Core Concepts

This paper explores the equivalence between spatial and temporal quantum correlations, arguing that the thermoﬁeld double state, representing entangled black holes connected by an Einstein-Rosen bridge, can be equivalently described as the temporal evolution of a single black hole. This suggests a potential connection between the interior solution of BTZ black holes and dS/CFT correspondence.

Abstract

Racorean, O. (2024, October 8). Eternal black holes and temporal quantum correlations. arXiv.org. https://arxiv.org/abs/2304.00982v2

This paper investigates the implications of the equivalence between spatial and temporal quantum correlations within the framework of AdS/CFT duality, particularly in the context of black hole physics. The author aims to demonstrate that the thermofield double state, typically interpreted as two entangled black holes connected by a spatial wormhole, can be equivalently understood as the temporal evolution of a single black hole connected by a "temporal wormhole."

The author employs theoretical arguments and mathematical derivations based on quantum mechanics, general relativity, and the AdS/CFT correspondence. The paper starts by establishing the equivalence of spatial and temporal correlations in quantum theory, utilizing concepts like partial transposition and the Jamiołkowski isomorphism. This equivalence is then extended to the AdS/CFT duality, where the thermofield double state is analyzed in the high-temperature limit. Finally, the author derives a metric resembling a static de Sitter space by interchanging the roles of space and time coordinates in the BTZ black hole metric.

- The paper demonstrates that in the high-temperature limit, the thermofield double state, representing two entangled CFTs dual to two spatially separated black holes connected by an Einstein-Rosen bridge, is equivalent to the temporal correlation of a single CFT evolving unitarily between two times.
- This suggests that the spatial wormhole connecting two black holes at one time can be equivalently viewed as a "temporal wormhole" connecting a single black hole at two different times.
- By interchanging the roles of space and time coordinates in the BTZ black hole metric, the author derives a metric resembling a static de Sitter space, hinting at a potential connection between the BTZ black hole interior and dS/CFT correspondence.

- The equivalence of spatial and temporal quantum correlations has profound implications for our understanding of black hole physics within the AdS/CFT duality framework.
- The concept of "temporal wormholes" provides a novel perspective on the nature of spacetime and entanglement in the context of black holes.
- The derived metric suggests a potential connection between the interior solution of BTZ black holes and dS/CFT correspondence, opening up new avenues for research in this area.

This research significantly contributes to our understanding of quantum gravity and the relationship between quantum information and spacetime geometry. The proposed equivalence between spatial and temporal wormholes offers a new perspective on the nature of entanglement and its role in black hole physics. Additionally, the potential connection to dS/CFT correspondence opens up exciting possibilities for exploring quantum gravity in de Sitter space.

The paper primarily focuses on theoretical arguments and mathematical derivations. Further research involving numerical simulations and potentially experimental verification would be valuable to strengthen the proposed ideas. Additionally, exploring the implications of these findings for other types of black holes and more general spacetimes would be a fruitful avenue for future investigation.

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Quotes

"It was shown in recent works that quantum theory may support a uniﬁcation of the notions of space and time, as such, treating spatial and time correlations equally."
"The partial transposition of the maximally entangled state of two quantum systems exactly matches the correlations of one quantum system that evolves unitary between two distinct moments of time."
"We may see the spatial wormhole as an Einstein-Rosen bridge connecting two spatially separated black holes on the same space-like hypersurface while the temporal wormhole as an Einstein-Rosen bridge connecting two temporally separated black holes on two diﬀerent space-like hypersurfaces."

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by Ovidiu Racor... at **arxiv.org** 10-10-2024

Deeper Inquiries

The concept of temporal wormholes, as presented in the paper, offers a novel perspective on the black hole information paradox. This paradox arises from the conflict between the principles of quantum mechanics, which dictate that information cannot be destroyed, and the classical picture of black holes, which suggests that information falling into a black hole is lost forever.
Here's how temporal wormholes could potentially resolve this:
Non-destructive Information Transfer: If temporal wormholes connect a black hole at one time to itself at another time, information falling into the black hole wouldn't be destroyed. Instead, it could be viewed as being transferred through the wormhole to a later point in the black hole's evolution, potentially even beyond the singularity where our current understanding of physics breaks down.
Emergent Hawking Radiation: The paper suggests that the interior solution of the BTZ black hole, which is connected to the concept of temporal wormholes, might have an interpretation within the dS/CFT correspondence framework. This framework relates the physics within a de Sitter spacetime to a conformal field theory on its boundary. If this connection holds, information could be encoded in the entanglement structure of the CFT, and this entanglement could manifest as correlations in the Hawking radiation emitted by the black hole, thus preserving information.
Redefining "Lost" Information: Temporal wormholes challenge the conventional notion of information being "lost" within a black hole. If information is merely inaccessible to observers outside the black hole for a certain period, potentially reappearing at a later time, it might not be considered truly lost. This perspective could reconcile the seemingly contradictory principles of information conservation and black hole physics.
However, it's crucial to acknowledge that the concept of temporal wormholes is still highly speculative. Further research is needed to determine their viability and fully explore their implications for the black hole information paradox.

While the paper proposes an intriguing equivalence between spatial and temporal quantum correlations, particularly in the context of AdS/CFT duality, it's conceivable that this equivalence might not hold universally, especially in extreme gravitational scenarios.
Here are some situations where the equivalence might break down and their potential implications:
Strong Gravitational Fields: In regions of extreme gravity, such as near the singularity of a black hole or in the very early universe, the fabric of spacetime itself is significantly warped. This extreme curvature could potentially disrupt the delicate interplay between spatial and temporal correlations, leading to a breakdown of the equivalence. Such a breakdown might imply that our current understanding of quantum mechanics and general relativity is incomplete in these extreme regimes.
Time-Dependent Backgrounds: The paper primarily focuses on static spacetimes like the BTZ black hole. However, in more dynamic and evolving spacetimes, such as those found in cosmological models or during black hole mergers, the distinction between space and time becomes less clear-cut. This ambiguity could lead to a breakdown of the equivalence, suggesting that a more general framework is needed to describe quantum correlations in time-dependent gravitational backgrounds.
Quantum Gravity Effects: At the Planck scale, where quantum effects become significant for gravity, the very notions of space and time are expected to be fundamentally altered. In such a scenario, the equivalence between spatial and temporal correlations might not hold, hinting at a deeper connection between quantum entanglement, spacetime structure, and the emergence of classical reality from a quantum gravity theory.
If the equivalence were to break down, it would have profound implications for our understanding of the universe:
New Physics: It could point towards new physics beyond the Standard Model and general relativity, potentially offering clues about the nature of quantum gravity.
Revised Quantum Mechanics: It might necessitate a revision of our understanding of quantum mechanics, particularly in the context of strong gravity and curved spacetime.
Rethinking Causality: The breakdown could challenge our understanding of causality and the arrow of time, potentially opening up possibilities for exotic phenomena like closed timelike curves.
Exploring these scenarios where the equivalence might break down is crucial for pushing the boundaries of our knowledge and developing a more complete theory of quantum gravity.

The idea of time being subject to quantum correlations, as suggested by the equivalence between spatial and temporal correlations, has profound philosophical and scientific implications, particularly for our understanding of causality and free will.
Here's how it might affect our perception:
Blurred Cause and Effect: If time is not absolute but rather entangled with quantum systems, the strict order of cause and effect could become blurred at the quantum level. Events might not have a definite causal relationship, leading to a more probabilistic view of causality, where multiple potential pasts and futures coexist in a superposition of states.
Retrocausality: Quantum correlations in time could potentially allow for retrocausality, where future events seemingly influence the past. While seemingly paradoxical, this concept has been explored in certain interpretations of quantum mechanics, and the entanglement of time could provide a mechanism for such effects.
Illusion of Free Will: If our actions are predetermined by quantum correlations that extend across time, it raises questions about the nature of free will. Our choices might be perceived as inevitable outcomes of a pre-existing entangled state, challenging the notion of genuine freedom in our actions.
However, it's important to note:
Emergent Classicality: While quantum correlations might blur causality at the microscopic level, the macroscopic world we experience appears to follow classical rules of cause and effect. Understanding how this classicality emerges from a fundamentally quantum reality is a major challenge.
Interpretational Issues: The implications for free will depend heavily on the interpretation of quantum mechanics one adopts. Some interpretations might preserve a notion of free will, while others might suggest a more deterministic universe.
The concept of time being subject to quantum correlations is still highly speculative. Further research is needed to determine its validity and explore its full implications for our understanding of causality, free will, and the nature of reality itself.

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