However, attempts at a quantum theory of gravity lead to nonlocal, Lorentz-invariant equations of motion whose phenomenology implies nonlinearities in the modified Schrodinger equation for massive quantum systems . I will describe our experimental work that (incidentally) probes such a hypothesis. We use single photon detectors to probe the motional states of a superfluid Helium-4 resonator of mass ~ 1 ng. The arrival times of Stokes and anti-Stokes photons (scattered by the resonator’s acoustic mode) are used to measure the resonator’s phonon coherences . With the mechanical resonator initialized to a coherent state (displaced thermal state of mean phonon number ~ 40,000 and phonon number variance ~ 1), a sensitive precision measurement of its coherence allows us to bound such nonlocality length scales to < 10^-18 m, comparable to the bound given by experiments at the Large Hadron Collider (< 10^-19 m). I will also describe our ongoing efforts to improve this bound by ~ 6 orders of magnitude.
 A. Belenchia et al., Physical Review Letters 116, 161303 (2016)
 Y.S.S. Patil et al., Physical Review Letters 128, 183601 (2022)