Composite particles with minimum uncertainty in spacetime

Composite particles such as atoms and molecules are promising tools for future experiments testing fundamental physics. However, as experiments advance in complexity and precision, the loss of spatial coherence is a problem which will only increase. In all theoretical studies of propagating composite particles, their internal energy components delocalise, and their spatial coherence is destroyed. This calls into question the suitability of composite particles as experimental tools, and is contrary to our understanding of atoms and molecules as cohesive entities with well-localised spacetime trajectories.
Here, we show the optimal way to prepare composite particles to fully avoid the delocalization and related loss of spatial coherence. We find the correct approach needed to discuss limitations on the space-time trajectories of composite quantum particles: it requires a new uncertainty principle which includes mass as an operator. We show that the quantum states which minimise the inequality propagate coherently in spacetime, and transform covariantly under boosts. This result highlights the fundamental differences between phase and configuration space for composite particles, while the new minimum uncertainty states will find applications in upcoming precision experimental tests.