Proposal for an experiment to measure the Hausdorff dimensionof quantum-mechanical trajectories

We make a proposal for a Gedanken experiment, based on the Aharonov-Bohm effect, regarding how to measure in principle the zigzagness of the trajectory of propagation (aberration from its classical trajectory) of a massive particle in quantum mechanics. Experiment I is conceived to show that contributions from quantum paths aberrating from the classical trajectory are directly observable. Experiment II is conceived to measure average length, scaling behavior, and critical exponent (Hausdorff dimension) of quantum-mechanical paths.