I originally posted it here: http://physics.stackexchange.com/questions/183041/equivalence-principle-for-test-fields In order to get a more professional answer, I paste it in the following.
My question is very simple. We all know that, for a test particle(classical) in a gravitational field, the motion is only determined by the geodesic lines(let's forget about the initial conditions for now), and has no dependence on the "structure" of the particle, such as spin(in the classical sense), charge, etc..
But let's now consider the motion of a test field, scalar, spinor, vector or tensor, under gravity. I know how to describe this kind of motion using the corresponding field equations, Klein-Gordon equation, covariant Dirac equation, or master equations accounting for any masslesss fields. Of course, the results do depend on the spin(quantum). But is there a way to think about this in a "equivalence principle" sense, which can satisfactorily account for the difference due to spin?
Thank you in advance!