivable observational consequences. The information paradox hinges on the concepts of a pure quantum state, the unitarity of quantum mechanics, and Hawking's semi-classical calculation of black hole evaporation. I used the qualifier "at best" above because, for me, the concept of a quantum state is far more restrictive than required by the paradox while unitarity is not a property of nature but rather of a mathematical model and is already violated by the process of making a measurement. Furthermore, the semi-classical calculation of Hawking is surely of limited applicability.
This review paper is intended for scholars with different backgrounds, possibly in only one of the subjects covered, and therefore little background knowledge is assumed. The first part is an introduction to classical and quantum information theory (CIT, QIT): basic definitions and tools of CIT are introduced, such as the information content of a random variable, the typical set, and some principles of data compression. Some concepts and results of QIT are then introduced, such as the qubit, the pure and mixed states, the Holevo theorem, the no-cloning theorem, and the quantum complementarity. In the second part, two applications of QIT to open problems in theoretical physics are discussed. The black hole (BH) information paradox is related to the phenomenon of the Hawking radiation (HR). Consid- ering a BH starting in a pure state, after its complete evaporation only the Hawking radiation will remain, which is shown to be in a mixed state. This either describes a non-unitary evolution of an isolated system, contradicting the evolution postulate of quantum mechanics and violating the no-cloning theorem, or it implies that the initial information content can escape the BH, therefore contradicting general relativity. The progress toward the solution of the paradox is discussed. The renormalization group (RG) aims at the extraction of the macroscopic description of a physical system from its microscopic description. This passage from microscopic to macroscopic can be described in terms of several steps from one scale to another, and is therefore formalized as the action of a group. The c-theorem proves the existence, under certain conditions, of a function which is monotonically decreasing along the group transformations. This result suggests an interpretation of this function as entropy, and its use to study the information flow along the RG transformations.