Optically levitated dielectric spheres are quantum-limited impulse sensors. In this talk, I will discuss their potential to discover MeV-scale, invisible states emitted in nuclear decays, including sterile neutrinos, axions, or other nucleon-coupled scalars, as well as the possibility of carrying out precision tests of electroweak physics. I will also describe how manipulating the state of ingoing light can increase the sensitivity of these devices beyond the standard quantum limit.