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Feynman paths and weak values

Entropy 20(5)
Flack, R.Hiley, B. Department of Physics and Astronomy,
University College London,
London, UK
2018 Physics

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 et al.

The article was published in: Entropy 20(5): 367.

This work was supported (in part) by the Fetzer Franklin Fund of the John E. Fetzer Memorial Trust.