Robert Flack and Basil J. Hiley
Forthcoming in S. Gao (eds.). Protective Measurements and Quantum Reality: Toward a New Understanding of Quantum Mechanics. Cambridge: Cambridge University Press (2014).
In this paper we show how the weak values, <x(t)|Pμ|ψ(t0)>/<x(t)|ψ(t0)>, are related to the T0μ(x, t) component of the energy-momentum tensor. This enables the local energy and momentum to be measured using weak measurement techniques. We also show how the Bohm energy and momentum are related to T0μ(x, t) and therefore it follows that these quantities can also be measured using the same methods. Thus the Bohm ‘trajectories’ can be empirically determined as was shown by Kocsis et al in the case of photons. Because of the difficulties with the notion of a photon trajectory, we argue the case for determining experimentally similar trajectories for atoms where a trajectory does not cause these particular difficulties. Full text