Newton, entanglement, and the graviton

Abstract: Many experiments have recently been proposed to test whether non-relativistic gravitational interactions can generate entanglement. In this note, I consider the extent to which these experiments can test if the graviton exists. Assuming unitarity and Lorentz invariance of the $S$-matrix, I demonstrate that this "Newtonian entanglement" requires the existence of massless bosons, universally coupled to mass, in the Hilbert space of low-energy scattering states. These bosons could be the usual spin-2 gravitons, but in principle there are other possibilities like spin-0 scalar gravitons. I suggest a concept for a more refined experiment to rule these out. The special role of $d=3+1$ spacetime dimensions and the possibility that unitarity is violated by gravity are highlighted.