On the polarization states of the de Broglie gravitational wave

The pilot-wave theory is an alternative, but less used, interpretation of Quantum Mechanics. In that framework, elementary particles are guided by a wave and move along well defined trajectories. A fascinating idea is the possibility to describe the de Broglie wave as oscillations of the gravitational field, thereby giving geometrical meaning to the pilot-wave of a quantum corpuscle. In this work we will investigate the polarizations of the de Broglie gravitational wave and we will find that the spin-2 metric perturbation breaks down into two tensor (helicity-2), two vector (helicity-1) and two scalar (helicity-0) components. We will show that these dynamical variables satisfy the equation of the harmonic oscillator, meaning that they represent the physical degrees of freedom of the wave. We will also propose a method to measure the scalar modes, containing longitudinal components that are absent in standard transverse gravitational waves.