Towards the Particle Spectrum, Tickled by a Distant Massive Object

To investigate the gravitational effects of massive objects on a typical observer, we studied the dynamics of a test particle following BMS3 geodesics. We constructed the BMS3 framework using the canonical phase space formalism and the corresponding Hamiltonian. We focused on analyzing these effects at fine scales of spacetime, which led us to quantization of the phase space. By deriving and studying the solutions of the quantum equations of motion for the test particle, we obtained its energy spectrum and explored the behavior of its wave function. These findings offer a fresh perspective on gravitational interactions in the context of quantum mechanics, providing an alternative approach to traditional quantum field theory analyses.