  We explore the possibility that the connection between spin and statistics in
quantum physics is of dynamical origin. We suggest that the gravitational field
could provide a fully local mechanism for the phase that arises when fermionic
and bosonic particles are exchanged. Our results hold even if the symmetry of
space and time is Galilean, thus establishing that special relativity is not
needed to explain the existence of spin (although it does motivate the
introduction of creation and annihilation of particles, but this is a separate
issue). We provide a model for the coupling between a particle of general spin
and the gravitational field and discuss it within the context of both the
equivalence principle and the Sagnac effect. This leads us to present a new
experiment for testing the quantum nature of the gravitational field.
