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.
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BibTeX
@misc{ferreiro2026when,
title = {{When quantum field theory kicks in: the relation between matter, gravity and energy}},
author = {Antonio Ferreiro and Andrea Cavallaro},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10588},
eprint = {2610.10588},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10588},
}
RIS
TY - UNPB
TI - When quantum field theory kicks in: the relation between matter, gravity and energy
AU - Antonio Ferreiro
AU - Andrea Cavallaro
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.10588
UR - https://arxiv.org/abs/2610.10588
AB - 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.
ER -