Control of particle propagation beyond the uncertainty limit by interference between position and momentum

TL;DR

This paper demonstrates that quantum interference can control particle propagation beyond classical limits, challenging Newtonian causality by violating a propagation inequality through optimized Gaussian superpositions.

Contribution

It introduces a quantitative method to localize wavefunction components and shows that optimized superpositions violate classical propagation bounds by over 5%.

Findings

Violation of particle propagation inequality by more than 5%.

Quantum interference relates initial and future positions beyond classical causality.

Fundamental link between quantum interference and causality limits.

Abstract

As shown in Phys. Rev. A 96, 020101(R) (2017), it is possible to demonstrate that quantum particles do not move along straight lines in free space by increasing the probability of finding the particles within narrow intervals of position and momentum beyond the "either/or" limit of 0.5 using constructive quantum interference between a component localized in position and a component localized in momentum. The probability of finding the particle in a corresponding spatial interval at a later time then violates the lower bound of the particle propagation inequality which is based on the validity of Newton's first law. In this paper, the problem of localizing the two state components in their respective target intervals is addressed by introducing a set of three coefficients that describe the localization of arbitrary wavefunctions quantitatively. This characterization is applied to a superposition of Gaussians, obtaining a violation of the particle propagation inequality by more than 5 percent if the width of the Gaussian wavefunction is optimized along with the size of the position and momentum intervals. It is shown that the violation of the particle propagation inequality originates from the fundamental way in which quantum interferences relate initial position and momentum to the future positions of a particle, indicating that the violation is a fundamental feature of causality in the quantum limit.