Time averaging of weak values - consequences for time-energy and coordinate-momentum uncertainty

Abstract

Using the quantum transition path time probability distribution we show that time averaging of weak values leads to unexpected results. We prove a weak value time energy uncertainty principle and time energy commutation relation. We also find that time averaging allows one to predict in advance the momentum of a particle at a post selected point in space with accuracy greater than the limit of $\hslash /2$ as dictated by the uncertainty principle. This comes at a cost - it is not possible at the same time to predict when the particle will arrive at the post selected point. A specific example is provided for one dimensional scattering from a square barrier.

14 pages, 2 figures

References in corpus (3)

• Grounding Bohmian Mechanics in Weak Values and Bayesianism
• Sequential weak measurement
• Weak Measurement and its Experimental Realisation

Cited by in corpus (4)

• Determination of weak values of quantum operators using only strong measurements
• The influence of the symmetry of identical particles on flight times
• Uncertainty relations for time averaged weak values
• Superluminal tunneling times without superluminal signaling: Fading of the MacColl-Hartman effect at early times