Any consistent coupling between classical gravity and quantum matter is fundamentally irreversible

Thomas D. Galley1, Flaminia Giacomini2, and John H. Selby3

1Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
2Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland
3ICTQT, University of Gdańsk, Wita Stwosza 63, 80-308 Gdańsk, Poland

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When gravity is sourced by a quantum system, there is tension between its role as the mediator of a fundamental interaction, which is expected to acquire nonclassical features, and its role in determining the properties of spacetime, which is inherently classical. Fundamentally, this tension should result in breaking one of the fundamental principles of quantum theory or general relativity, but it is usually hard to assess which one without resorting to a specific model. Here, we answer this question in a theory-independent way using General Probabilistic Theories (GPTs). We consider the interactions of the gravitational field with a single matter system, and derive a no-go theorem showing that when gravity is classical at least one of the following assumptions needs to be violated: (i) Matter degrees of freedom are described by fully non-classical degrees of freedom; (ii) Interactions between matter degrees of freedom and the gravitational field are reversible; (iii) Matter degrees of freedom back-react on the gravitational field. We argue that this implies that theories of classical gravity and quantum matter must be fundamentally irreversible, as is the case in the recent model of Oppenheim et al. Conversely if we require that the interaction between quantum matter and the gravitational field is reversible, then the gravitational field must be non-classical.

A central question in modern physics is how to unify quantum theory and general relativity. Historically many arguments have been put forward claiming that unification of the two theories can only be obtained by quantizing the gravitational field, and indeed most approaches towards unification attempt to do so. In this paper we show that existing arguments for quantizing the gravitational field make important underlying assumptions such as reversibility of interactions and the possibility of preparing quantum superposition states. We prove a theorem, which does not depend on any theoretical description of gravity and matter, showing that any consistent coupling between classical gravity and fully quantum matter must be irreversible. This shows that consistency requirements alone do not dictate that gravity must be quantized, and moreover any attempt to unify classical gravity and fully quantum matter must necessarily feature irreversible interactions between matter and the gravitational field.

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Cited by

[1] Thomas Galley, "Might There Be No Quantum Gravity After All?", Physics 16, 203 (2023).

[2] Isaac Layton and Jonathan Oppenheim, "The Classical-Quantum Limit", PRX Quantum 5 2, 020331 (2024).

[3] Andrea Di Biagio, "Diagrams and GPTs for Quantum Gravity", Quantum Views 8, 78 (2024).

[4] Jonathan Oppenheim, Andrea Russo, and Zachary Weller-Davies, "Diffeomorphism invariant classical-quantum path integrals for Nordstrom gravity", arXiv:2401.05514, (2024).

[5] Zachary Weller-Davies, "Quantum gravity with dynamical wave-function collapse via a classical scalar field", arXiv:2402.17024, (2024).

[6] Durmuş Demir, "Emergent Gravity Completion in Quantum Field Theory, and Affine Condensation in Open and Closed Strings", arXiv:2312.16270, (2023).

[7] Lin-Qing Chen and Flaminia Giacomini, "Quantum effects in gravity beyond the Newton potential from a delocalised quantum source", arXiv:2402.10288, (2024).

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