Quantum Postulates and the Strong Principle of Equivalence

Abstract

Einstein’s equations of GRT connect quantized non-gravitational matter described by its energy—momentum tensor T μν and gravitational fields described by the metric tensor g μν of a Riemannian spacetime. In order to avoid physical and mathematical inconsistencies resulting otherwise from Einstein’s equations, one has to consider quantization of gravitational fields (see Chapter 1). The quantum procedure should unify or at least harmonize classical and quantum theory.* On the other hand, GRT is not genuine field theory. This is due to (i) the identification of gravitational field and spacetime metric (statement of the weak principle of equivalence) and (ii) the universal gravitational coupling making gravity itself a source of gravitational field (this is, together with (i), a formulation of the strong principle of equivalence). As a consequence of this strong principle, Einstein’s equations show a typical nonlinearity producing back-reaction effects. It makes all quantization rules problematical which transform a usual classical field theory into a quantum field theory. In particular, one has to decide whether this quantization shows the existence of gravitons in the same sense as the physical existence of photons is considered to be verified. To discuss this problem, one must consider both quantized vacuum fields (together with the measurement of vacuum quantum effects) and the effects resulting from the coupling of gravitational fields to quantized non-gravitational matter.