On the Relation between General Relativity and Quantum Theory: Difficulties as Seen by a Non-Expert

Abstract

The basic mathematical assumptions underlying classical general relativity and its physical interpretation are reviewed. Those structural features which arise from the non-existence of an a priori, given spacetime metric and associated isometry group are stressed, and it is emphasized that general relativity is not just a Poincare-invariant theory with a complicated gauge group. Then the fundamental assumptions on which special-relativistic quantum field theories have been based are considered and compared with general relativity from a mathematical and physical point of view. Two (old fashioned?) types of attempts to “quantize gravity” are then briefly discussed: (i) perturbation theory starting with linearized, free Einstein gravity, and (ii) canonical quantization starting from the ADM-dynamics. This is done only to illustrate difficulties which arise in “quantizing” gravity and to explain to quantum field theorists the point of view of at least one classically oriented relativist with the aim of improving communication and mutual understanding.