Foundations of Physics

, Volume 48, Issue 2, pp 237–252 | Cite as

How Not to Establish the Non-renormalizability of Gravity

  • Juliusz Doboszewski
  • Niels Linnemann


General relativity cannot be formulated as a perturbatively renormalizable quantum field theory. An argument relying on the validity of the Bekenstein–Hawking entropy formula aims at dismissing gravity as non-renormalizable per se, against hopes (underlying programs such as Asymptotic Safety) that d-dimensional GR could turn out to have a non-perturbatively renormalizable d–dimensional quantum field theoretic formulation. In this note we discuss various forms of highly problematic semi-classical extrapolations assumed by both sides of the debate concerning what we call The Entropy Argument, and show that a large class of dimensional reduction scenarios leads to the blow-up of Bekenstein–Hawking entropy.


Renormalizability of gravity Bekenstein–Hawking formula Asymptotic safety Dimensional reduction Quantum gravity 



J. D.’s work was partly performed under a collaborative agreement between the University of Illinois at Chicago and the University of Geneva and made possible by Grant Number 56314 from the John Templeton Foundation and its contents are solely the responsibility of the authors and do not necessarily represent the official views of the John Templeton Foundation. N. L. would like to thank the Swiss National Science Foundation for financial support (105212_165702), and the Lorentz Center in Leiden for providing the platform for an enriching conference on Quantum Spacetime and the Renormalization Group. N. L. would also like to thank the the participants of this conference for valuable feedback. Both authors would like to thank Claus Beisbart, Vincent Lam, Max Niedermaier, Carina Prunkl, Christian Wüthrich and an anonymous referee for valuable feedback.


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Authors and Affiliations

  1. 1.Department of PhilosophyJagiellonian UniversityKrakówPoland
  2. 2.Department of PhilosophyUniversity of GenevaGenève 4Switzerland

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