Zeno Paradox for Bohmian Trajectories: The Unfolding of the Metatron

Maurice de Gosson, Basil Hiley

Published 2010-10-13, updated 2011-09-05Version 3

We analyse the track of an {\alpha}-particle passing through a cloud chamber using the Bohm theory and show that the resulting classical track has its origins in the quantum Zeno effect. By assuming the ionised gas molecules reveal the positions of the {\alpha}-particle on its trajectory and using these positions in a short time propagator technique developed by de Gosson, we show it is the failure of the quantum potential to develop quickly enough that leads to the appearance of the classical trajectory. Bohm and Hiley have already argued that it is this failure of the quantum potential to develop appropriately that prevents an Auger electron from undergoing a transition if continuously watched. This allows us to conclude that, in general, it is the suppression of the quantum potential that accounts for the quantum Zeno effect.