Weak Values of Momentum of the Electromagnetic Field: Average Momentum Flow Lines, Not Photon Trajectories

In a recent paper Mahler et al. have argued that the experi- ments of Kocsis et al. provide experimental evidence for Bohmian mechanics. Unfortunately these experiments used relativistic, zero rest mass photons whereas Bohmian mechanics is based on non-relativistic Schr ̈odinger particles having non-zero rest mass. The experimental results can be accounted for in terms of a different approach based on the electromagnetic field that was already outlined by Bohm in an appendix of the second of his 1952 papers.

A subsequent develop- ment of this approach by Bohm, Hiley, Holland, Kaloyerou, Lam and Dewdney, shows in detail how this theory accounts for experimental quantum phenomena in general. Using this theory, we are led to the conclusion that the experiments have constructed mean momentum flow lines by measuring the real part of what we term the weak Poynt- ing vector. These results support and clarify the analysis of Bliokh et al.

The experimental flow lines can be constructed independently of the number of photons in the beam leading to the conclusion that flow lines cannot be interpreted as ‘photon trajectories’. We discuss exactly how the notion of a photon arises in the field approach in the light of weak values.

The article was published in: arXiv:1611.06510

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