Making a Quantum Universe: Symmetry and Gravity

So far none of attempts to quantize gravity had led to a satisfactory model that not only describe gravity in the realm of a quantum world, but also its relation to elementary particles and other fundamental forces. Among other questions any quantum gravity model should explain are the origin of arrow of time, dimension of spacetime, and puzzles of semi-classical treatment of black holes. Here we outline preliminary results for a model of quantum universe in which gravity is fundamentally and by construction quantic. The model is based on 3 well motivated assumptions with compelling observational and theoretical evidence: Quantum mechanics is valid at all scales; Quantum systems are described by their symmetries; The Universe has infinite degrees of freedom. The last assumption means that the Hilbert space of the Universe has $SU(N\rightarrow \infty) \cong \text{area preserving Diff.} (S_2)$ symmetry and is parameterize by two angular variables. But in absence of a background spacetime dynamics is trivial and the Universe static. Nonetheless, we show that quantum fluctuations break the symmetry, divide the Universe to subsystems and add two continuous parameters to the dynamics: {\it distance} and {\it time}. We interpret the parameter space of the Hilbert space as the perceived classical spacetime and Einstein equation as projection of the dynamics in the Hilbert space on its parameter space. Finite dimensional symmetries of elementary particles emerge as a consequence of symmetry breaking without having any implication for the infinite dimensional symmetry. For this reason gravity is a universal force.