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Published Oct 29, 2023• 0 citations
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Abstract

In this article, we discuss through a principle of action the quantum information in relation to the information paradox.The information paradox, which arises in black hole physics, suggests that information can be lost when matter falls into a black hole, which contradicts the principle of information conservation in physics.We propose that the principle of action, which asserts that the action of a physical system is conserved, can be applied to information, showing that information is conserved in a similar way to energy and momentum.Through mathematical models and theoretical analysis, we show that the conservation of information can be understood as a result of the evolution of a system and probability amplitudes in quantum mechanics.

DOI
10.31219/osf.io/u2nbf

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In this article, we discuss through a principle of action the quantum information in relation to the information paradox.The information paradox, which arises in black hole physics, suggests that information can be lost when matter falls into a black hole, which contradicts the principle of information conservation in physics.We propose that the principle of action, which asserts that the action of a physical system is conserved, can be applied to information, showing that information is conserved in a similar way to energy and momentum.Through mathematical models and theoretical analysis, we show that the conservation of information can be understood as a result of the evolution of a system and probability amplitudes in quantum mechanics.
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.
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 concept of a fundamental conservation law for physical information is introduced. Building on the long‑standing analogy between thermodynamic entropy and Shannon information, we postulate that the total information content of an isolated system, denoted I(t), remains constant over time: I(t)=constant. This proposal is examined in the context of non‑relativistic quantum mechanics and quantum field theory. By constructing an information current and deriving a continuity equation from the Schrödinger equation, we demonstrate that the conservation of I(t) is mathematically consistent with unitary evolution. The implications of this law for the measurement problem, decoherence, and the black‑hole information paradox are discussed. A list of twenty novel research directions that could lead to Nobel‑level breakthroughs is presented, each grounded in a previously unobserved physical observable. The work offers a new perspective that may unify energy, momentum, and information as co‑equal pillars of physical law.
We seek to examine the ontological aspects of the resolution of the black hole information paradox. Several concepts which are now central to our understanding of quantum mechanics arose from our resolution to this paradox, and these concepts point to the conservation of all information, even on a quantum level. If quantum information is conserved and can never be erased or destroyed, then this indicates that all information is at least theoretically, ultimately retrievable and knowable from the event horizon of the universe. Ontologically, this supports the contention that a repository of all information in the universe must therefore exist. Herein, we trace the steps in this contention and conclude with the argument that our understanding of the universe points to the existence of an omniscient entity.
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.
The complete evaporation of black holes, as a natural endpoint of Hawking radiation, gives rise to the black hole information paradox, which fundamentally challenges the principles of unitarity and information conservation in quantum mechanics. Although the AdS/CFT correspondence indicates that information is preserved during black hole evaporation, the precise mechanism by which it is recovered from the Hawking radiation remains an open question. To explore a potential resolution, we investigate information transfer in a spin-chain model featuring an effective horizon realized via position-dependent couplings within an XY spin chain. We derive and demonstrate Page curve-like behavior, and analyze the transmission of quantum resources, such as entanglement and coherence, across the effective horizon. Our results show that quantum resources initially localized within an interior subsystem can be transferred to the exterior via particle radiation through the horizon. This study provides a novel perspective from quantum simulation on how information may escape from black holes, thereby contributing to the further understanding of the black hole information paradox.