When quantum field theory kicks in: the relation between matter, gravity and energy

Abstract

The existence of energy is the main criterion for (i) providing a common core to the materiality of all types of classical matter and (ii) denying that the gravitational field of General Relativity is a type of matter. Extending this criterion to quantum field theory, though formally straightforward, carries new conceptual consequences for the interpretation of gravity. Renormalization of the quantum matter stress-energy tensor forces a local, purely geometric term, built from the metric alone, into the conserved stress-energy, and this has two faces. It grants the metric a material significance alongside its spatio-temporal one (the egalitarian view); and it binds gravitational to non-gravitational energy so tightly that the two cannot be split apart without a choice of vacuum that a generic spacetime does not supply (the unificationist view). The latter poses a dilemma: either gravitational energy is meaningless, but then so is the energy of the non-gravitational quantum fields, and only classical fields remain matter; or both are meaningful, and the metric thereby acquires the material significance of a matter field. On neither horn does the classical divide between matter and spacetime survive quantization.