Testing trajectory-based determinism via time probability distributions

It is notorious that quantum mechanics (QM) cannot predict well-defined values for all physical quantities. Less well-known, however, is the fact that QM is unable to furnish probabilistic predictions even in emblematic scenarios such as the double-slit experiment. In contrast, equipped with postulate trajectories, Bohmian mechanics (BM) has inherited more predictive power. It follows that, contrary to common belief, QM and BM are not just different interpretations but distinct theories. This work formalizes the aforementioned assertions and illustrates them through three case studies: (i) free particle, (ii) free fall under a uniform gravitational field, and (iii) the double-slit experiment. Specifically, we introduce a prescription for constructing a flight-time probability distribution within generic trajectory-equipped theories. We then apply our formalism to BM and derive probability distributions that are unreachable by QM. Our results can, in principle, be tested against real experiments, thereby assessing the validity of Bohmian trajectories.