Quantum Theory and Gravitation

Abstract

Einstein’s General Relativity Theory (GRT) was originally formulated as a classical field theory, and the question if it can or even must be quantized is one of the fundamental questions which has not been finally answered until now. The consideration of this problem is not so much justified by formal analogies between electromagnetic and gravitational theories, and even less by metaphysical belief in the quantrum structure of nature, but by the fact that matter fields must be quantized. This means that the character of the coupling between quantized matter and gravity must be clarified. The main aspect of the problem is whether this requires gravity to be quantized too. If one refers to Einstein’s GRT, the problem is now to understand Einstein’s equations

$$ G_{\mu v} \equiv R_{\mu v} - {}^{\frac{1} {2}}g_{\mu v} R = - \kappa T_{\mu v} $$

(1)

(where κ = 8πG/c ⁴) in the case of quantized matter, i.e., in the case where the energy—momentum tensor T _μν describes quantized matter.