A no-go theorem on the nature of the gravitational field beyond quantum theory

Thomas D. Galley1, Flaminia Giacomini1, and John H. Selby2

1Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, N2L 2Y5, Canada
2ICTQT, University of Gdańsk, Wita Stwosza 63, 80-308 Gdańsk, Poland

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Recently, table-top experiments involving massive quantum systems have been proposed to test the interface of quantum theory and gravity. In particular, the crucial point of the debate is whether it is possible to conclude anything on the quantum nature of the gravitational field, provided that two quantum systems become entangled solely due to the gravitational interaction. Typically, this question has been addressed by assuming a specific physical theory to describe the gravitational interaction, but no systematic approach to characterise the set of possible gravitational theories which are compatible with the observation of entanglement has been proposed. Here, we remedy this by introducing the framework of Generalised Probabilistic Theories (GPTs) to the study of the nature of the gravitational field. This framework enables us to systematically study all theories compatible with the detection of entanglement generated via the gravitational interaction between two systems. We prove a no-go theorem stating that the following statements are incompatible: i) gravity is able to generate entanglement; ii) gravity mediates the interaction between the systems; iii) gravity is classical. We analyse the violation of each condition, in particular with respect to alternative non-linear models such as the Schrödinger-Newton equation and Collapse Models.

In recent years, there has been a surge of interest in table-top experiments to test the quantum nature of the gravitational field. The goal of these papers is to demonstrate the quantum nature of the gravitational field based on the generation of entanglement between two quantum systems which interact solely gravitationally. This type of experiment will most likely be within the reach of technology in the next few decades.

In this paper we take a theory-independent approach which allows us to constrain the nature of the gravitational field independently of the specific model assumed for gravity. In order to do so, we introduce the tools of Generalised Probabilistic Theories to the study of the gravitational field. We prove a no-go theorem which makes precise exactly which properties of the gravitational field are consistent with the observation of gravitationally induced entanglement. The strength of this approach is to provide a method to test the internal consistency of different assumptions. One possibility we find is that the gravitational field need not be quantum, but could be described by some other non-classical theory.

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