Probing classical and quantum violations of the equivalence of active and passive gravitational mass

The equivalence of active and passive (EAP) gravitational mass is one of the most fundamental principles of gravity. But in contrast to the usual equivalence of inertial and (passive) gravitational mass, the EAP has not received much attention. Here we revisit this principle and show how it can be used to probe quantum gravity in laboratory-based experiments. We first examine how the dynamics under EAP violations affects classical systems and show that new laboratory tests can be performed, to improve over the current experimental bounds and to test new manifestations of EAP violations. We then extend the analysis to the quantum domain, where quantized energy contributes to mass and the EAP principle can thus shed light on how quantum source masses would gravitate. We show that experiments with cold polar molecules, and future experiments with nuclear atomic clocks, can test the quantum EAP in a regime where quantum gravity phenomenology could become relevant. Our results open new opportunities for fundamental tests of gravity in high-precision laboratory experiments that can shed light on foundational principles of gravity and its interface with quantum theory.