Spacetime-Free Approach to Quantum Theory and Effective Spacetime Structure

Raasakka, Matti

doi:10.3842/sigma.2017.006

Cited by 9 publications

(10 citation statements)

References 88 publications

(193 reference statements)

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“…As this work was being completed we became aware of a paper with related goals [28]. There are also potential connections with a number of approaches to quantum gravity, including loop quantum gravity [29], quantum graphity [30], holographic space-time [31,32], and random dynamics [33]; we do not investigate these directly here.…”

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confidence: 99%

Space from Hilbert space: Recovering geometry from bulk entanglement

2017

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We examine how to construct a spatial manifold and its geometry from the entanglement structure of an abstract quantum state in Hilbert space. Given a decomposition of Hilbert space H into a tensor product of factors, we consider a class of "redundancy-constrained states" in H that generalize the area-law behavior for entanglement entropy usually found in condensed-matter systems with gapped local Hamiltonians. Using mutual information to define a distance measure on the graph, we employ classical multidimensional scaling to extract the best-fit spatial dimensionality of the emergent geometry. We then show that entanglement perturbations on such emergent geometries naturally give rise to local modifications of spatial curvature which obey a (spatial) analog of Einstein's equation. The Hilbert space corresponding to a region of flat space is finite-dimensional and scales as the volume, though the entropy (and the maximum change thereof) scales like the area of the boundary. A version of the ER=EPR conjecture is recovered, in that perturbations that entangle distant parts of the emergent geometry generate a configuration that may be considered as a highly quantum wormhole.

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confidence: 99%

Space from Hilbert space: Recovering geometry from bulk entanglement

2017

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“…In [16] we introduced a spacetime-free framework for quantum theory, which is based on the construction of the kinematical quantum observable algebra "from the ground up" as the free product of component algebras corresponding to individual observables. The physical observable algebra was suggested to be obtained via the GNS representation induced by some reference state, such as the vacuum.…”

Section: Summary and Discussionmentioning

confidence: 99%

Local Lorentz covariance in finite-dimensional local quantum physics

Raasakka¹

2017

Phys. Rev. D

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We show that local Lorentz covariance arises canonically as the group of transformations between local thermal states in the framework of Local Quantum Physics, given the following three postulates: (i) Local observable algebras are finite-dimensional. (ii) Minimal local observable algebras are isomorphic to M2(C), the observable algebra of a single qubit. (iii) The vacuum restricted to any minimal local observable algebra is a non-maximally mixed thermal state. The derivation reveals a new and surprising relation between spacetime structure and local quantum states. In particular, we show how local restrictions of the vacuum can determine the connection between different local inertial reference frames.

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“…However, the account of space is instead developed based on results coming out of quantum gravity research, as detailed in the next section. 24 More recently, a programmatic spacetime-free approach to algebraic quantum theory has been proposed by Raasakka (2017). 25 Even having such results might not settle whether entanglement is the relation in virtue of which nonspatial elements make up a world for the simple reason that the exact nature of these elements remains unexplored with the present focus on the world-making relation.…”

Section: Entanglement In Quantum Field Theorymentioning

confidence: 99%

Entanglement as the world-making relation: distance from entanglement

Jaksland

2020

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Distance, it is often argued, is the only coherent and empirically adequate worldmaking relation that can glue together the elements of the world. This paper offers entanglement as an alternative world-making relation. Entanglement is interesting since it is consistent even with quantum gravity theories that do not feature space at the fundamental level. The paper thereby defends the metaphysical salience of such non-spatial theories. An account of distance (space) is the predominant problem of empirical adequacy facing entanglement as a world-making relation. A resolution of this obstacle utilizes insights from the Ryu-Takayanagi formula (a holographic relation between entanglement and spacetime) and Susskind and Maldacena's related ER = EPR conjecture (a relation between bell pairs and wormholes). Together these indicate how distance can be recovered from entanglement and thus carves the way for entanglement fundamentalism.

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Spacetime-Free Approach to Quantum Theory and Effective Spacetime Structure

Cited by 9 publications

References 88 publications

Space from Hilbert space: Recovering geometry from bulk entanglement

Space from Hilbert space: Recovering geometry from bulk entanglement

Local Lorentz covariance in finite-dimensional local quantum physics

Entanglement as the world-making relation: distance from entanglement

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