Emergence of geometry in quantum states

Wen-Cong Gan, Fu-Wen Shu, Meng-He Wu

We study a conjectured correspondence between any codimension-two convex surface and a quantum state (SS-duality for short). By applying thermofield double formalism to the SS-duality, we show that thermal geometries naturally emerge as a result of hidden quantum entanglement between two boundary CFTs. We therefore propose a general framework to emerge the thermal geometry from CFT at finite temperature, without knowing many details about the thermal CFT. As an example, the case of 2d CFT is considered. We calculate its information metric and show that it is either BTZ black hole or thermal AdS as expected.

Julian Schwinger

Philip Tee

Recent advances in emergent geometry have identified a new class of models that represent spacetime as the graph obtained as the ground state of interacting Ising spins.These models have many desirable features, including stable excitations possessing many of the characteristics of a quantum particle.We analyze the dynamics of such excitations, including a detailed treatment of the edge states not previously addressed.Using a minimal prescription for the interaction of defects we numerically investigate approximate bounds to the speed of propagation of such a "particle".We discover, using numerical simulations, that there may be a Lieb-Robinson bound to propagation that could point the way to how a causal structure could be accommodated in this class of emergent geometry models.

Samuel L. Braunstein, Carlton M. Caves

Bogdan Mielnik

James B. Hartle

Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But quantum mechanics needs to be generalized further for quantum gravity where spacetime geometry is fluctuating and without definite value. This paper reviews a fully four-dimensional, sum-over-histories, generalized quantum mechanics of cosmological spacetime geometry. This generalization is constructed within the framework of generalized quantum theory. This is a minimal set of principles for quantum theory abstracted from the modern quantum mechanics of closed systems, most generally the universe. In this generalization, states of fields on spacelike surfaces and their unitary evolution are emergent properties appropriate when spacetime geometry behaves approximately classically. The principles of generalized quantum theory allow for the further generalization that would be necessary were spacetime not fundamental. Emergent spacetime phenomena are discussed in general and illustrated with the example of the classical spacetime geometries with large spacelike surfaces that emerge from the `no-boundary' wave function of the universe. These must be Lorentzian with one, and only one, time direction. The essay concludes by raising the question of whether quantum mechanics itself is emergent.