On free fall of fermions and antifermions

Abstract

We propose a model describing spin-half quantum particles in curved spacetime in the framework of quantum field theory. Our model is based on embodying Einstein's equivalence principle and general covariance in the definition of quantum-particle states. With this model at hand, we compute several observables which characterise spin-half quantum particles in a gravitational field. In particular, we find that spin precesses in a normal Fermi frame, even in the absence of torsion. The effect appears to be complementary to free-fall non-universality we have recently reported about for spinless quantum particles. Furthermore, we find that quantum-particle gravitational-potential energy is insensitive to wave-packet spreading in the Earth's gravitational field, that is responsible for the non-universality of free fall in quantum theory. This theoretical result provides another channel for the experimental study of our quantum-particle model by using gravitational spectrometers. Finally, we also find that (elementary) fermions and antifermions are indistinguishable in gravity.