Analogue gravity simulation of superpositions of spacetimes

Abstract

Taking the principles of quantum mechanics as they stand and applying them to gravity, leads to the conclusion that one might be able to generate superpositions of spacetimes, at least formally. We analyze such a possibility from an analogue gravity perspective. We present an analogue toy model consisting of a Bose-Einstein condensate in a double-well potential and identify the states that could potentially be interpreted as superposition of effective spacetimes. These states are unstable and the source of instability from a microscopic point of view can be related to the absence of a well-defined causal structure in the effective geometric description. We explore the consequences of these instabilities and argue that they resonate with Penrose's ideas about the decay that superpositions of states with sufficiently different gravitational fields associated should experience.

arXiv comment13 pages, 2 figures, shortened version that matches the published one

References in corpus (24)

• Feshbach Resonances in Ultracold Gases
• Decoherence, the measurement problem, and interpretations of quantum mechanics
• Models of Wave-function Collapse, Underlying Theories, and Experimental Tests
• Analogue Gravity
• Acoustic black holes: horizons, ergospheres, and Hawking radiation
• Observation of quantum Hawking radiation and its entanglement in an analogue black hole
• Quantum Gravity from Causal Dynamical Triangulations: A Review
• Fragmentation of Bose-Einstein Condensates
• Sonic black holes in dilute Bose-Einstein condensates
• The causal set approach to quantum gravity
• Stochastic Gravity: Theory and Applications
• Underground test of gravity-related wave function collapse
• Negative mass hydrodynamics in a Spin-Orbit--Coupled Bose-Einstein Condensate
• Gravitationally induced inhibitions of dispersion according to the Schrödinger-Newton Equation
• Parameter Diagrams of the GRW and CSL Theories of Wave Function Collapse
• Gravity, energy conservation and parameter values in collapse models
• Bounds on collapse models from cold-atom experiments
• Exploring the unification of quantum theory and general relativity with a Bose-Einstein condensate
• Quantum space-time fluctuations and primary state diffusion
• Quantum evolution in spacetime foam
• A Tentative Expression of the Karolyhazy Uncertainty of the Space-Time Structure through Vacuum Spreads in Quantum Gravity
• Gravitational Decoherence, Alternative Quantum Theories and Semiclassical Gravity
• Chronology Protection Implementation in Analogue Gravity
• How the quantum emerges from gravity

Cited by in corpus (7)

• Quantum signatures of black hole mass superpositions
• Quantum superpositions of Minkowski spacetime
• Entanglement harvesting in quantum superposed spacetime
• Hawking radiation from an analogue bouncing geometry
• The sounds of science a symphony for many instruments and voices part II
• Analogue simulation of quantum gravity black hole models in a dc-SQUID array
• Space-time superpositions as fluctuating geometries