Gas of wormholes: a possible ground state of Quantum Gravity

Abstract

In order to gain insight into the possible Ground State of Quantized Einstein's Gravity, we have derived a variational calculation of the energy of the quantum gravitational field in an open space, as measured by an asymptotic observer living in an asymptotically flat space-time. We find that for Quantum Gravity (QG) it is energetically favourable to perform its quantum fluctuations not upon flat space-time but around a ``gas'' of wormholes of mass m_p, the Planck mass (m_p ~= 10^{19}GeV) and average distance l_p, the Planck length a_p(a_p ~= 10^{-33}cm). As a result, assuming such configuration to be a good approximation to the true Ground State of Quantum Gravity, space-time, the arena of physical reality, turns out to be well described by Wheeler's quantum foam and adequately modeled by a space-time lattice with lattice constant l_p, the Planck lattice.Comment: 56 pages, revised version to appear in General Relativity and Gravitation (2000