Elastic Gravity

An abstract of a fantasy quantum gravity paper

The idea that gravity is emergent and not fundamental has been around since Andrei Sakharov. Among the more recent approaches to emergent gravity are the entropic gravity (Verlinde) and gravity from entanglement (Van Raamsdonk). In this paper we construct a model where macroscopic gravity emerges in a quantum system with a large number of highly entangled states. The linearity and unitarity of the quantum world is then translated into the elasticity in the gravitational world: any local attractive effects are counteracted by the larger-scale repulsive effects, producing a globally hyperbolic spacetime admitting a spatial slice with zero mean curvature. We identify this slice with a comoving frame in a Friedman-Robertson-Walker-de Sitter spacetime, and the effective large-scale elastic repulsive force with dark energy. We then find that the matching conditions between the two scales manifest as interaction-free dust, mimicking the appearance of dark matter. We also explore some of the small-scale predictions of this model. One of the more intriguing consequences is the Penrose-like upper limit on the complexity of a coherent state, resulting in the largest possible Schrodinger’s cat mass of about 1 Planck mass. This result offers hints for possible approaches toward modeling the quantum/classical transition and a deterministic view of the Born rule as a manifestation of the hidden residual entanglement of a classical detector and a quantum system under measurement.