Preprint Article Version 1 This version is not peer-reviewed

# Feynman Paths and Weak Values

Version 1 : Received: 16 April 2018 / Approved: 18 April 2018 / Online: 18 April 2018 (14:29:26 CEST)

A peer-reviewed article of this Preprint also exists.

Flack, R.; Hiley, B.J. Feynman Paths and Weak Values. Entropy 2018, 20, 367. Flack, R.; Hiley, B.J. Feynman Paths and Weak Values. Entropy 2018, 20, 367.

Journal reference: Entropy 2018, 20, 367
DOI: 10.3390/e20050367

## Abstract

There has been a recent revival of interest in the notion of a trajectory' of a quantum particle. In this paper we detail the relationship between Dirac's ideas, Feynman paths and the Bohm approach. The key to the relationship is the weak value of the momentum which Feynman calls a transition probability amplitude. With this identification we are able to conclude that a Bohm trajectory' is the average of an ensemble of actual individual stochastic Feynman paths. This implies that they can be interpreted as the mean momentum flow of a set of individual quantum processes and not the path of an individual particle. This enables us to give a clearer account of the experimental two-slit results of Kocsis {\em et al.}}

## Subject Areas

Dirac 'trajectories'; Feynman paths; Weak values; Bohm approach.