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arXiv:0902.2361

Fundamental destruction of information and conservation laws

Jonathan Oppenheim, Benni Reznik

Published Feb 13, 2009• 9 citations

Abstract

Theories which have fundamental information destruction or decoherence are motivated by the black hole information paradox where one appears to have pure states evolving into mixed states. However such theories have either violated conservation laws, or are highly non-local. Here, we show that the tension between conservation laws and locality can be circumvented by constructing a relational theory of information destruction. In terms of conservation laws, we derive a generalisation of Noether's theorem for general theories, and show that symmetries imply a strong restriction on the type of evolution permissable. With respect to locality, we distinguish violations of causality from the creation or destruction of space-like seperated correlations. We show that violations of causality need not occur in a relational framework, although one can have situations where correlations decay faster than one might otherwise expect or can be created over spatial distances. This creation or destruction of correlations cannot be used to signal superluminally, and thus no violation of causality occurs. We prove that theories with information destruction can be made time-symmetric, thus impossing no arrow of time.

DOI: 10.48550/arxiv.0902.2361

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Theories which have fundamental information destruction or decoherence are motivated by the black hole information paradox where one appears to have pure states evolving into mixed states. However such theories have either violated conservation laws, or are highly non-local. Here, we show that the tension between conservation laws and locality can be circumvented by constructing a relational theory of information destruction. In terms of conservation laws, we derive a generalisation of Noether's theorem for general theories, and show that symmetries imply a strong restriction on the type of evolution permissable. With respect to locality, we distinguish violations of causality from the creation or destruction of space-like seperated correlations. We show that violations of causality need not occur in a relational framework, although one can have situations where correlations decay faster than one might otherwise expect or can be created over spatial distances. This creation or destruction of correlations cannot be used to signal superluminally, and thus no violation of causality occurs. We prove that theories with information destruction can be made time-symmetric, thus impossing no arrow of time.

The introduction of a relational time in quantum gravity naturally implies that pure quantum states evolve into mixed quantum states. We show, using a recently proposed concrete implementation, that the rate at which pure states naturally evolve into mixed ones is faster than that due to collapsing into a black hole that later evaporates. This is rather remarkable since the fundamental mechanism for decoherence is usually very weak. Therefore the "black hole information puzzle" is rendered de-facto unobservable.

Suppose a black hole forms from a pure quantum state

\ketψ

. The black hole information loss paradox arises from semiclassical arguments suggesting that, even in a closed system, the process of black hole formation and evaporation evolves a pure state into a mixed state. Resolution to the paradox typically demands violation of quantum mechanics or relativity in domains where they should hold. Instead, I propose that in a complete theory of quantum gravity, any region

\mathcal{U}

that could collapse into a black hole should already be described by a mixed state, thus bypassing the paradox entirely. To that end, I present a model in which the universe is in a quantum error-corrected state, such that any local black hole appears mixed and encodes no information locally.

The law of conservation of causality is one of the cornerstones of the AU-field axiomatics, allowing us to reconcile nonlocality with the principle of the absence of an information paradox. THE PROBLEM OF CAUSALITY IN NON-LOCAL THEORIES In special relativity, causality is provided by the finiteness of the speed of light: no influence can propagate faster, otherwise it would be possible to build closed time loops and violate the causality principle (the effect cannot precede the cause). However, in the Acta Universi hypothesis, the AU field shows non-local correlations with an effective rate(based on the interpretation of quantum entanglement and possible UAP phenomena). This raises a question: how is causality preserved? Answer of the AU model: causality is preserved not at the signal level, but at the level of the event archive structure. Space-time is not fundamental, but is derived from the correlations of the AU field. Therefore, "fast" correlations do not violate causality, since they do not transfer information in the classical sense.

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 EPR paradox, showing the incompatibility between causality and quantum mechanics, leads, especially after Bell's theorem and the experiments based on it, to a deep crisis of the causality principle. A complete redefinition of the entanglement concept, based on the impossibility of violation of conservation laws and on the generalization to a 5-dimensional space, leads to the recovery of the classical and fundamental idea for the physics of causality. The absolute validity of conservation laws, induces moreover, in the cases where they would be otherwise violated, topology changes which make possible "tunneling processes" (like wormholes in astrophysics) which connect separate spacetimes. It can be shown that such a phenomenon is a-luminal , opening the door, without overcoming light speed, to a conceivable time-machine.