Shah, Dhairya: Worldline Consistency as a Constraint on Classical and Quantum Histories

We formulate a condition for the admissibility of parametrized trajectories in relativistic spacetime based on compatibility between worldline ordering and causal structure. A trajectory represents the history of a single physical system only if its parameter ordering agrees with the causal ordering defined by the spacetime metric. It follows that any trajectory for which this condition fails cannot be realized as a future directed causal worldline in a spacetime. Such trajectories therefore do