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arXiv:1307.1604

Can a wormhole be interpreted as an EPR pair?

Hrvoje Nikolić

Published Jul 5, 2013• 2 citations
arXivHTMLPDF

Abstract

Recently, Maldacena and Susskind arXiv:1306.0533 and Jensen and Karch arXiv:1307.1132 argued that a wormhole can be interpreted as an EPR pair. We point out that a convincing justification of such an interpretation would require a quantitative evidence that correlations between two ends of the wormhole are equal to those between the members of the EPR pair. As long as the existing results do not contain such evidence, the interpretation of wormhole as an EPR pair does not seem justified.

DOI
10.48550/arxiv.1307.1604

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Recently, Maldacena and Susskind arXiv:1306.0533 and Jensen and Karch arXiv:1307.1132 argued that a wormhole can be interpreted as an EPR pair. We point out that a convincing justification of such an interpretation would require a quantitative evidence that correlations between two ends of the wormhole are equal to those between the members of the EPR pair. As long as the existing results do not contain such evidence, the interpretation of wormhole as an EPR pair does not seem justified.
Maldacena and Susskind have proposed a correspondence between wormholes and entanglement, dubbed ER=EPR. We study this in the context of three-dimensional topological quantum field theory (TQFT), where we show that the formation of a wormhole is the same process as creating a particle–antiparticle pair. A key feature of the ER=EPR proposal is that certain apparently entangled degrees of freedom turn out to be the same. We name this phenomenon ‘fake entanglement’, and show how it arises in our TQFT model.
Maldacena and Susskind have proposed a correspondence between wormholes and entanglement, dubbed ER=EPR. We study this in the context of three-dimensional topological quantum field theory (TQFT), where we show that the formation of a wormhole is the same process as creating a particle–antiparticle pair. A key feature of the ER=EPR proposal is that certain apparently entangled degrees of freedom turn out to be the same. We name this phenomenon ‘fake entanglement’, and show how it arises in our TQFT model.
We consider the two-particle wave function of an Einstein-Podolsky-Rosen system, given by a two-dimensional relativistic scalar field model. The Bohm-de Broglie interpretation is applied and the quantum potential is viewed as modifying the Minkowski geometry. In this way an effective metric, which is analogous to a black hole metric in some limited region, is obtained in one case and a particular metric with singularities appears in the other case, opening the possibility, following Holland, of interpreting the EPR correlations as being originated by an effective wormhole geometry, through which the physical signals can propagate.
If spacetime is built out of quantum bits, does the shape of space depend on how the bits are entangled? The ER=EPR\mathrm{ER}=\mathrm{EPR}ER=EPR conjecture relates the entanglement entropy of a collection of black holes to the cross sectional area of Einstein-Rosen (ER) bridges (or wormholes) connecting them. We show that the geometrical entropy of classical ER bridges satisfies the subadditivity, triangle, strong subadditivity, and Cadney-Linden-Winter inequalities. These are nontrivial properties of entanglement entropy, so this is evidence for ER=EPR\mathrm{ER}=\mathrm{EPR}ER=EPR. We further show that the entanglement entropy associated with classical ER bridges has nonpositive tripartite information. This is not a property of entanglement entropy, in general. For example, the entangled four qubit pure state ∣GHZ4⟩=(∣0000⟩+∣1111⟩)/2|GH{Z}_{4}⟩=(|0000⟩+|1111⟩)/\sqrt{2}∣GHZ4​⟩=(∣0000⟩+∣1111⟩)/2​ has positive tripartite information, so this state cannot be described by a classical ER bridge. Large black holes with massive amounts of entanglement between them can fail to have a classical ER bridge if they are built out of ∣GHZ4⟩|GH{Z}_{4}⟩∣GHZ4​⟩ states. States with nonpositive tripartite information are called monogamous. We conclude that classical ER bridges require monogamous EPR correlations.
Abstract The various Bell Inequalities used to interpret the results of EPR-Bohm experiments are shown to be inappropriate for such experiments. The inequalities do not allow for correlation between the particles, which is the basis for such experiments, and therefore are irrelevant. Claims that the results of such experiments, because they violate the inequalities, require the conclusion that the measurement of one particle in an "entangled" pair can instantly affect the state of its partner, even at great distances, are untrue and need to be modified.
FINDING: Traversable wormholes are realized as quantum-information protocols — the 2022 Google/Caltech experiment simulated a traversable wormhole on a quantum processor, transmitting a qubit through a holographic dual, confirming ER=EPR as an operational transport channel. MATH: Core relations: - ER=EPR duality: Einstein-Rosen bridge ≡ Einstein-Podolsky-Rosen entanglement. Wormhole connectivity ↔ entanglement entropy S = -Tr(ρ ln ρ). - Traversable condition (Gao-Jafferis-Wall): coupling two CFT boundaries via double-trace deformation δS = ∫ d^d x h_{ij} T^{ij}_L T^{ij}_R opens the throat; requires ANEC violation: ∫ T_{μν} k^μ k^ν dλ < 0. - Multi-mouth (arXiv:2012.07821): three-mouth wormhole has fundamental group F₂ (free group on 2 generators), i.e., π₁ = ⟨a,b | ∅⟩ — topology of a 3-punctured sphere × time. - SYK model: N Majorana fermions, coupling J, scrambling time t_* ~ (β/2π) ln N. Wormhole signal ∝ N^{-1} at early times, grows as e^{2πt/β} until t_*. - Quantum teleportation fi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com