What is the current status of the problem of quantum gravity and the question regarding the reality of spacetime singularities ?
The demand for consistency between a quantum description of matter and a geometric description of spacetime , as well as the appearance of singularities ( where curvature length scales become microscopic ) , indicate the need for a full theory of quantum gravity : for an adequate description of the interior of black holes , and of the very early universe , a theory is required in which gravity and the associated geometry of spacetime are described in the language of quantum physics .