By Damián Pitalúa-García.
Submitted to arXiv on Monday 6 September 2021.
Although the standard viewpoint in theoretical physics is that the unification of quantum theory and general relativity requires the quantization of gravity and spacetime, there is not consensus about whether spacetime must fundamentally have any quantum features. Since the violation of Bell inequalities is one of the most striking features of quantum theory, we assume that the satisfaction of Bell inequalities by spacetime degrees of freedom in a spacelike separated experiment is a sensible condition for spacetime to be called “classical”. Here we show a theorem stating that spacetime degrees of freedom violate Bell inequalities in a background Minkowski spacetime if a few properties of general relativity and quantum theory have a broad range of validity, and if the quantum state reduction upon measurement is a real physical process that is completed superluminally when acting on distant quantum particles in a quantum entangled state. In contrast to the Eppley-Hannah argument for the necessity of quantizing the gravitational field, we discuss the validity of our assumptions, our thought experiment does not require to manipulate or detect gravitational waves, and our theorem does not rely on the conservation of momentum or on the uncertainty principle.