Weak Value and the Wave-Particle Duality

TL;DR

This paper explores the connection between weak values in quantum mechanics and wave-particle duality, showing how real and imaginary parts relate to particle and wave aspects, respectively, and demonstrates this in the double slit experiment.

Contribution

It reveals a direct link between weak values and wave-particle duality, providing new insights into quantum foundations and measurement without destroying interference.

Findings

Weak value's real part relates to particle nature.

Imaginary part relates to wave nature.

Particle trajectories inferred without destroying interference.

Abstract

The weak value, introduced by Aharonov et al. to extend the conventional scope of physical observables in quantum mechanics, is an intriguing concept which sheds new light on quantum foundations and is also useful for precision measurement, but it poses serious questions on its physical meaning due to the unconventional features including the complexity of its value. In this paper we point out that the weak value has a direct connection with the wave-particle duality, in the sense that the wave nature manifests itself in the imaginary part while the particle nature in the real part. This is illustrated by the double slit experiment, where we argue, with no conflict with complementarity, that the trajectory of the particle can be inferred based on the weak value without destroying the interference.