Quantum mechanix plus Newtonian gravity violates the universality of free fall

Abstract

Classical point particles in Newtonian gravity obey, as they do in general relativity, the universality of free fall. However, classical structured particles, (for instance with a mass quadrupole moment), need not obey the universality of free fall. Quantum mechanically, an elementary “point” particle (in the particle physics sense) can be described by a localized wave packet, for which we can define a probability quadrupole moment. This probability quadrupole can, under plausible hypotheses, affect the universality of free fall. (So point-like elementary particles, in the particle physics sense, can and indeed must nevertheless have structure in the general relativistic sense once wave packet effects are included.) This raises an important issue of principle, as possible quantum violations of the universality of free fall would fundamentally impact on our ideas of what “quantum gravity” might look like. I will present an estimate of the size of the effect, and discuss where if at all it might be measured.