Weekly Papers on Quantum Foundations (9)

Authors: Sung-Sik Lee

In this paper, we study a possibility where gravity and time emerge from quantum matter. Within the Hilbert space of matter fields defined on a spatial manifold, we consider a sub-Hilbert space spanned by states which are parameterized by spatial metric. In those states, metric is introduced as a collective variable that controls local structures of entanglement. The underlying matter fields endow the states labeled by metric with an unambiguous inner product. Then we construct a Hamiltonian for the matter fields that is an endomorphism of the sub-Hilbert space, thereby inducing a quantum Hamiltonian of the metric. It is shown that there exists a matter Hamiltonian that induces the general relativity in the semi-classical field theory limit. Although the Hamiltonian is not local in the absolute sense, it has a weaker notion of locality, called relative locality : the range of interactions is set by the entanglement present in target states on which the Hamiltonian acts. In general, normalizable states are not invariant under the transformations generated by the Hamiltonian. As a result, a physical state spontaneously breaks the Hamiltonian constraint, and picks a moment of time. The subsequent flow of time can be understood as a Goldstone mode associated with the broken symmetry. The construction allows one to study dynamics of gravity from the perspective of matter fields. The Hawking radiation corresponds to a unitary evolution where entanglement across horizon is gradually transferred from color degrees of freedom to singlet degrees of freedom. The underlying quantum states remain pure as evaporating black holes keep entanglement with early Hawking radiations in the singlet sector which is not captured by the Bekenstein-Hawking entropy.

McCoy, C.D. (2017) Can Typicality Arguments Dissolve Cosmology’s Flatness Problem? Philosophy of Science, 84 (5). pp. 1239-1252.
McCoy, C.D. (2018) The Universe Never Had a Chance. In: UNSPECIFIED.
Graffigna, Matías (2016) The Possibility of a New Metaphysics for Quantum Mechanics from Meinong’s Theory of Objects. Probing the Meaning of Quantum Mechanics: Superpositions, Dynamics, Semantics and Identity. pp. 280-307.
Baker, David John (2018) On Spacetime Functionalism. [Preprint]
In order to understand the detailed mechanism by which a fundamental discreteness can provide a finite entanglement entropy, we consider the entanglement entropy of two classes of free massless scalar fields on causal sets that are well approximated by causal diamonds in Minkowski spacetime of dimensions 2, 3 and 4. The first class is defined from discretised versions of the continuum retarded Green functions, while the second uses the causal set’s retarded nonlocal d’Alembertians parametrised by a length scale l k . In both cases we provide numerical evidence that the area law is recovered when the double-cutoff prescription proposed in Sorkin and Yazdi (2016 Entanglement entropy in causal set theory (arXiv:1611.10281)) is imposed. We discuss in detail the need for this double cutoff by studying the effect of two cutoffs on the quantum field and, in particular, on the entanglement entropy, in isolation. In so doing, we get a novel interpretation for wh…
Swanson, Noel (2018) How to be a Relativistic Spacetime State Realist. [Preprint]
For two people to send each other a message, it usually takes a minimum of two particles. But quantum superposition makes it possible with just one

Enter the machine

Enter the machine, Published online: 26 February 2018; doi:10.1038/s41567-018-0061-8

Quantum tomography infers quantum states from measurement data, but it becomes infeasible for large systems. Machine learning enables tomography of highly entangled many-body states and suggests a new powerful approach to this problem.

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