Derivation of Emergent Spacetime Metric, Gravitational Potential and Speed of Light in Superfluid Vacuum Theory

Abstract

Within the frameworks of the logarithmic superfluid model of physical vacuum, we demonstrate the emergence of four-dimensional curved spacetime from the dynamics of quantum Bose liquid in three-dimensional Euclidean space. We derive the metric tensor of this spacetime and study its special cases and limits, such as the linear-phase flow and linearized gravity limit. We show that the value of speed of light, which is a fundamental parameter in a theory of relativity, is a derived notion in superfluid vacuum theory: its value is a combination of the Planck constant and original parameters of the background superfluid. As for the gravitational potential, then it can be defined in terms of the quantum information entropy of the background superfluid. Thus, relativistic gravity and curved spacetime are shown to result from the dynamics of quantum excitations of the background superfluid being projected onto the measurement apparatus of a relativistic observer.