Any consistent coupling between classical gravity and quantum matter is fundamentally irreversible
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
| Published: | 2023-10-16, volume 7, page 1142 |
| Eprint: | arXiv:2301.10261v2 |
| Doi: | https://doi.org/10.22331/q-2023-10-16-1142 |
| Citation: | Quantum 7, 1142 (2023). |
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Abstract
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.
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[1] M Bahrami, A Bassi, S McMillen, M Paternostro, and H Ulbricht. ``Is gravity quantum?'' (2015). arXiv:1507.05733.
arXiv:1507.05733
[2] Charis Anastopoulos and Bei-Lok Hu. ``Probing a gravitational cat state''. Class. Quant. Grav. 32, 165022 (2015).
https://doi.org/10.1088/0264-9381/32/16/165022
[3] Sougato Bose, Anupam Mazumdar, Gavin W Morley, Hendrik Ulbricht, Marko Toroš, Mauro Paternostro, Andrew A Geraci, Peter F Barker, MS Kim, and Gerard Milburn. ``Spin entanglement witness for quantum gravity''. Phys. Rev. Lett. 119, 240401 (2017).
https://doi.org/10.1103/PhysRevLett.119.240401
[4] Chiara Marletto and Vlatko Vedral. ``Gravitationally induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity''. Phys. Rev. Lett. 119, 240402 (2017).
https://doi.org/10.1103/PhysRevLett.119.240402
[5] Chiara Marletto and Vlatko Vedral. ``Why we need to quantise everything, including gravity''. npj Quantum Information 3, 1–5 (2017).
https://doi.org/10.1038/s41534-017-0028-0
[6] Matteo Carlesso, Mauro Paternostro, Hendrik Ulbricht, and Angelo Bassi. ``When Cavendish meets Feynman: A quantum torsion balance for testing the quantumness of gravity'' (2017). arXiv:1710.08695.
arXiv:1710.08695
[7] Michael JW Hall and Marcel Reginatto. ``On two recent proposals for witnessing nonclassical gravity''. J. Phys. A 51, 085303 (2018).
https://doi.org/10.1088/1751-8121/aaa734
[8] Chiara Marletto and Vlatko Vedral. ``When can gravity path-entangle two spatially superposed masses?''. Phys. Rev. D 98, 046001 (2018).
https://doi.org/10.1103/PhysRevD.98.046001
[9] Alessio Belenchia, Robert M Wald, Flaminia Giacomini, Esteban Castro-Ruiz, Časlav Brukner, and Markus Aspelmeyer. ``Quantum superposition of massive objects and the quantization of gravity''. Phys. Rev. D 98, 126009 (2018).
https://doi.org/10.1103/PhysRevD.98.126009
[10] Alessio Belenchia, Robert M Wald, Flaminia Giacomini, Esteban Castro-Ruiz, Časlav Brukner, and Markus Aspelmeyer. ``Information content of the gravitational field of a quantum superposition''. Int. J. Mod. Phys. D 28, 1943001 (2019).
https://doi.org/10.1142/S0218271819430016
[11] Marios Christodoulou and Carlo Rovelli. ``On the possibility of laboratory evidence for quantum superposition of geometries''. Phys. Lett. B 792, 64–68 (2019).
https://doi.org/10.1016/j.physletb.2019.03.015
[12] Charis Anastopoulos and Bei-Lok Hu. ``Quantum superposition of two gravitational cat states''. Class. Quant. Grav. 37, 235012 (2020).
https://doi.org/10.1088/1361-6382/abbe6f
[13] Richard Howl, Vlatko Vedral, Devang Naik, Marios Christodoulou, Carlo Rovelli, and Aditya Iyer. ``Non-gaussianity as a signature of a quantum theory of gravity''. PRX Quantum 2, 010325 (2021).
https://doi.org/10.1103/PRXQuantum.2.010325
[14] Ryan J Marshman, Anupam Mazumdar, and Sougato Bose. ``Locality and entanglement in table-top testing of the quantum nature of linearized gravity''. Phys. Rev. A 101, 052110 (2020).
https://doi.org/10.1103/PhysRevA.101.052110
[15] Hadrien Chevalier, A. J. Paige, and M. S. Kim. ``Witnessing the nonclassical nature of gravity in the presence of unknown interactions''. Phys. Rev. A 102, 022428 (2020). arXiv:2005.13922.
https://doi.org/10.1103/PhysRevA.102.022428
arXiv:2005.13922
[16] Tanjung Krisnanda, Guo Yao Tham, Mauro Paternostro, and Tomasz Paterek. ``Observable quantum entanglement due to gravity''. npj Quantum Information 6, 1–6 (2020).
https://doi.org/10.1038/s41534-020-0243-y
[17] Chiara Marletto and Vlatko Vedral. ``Witnessing nonclassicality beyond quantum theory''. Phys. Rev. D 102, 086012 (2020).
https://doi.org/10.1103/PhysRevD.102.086012
[18] Thomas D. Galley, Flaminia Giacomini, and John H. Selby. ``A no-go theorem on the nature of the gravitational field beyond quantum theory''. Quantum 6, 779 (2022).
https://doi.org/10.22331/q-2022-08-17-779
[19] Soham Pal, Priya Batra, Tanjung Krisnanda, Tomasz Paterek, and T. S. Mahesh. ``Experimental localisation of quantum entanglement through monitored classical mediator''. Quantum 5, 478 (2021).
https://doi.org/10.22331/q-2021-06-17-478
[20] Daniel Carney, Holger Müller, and Jacob M. Taylor. ``Using an Atom Interferometer to Infer Gravitational Entanglement Generation''. PRX Quantum 2, 030330 (2021). arXiv:2101.11629.
https://doi.org/10.1103/PRXQuantum.2.030330
arXiv:2101.11629
[21] Kirill Streltsov, Julen Simon Pedernales, and Martin Bodo Plenio. ``On the significance of interferometric revivals for the fundamental description of gravity''. Universe 8 (2022).
https://doi.org/10.3390/universe8020058
[22] Daine L. Danielson, Gautam Satishchandran, and Robert M. Wald. ``Gravitationally mediated entanglement: Newtonian field versus gravitons''. Phys. Rev. D 105, 086001 (2022). arXiv:2112.10798.
https://doi.org/10.1103/PhysRevD.105.086001
arXiv:2112.10798
[23] Adrian Kent and Damián Pitalúa-García. ``Testing the nonclassicality of spacetime: What can we learn from Bell–Bose et al.-Marletto-Vedral experiments?''. Phys. Rev. D 104, 126030 (2021).
https://doi.org/10.1103/PhysRevD.104.126030
[24] Marios Christodoulou, Andrea Di Biagio, Markus Aspelmeyer, Časlav Brukner, Carlo Rovelli, and Richard Howl. ``Locally mediated entanglement in linearized quantum gravity''. Phys. Rev. Lett. 130, 100202 (2023). arXiv:2202.03368.
https://doi.org/10.1103/PhysRevLett.130.100202
arXiv:2202.03368
[25] Nick Huggett, Niels Linnemann, and Mike Schneider. ``Quantum Gravity in a Laboratory?'' (2022). arXiv:2205.09013.
arXiv:2205.09013
[26] Marios Christodoulou, Andrea Di Biagio, Richard Howl, and Carlo Rovelli. ``Gravity entanglement, quantum reference systems, degrees of freedom'' (2022). arXiv:2207.03138.
https://doi.org/10.1088/1361-6382/acb0aa
arXiv:2207.03138
[27] Daine L. Danielson, Gautam Satishchandran, and Robert M. Wald. ``Black Holes Decohere Quantum Superpositions'' (2022). arXiv:2205.06279.
https://doi.org/10.1142/S0218271822410036
arXiv:2205.06279
[28] Lin-Qing Chen, Flaminia Giacomini, and Carlo Rovelli. ``Quantum states of fields for quantum split sources''. Quantum 7, 958 (2023). arXiv:2207.10592.
https://doi.org/10.22331/q-2023-03-20-958
arXiv:2207.10592
[29] Eduardo Martín-Martínez and T. Rick Perche. ``What gravity mediated entanglement can really tell us about quantum gravity'' (2022). arXiv:2208.09489.
arXiv:2208.09489
[30] Chris Overstreet, Joseph Curti, Minjeong Kim, Peter Asenbaum, Mark A. Kasevich, and Flaminia Giacomini. ``Inference of gravitational field superposition from quantum measurements'' (2022). arXiv:2209.02214.
arXiv:2209.02214
[31] Markus Aspelmeyer. ``When Zeh Meets Feynman: How to Avoid the Appearance of a Classical World in Gravity Experiments''. Fundam. Theor. Phys. 204, 85–95 (2022). arXiv:2203.05587.
https://doi.org/10.1007/978-3-030-88781-0_5
arXiv:2203.05587
[32] John S Bell. ``On the Einstein Podolsky Rosen paradox''. Physics Physique Fizika 1, 195 (1964).
https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195
[33] Lucien Hardy. ``Quantum theory from five reasonable axioms'' (2001). arXiv:quant-ph/0101012.
arXiv:quant-ph/0101012
[34] Jonathan Barrett. ``Information processing in generalized probabilistic theories''. Physical Review A 75, 032304 (2007).
https://doi.org/10.1103/PhysRevA.75.032304
[35] L. Diosi and J. J. Halliwell. ``Coupling Classical and Quantum Variables using Continuous Quantum Measurement Theory''. Physical Review Letters 81, 2846–2849 (1998).
https://doi.org/10.1103/PhysRevLett.81.2846
[36] J. Caro and L. L. Salcedo. ``Impediments to mixing classical and quantum dynamics''. Physical Review A 60, 842–852 (1999).
https://doi.org/10.1103/PhysRevA.60.842
[37] Lajos Diósi, Nicolas Gisin, and Walter T. Strunz. ``Quantum approach to coupling classical and quantum dynamics''. Physical Review A 61, 022108 (2000).
https://doi.org/10.1103/PhysRevA.61.022108
[38] Daniel R. Terno. ``Inconsistency of quantum–classical dynamics, and what it implies''. Foundations of Physics 36, 102–111 (2006).
https://doi.org/10.1007/s10701-005-9007-y
[39] Hans-Thomas Elze. ``Linear dynamics of quantum-classical hybrids''. Physical Review A 85, 052109 (2012).
https://doi.org/10.1103/PhysRevA.85.052109
[40] Jonathan Oppenheim. ``A post-quantum theory of classical gravity?'' (2018). arXiv:1811.03116.
arXiv:1811.03116
[41] Jonathan Oppenheim, Carlo Sparaciari, Barbara Šoda, and Zachary Weller-Davies. ``Gravitationally induced decoherence vs space-time diffusion: testing the quantum nature of gravity'' (2022). arXiv:2203.01982.
arXiv:2203.01982
[42] Isaac Layton, Jonathan Oppenheim, and Zachary Weller-Davies. ``A healthier semi-classical dynamics'' (2022). arXiv:2208.11722.
arXiv:2208.11722
[43] Teiko Heinosaari, Leevi Leppäjärvi, and Martin Plávala. ``No-free-information principle in general probabilistic theories''. Quantum 3, 157 (2019).
https://doi.org/10.22331/q-2019-07-08-157
[44] Giulio Chiribella, Giacomo Mauro D`Ariano, and Paolo Perinotti. ``Probabilistic theories with purification''. Physical Review A 81, 062348 (2010).
https://doi.org/10.1103/PhysRevA.81.062348
[45] David Bohm. ``A suggested interpretation of the quantum theory in terms of" hidden" variables. I''. Physical review 85, 166 (1952).
https://doi.org/10.1103/PhysRev.85.166
[46] Hugh Everett. ``The theory of the universal wave function''. In The many-worlds interpretation of quantum mechanics. Pages 1–140. Princeton University Press (2015).
https://doi.org/10.1515/9781400868056
[47] Bogdan Mielnik. ``Mobility of nonlinear systems''. Journal of Mathematical Physics 21, 44–54 (1980).
https://doi.org/10.1063/1.524331
[48] M Reginatto and M J W Hall. ``Quantum-classical interactions and measurement: a consistent description using statistical ensembles on configuration space''. Journal of Physics: Conference Series 174, 012038 (2009).
https://doi.org/10.1088/1742-6596/174/1/012038
[49] Lucien Hardy. ``Probability theories with dynamic causal structure: a new framework for quantum gravity'' (2005). arXiv:gr-qc/0509120.
arXiv:gr-qc/0509120
[50] Giulio Chiribella, GM D’Ariano, Paolo Perinotti, and Benoit Valiron. ``Beyond quantum computers'' (2009). arXiv:0912.0195.
https://doi.org/10.1103/PhysRevA.88.022318
arXiv:0912.0195
[51] Ognyan Oreshkov, Fabio Costa, and Časlav Brukner. ``Quantum correlations with no causal order''. Nature communications 3, 1092 (2012).
https://doi.org/10.1038/ncomms2076
[52] Eugene P Wigner. ``Remarks on the mind-body question''. In Philosophical reflections and syntheses. Pages 247–260. Springer (1995).
https://doi.org/10.1007/978-3-642-78374-6_20
[53] Daniela Frauchiger and Renato Renner. ``Quantum theory cannot consistently describe the use of itself''. Nature communications 9, 3711 (2018).
https://doi.org/10.1038/s41467-018-05739-8
[54] Kok-Wei Bong, Aníbal Utreras-Alarcón, Farzad Ghafari, Yeong-Cherng Liang, Nora Tischler, Eric G. Cavalcanti, Geoff J. Pryde, and Howard M. Wiseman. ``A strong no-go theorem on the wigner's friend paradox''. Nature Physics 16, 1199–1205 (2020).
https://doi.org/10.1038/s41567-020-0990-x
[55] Eric G. Cavalcanti and Howard M. Wiseman. ``Implications of local friendliness violation for quantum causality''. Entropy 23 (2021).
https://doi.org/10.3390/e23080925
[56] David Schmid, Yìlè Yīng, and Matthew Leifer. ``A review and analysis of six extended wigner's friend arguments'' (2023). arXiv:2308.16220.
arXiv:2308.16220
[57] Yìlè Yīng, Marina Maciel Ansanelli, Andrea Di Biagio, Elie Wolfe, and Eric Gama Cavalcanti. ``Relating wigner's friend scenarios to nonclassical causal compatibility, monogamy relations, and fine tuning'' (2023). arXiv:2309.12987.
arXiv:2309.12987
[58] GM D'Ariano, Franco Manessi, and Paolo Perinotti. ``Determinism without causality''. Physica Scripta 2014, 014013 (2014).
https://doi.org/10.1088/0031-8949/2014/T163/014013
[59] John H Selby, Maria E Stasinou, Stefano Gogioso, and Bob Coecke. ``Time symmetry in quantum theories and beyond'' (2022). arXiv:2209.07867.
arXiv:2209.07867
[60] Matt Wilson, Giulio Chiribella, and Aleks Kissinger. ``Quantum supermaps are characterized by locality'' (2022). arXiv:2205.09844.
arXiv:2205.09844
[61] Venkatesh Vilasini, Nuriya Nurgalieva, and Lídia del Rio. ``Multi-agent paradoxes beyond quantum theory''. New Journal of Physics 21, 113028 (2019).
https://doi.org/10.1088/1367-2630/ab4fc4
[62] Nick Ormrod, V Vilasini, and Jonathan Barrett. ``Which theories have a measurement problem?'' (2023). arXiv:2303.03353.
arXiv:2303.03353
[63] Jonathan Barrett, Lucien Hardy, and Adrian Kent. ``No signaling and quantum key distribution''. Physical Review Letters 95, 010503 (2005).
https://doi.org/10.1103/PhysRevLett.95.010503
[64] Peter Janotta and Haye Hinrichsen. ``Generalized probability theories: what determines the structure of quantum theory?''. Journal of Physics A: Mathematical and Theoretical 47, 323001 (2014).
https://doi.org/10.1088/1751-8113/47/32/323001
[65] Martin Plávala. ``General probabilistic theories: An introduction'' (2021). arXiv:2103.07469.
arXiv:2103.07469
[66] Giacomo Mauro D'Ariano, Paolo Perinotti, and Alessandro Tosini. ``Information and disturbance in operational probabilistic theories'' (2019). arXiv:1907.07043.
https://doi.org/10.22331/q-2020-11-16-363
arXiv:1907.07043
[67] Stephen D. Bartlett, Terry Rudolph, and Robert W. Spekkens. ``Reference frames, superselection rules, and quantum information''. Rev. Mod. Phys. 79, 555–609 (2007).
https://doi.org/10.1103/RevModPhys.79.555
[68] Mohammad Bahrami, André Großardt, Sandro Donadi, and Angelo Bassi. ``The Schrödinger–Newton equation and its foundations''. New Journal of Physics 16, 115007 (2014).
https://doi.org/10.1088/1367-2630/16/11/115007
[69] Heinz-Peter Breuer and F. Petruccione. ``The theory of open quantum systems''. Oxford University Press. Oxford ; New York (2002).
https://doi.org/10.1093/acprof:oso/9780199213900.001.0001
[70] E G Beltrametti and S Bugajski. ``A classical extension of quantum mechanics''. Journal of Physics A: Mathematical and General 28, 3329–3343 (1995).
https://doi.org/10.1088/0305-4470/28/12/007
[71] Daniel Carney and Jacob M. Taylor. ``Strongly incoherent gravity'' (2023). arXiv:2301.08378.
arXiv:2301.08378
[72] Bogdan Mielnik. ``Generalized quantum mechanics''. Comm. Math. Phys. 37, 221–256 (1974).
https://doi.org/10.1007/BF01646346
[73] Asher Peres and Daniel Terno. ``Hybrid classical-quantum dynamics''. Physical Review A 63, 022101 (2001).
https://doi.org/10.1103/PhysRevA.63.022101
[74] John Selby and Bob Coecke. ``Leaks: quantum, classical, intermediate and more''. Entropy 19, 174 (2017).
https://doi.org/10.3390/e19040174
[75] John H. Selby, Carlo Maria Scandolo, and Bob Coecke. ``Reconstructing quantum theory from diagrammatic postulates''. Quantum 5, 445 (2021).
https://doi.org/10.22331/q-2021-04-28-445
[76] Bob Coecke, John Selby, and Sean Tull. ``Two roads to classicality'' (2017). arXiv:1701.07400.
arXiv:1701.07400
Cited by
[1] Thomas Galley, "Might There Be No Quantum Gravity After All?", Physics 16, 203 (2023).
[2] Nicolò Piccione, "Diffusion minimization via optimal smearing in collapse and hybrid classical-quantum gravitational models", Physical Review A 113 6, 062211 (2026).
[3] Oliviero Angeli and Matteo Carlesso, "Entanglement in Markovian hybrid classical-quantum theories of gravity", Physical Review D 112 2, 024047 (2025).
[4] Samuel Fedida and Adrian Kent, "Thermodynamics of readout devices and semiclassical gravity", Physical Review A 113 1, 012214 (2026).
[5] Isaac Layton and Harry J. D. Miller, "Restoring the second law to classical-quantum dynamics", Physical Review Research 8 2, 023238 (2026).
[6] Dhruba Jyoti Gogoi, Beyhan Puliçe, and Ali Övgün, "Quasinormal modes and greybody factors of charged symmergent black hole", The European Physical Journal C 85 11, 1243 (2025).
[7] Vittorio D'Esposito, Giuseppe Fabiano, Domenico Frattulillo, and Flavio Mercati, "Doubly Quantum Mechanics", Quantum 9, 1721 (2025).
[8] Jonathan Oppenheim, Emanuele Panella, and Andrew Pontzen, "Emergence of phantom cold dark matter from spacetime diffusion", Physical Review D 113 10, 103521 (2026).
[9] Jonathan Oppenheim, Carlo Sparaciari, Barbara Šoda, and Zachary Weller-Davies, "General form of continuous hybrid classical-quantum dynamics", Physical Review A 113 5, 052223 (2026).
[10] Jonathan Oppenheim, Andrea Russo, and Zachary Weller-Davies, "Diffeomorphism invariant classical-quantum path integrals for Nordström gravity", Physical Review D 110 2, 024007 (2024).
[11] Lin-Qing Chen and Flaminia Giacomini, "Quantum Effects in Gravity Beyond the Newton Potential from a Delocalized Quantum Source", Physical Review X 15 3, 031063 (2025).
[12] Iarley P. Lobo, Kelvin Sampaio, Gislaine Varão, Moises Rojas, and Valdir B. Bezerra, "LIV-decoherence on gravitational cat states", Physics Letters B 870, 139923 (2025).
[13] P. George Christopher and S. Shankaranarayanan, "Beyond entanglement: Diagnosing quantum mediator dynamics in gravitationally mediated experiments", Physical Review D 112 8, L081502 (2025).
[14] Spyridon Vossos, Elias Vossos, and Chariklis Ntelis, "The equations of motion in spacetime endowed with stationary metric of general relativity and the equivalent gravitational scalar generalized potential of special relativity", Classical and Quantum Gravity 43 4, 045008 (2026).
[15] Daniel R. Terno, Encyclopedia of Mathematical Physics 57 (2025) ISBN:9780323957069.
[16] Isaac Layton and Jonathan Oppenheim, "The Classical-Quantum Limit", PRX Quantum 5 2, 020331 (2024).
[17] Andrea Mari, Stefano Zippilli, and David Vitali, "Can gravity mediate the transmission of quantum information?", Physical Review D 113 2, L021905 (2026).
[18] Marek Wazny, Lehel Csillag, Miguel A. S. Pinto, and Tiberiu Harko, "Herglotz-type f(R, T) gravity", The European Physical Journal C 86 4, 430 (2026).
[19] Marek Wazny, "Black holes with regular scalar hair in Brans–Dicke gravity via the Herglotz variational principle", Physics Letters B 879, 140697 (2026).
[20] Daniel Carney, Manthos Karydas, Thilo Scharnhorst, Roshni Singh, and Jacob M. Taylor, "On the Quantum Mechanics of Entropic Forces", Physical Review X 15 3, 031038 (2025).
[21] Fabiano Feleppa, Gaetano Lambiase, and Sunny Vagnozzi, "Imprints of screened dark energy on nonlocal quantum correlations", Physical Review D 112 8, 084011 (2025).
[22] Filip Strubbe, "A five-dimensional classical framework for gravitational and quantum phenomena", Scientific Reports 16 1, 2965 (2025).
[23] Andrea Di Biagio, "Diagrams and GPTs for Quantum Gravity", Quantum Views 8, 78 (2024).
[24] Sougato Bose, Ivette Fuentes, Andrew A. Geraci, Saba Mehsar Khan, Sofia Qvarfort, Markus Rademacher, Muddassar Rashid, Marko Toroš, Hendrik Ulbricht, and Clara C. Wanjura, "Massive quantum systems as interfaces of quantum mechanics and gravity", Reviews of Modern Physics 97 1, 015003 (2025).
[25] Masahiro Hotta, Sebastian Murk, and Daniel R. Terno, "Classical-quantum gravity as quantum gravity in disguise", arXiv:2506.15291, (2025).
[26] Shogo Tomizuka and Hiroki Takeda, "Emergence of Non-Markovian Classical-Quantum Dynamics from Decoherence", arXiv:2604.06891, (2026).
[27] Nikolaos Mitrakos, Maria Papageorgiou, T. Rick Perche, and Marios Christodoulou, "When does entanglement through gravity imply gravitons?", arXiv:2601.03214, (2026).
[28] Tianfeng Feng, Chiara Marletto, and Vlatko Vedral, "Conservation Laws and the Non-Classicality of Gravity", arXiv:2311.08971, (2023).
[29] Durmuș Demir, "Emergent Gravity Completion in Quantum Field Theory, and Affine Condensation in Open and Closed Strings", arXiv:2312.16270, (2023).
[30] Zachary Weller-Davies, "Quantum gravity with dynamical wave-function collapse via a classical scalar field", arXiv:2402.17024, (2024).
[31] Jonathan Oppenheim and Muhammad Sajjad, "Stochastic modes in postquantum classical gravity", arXiv:2605.05375, (2026).
[32] Giuseppe Fabiano, Tomohiro Fujita, Akira Matsumura, and Daniel Carney, "Minimal noise in non-quantized gravity", arXiv:2603.26075, (2026).
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