Abstract
The relationship between the real part of the weak value of the momentum operator at a post selected position is discussed and the meaning of the experimentally determined stream-lines in the Toronto experiment of Kocsis et al is re-examined. We argue against interpreting the energy flow lines as photon trajectories. The possibility of performing an analogous experiment using atoms is proposed in order that a direct comparison can be made with the trajectories calculated by Philippidis, Dewdney and Hiley using the Bohm approach.
Highlights
The notion of a weak measurement has opened up new ways to explore quantum processes [3, 15, 25, 31, 35]
Weak values of the momentum operator gives us access to the components of the energy-momentum tensor which, in turn, have a direct significance for the Bohm approach
Following on from the important experimental work of Kocsis et al [25], who measured the energy flow lines shown in Figure 1, we have, in this paper, discussed the possibility of using similar techniques to measure the two-slit trajectories of atoms
Summary
The notion of a weak measurement has opened up new ways to explore quantum processes [3, 15, 25, 31, 35]. In contrast to the usual von Neumann or strong measurement, which gives information about the eigenvalues of a dynamical operator, weak measurements enable us to obtain information about small induced phase changes. This process allows us to experimentally investigate new features of a quantum process. Weak measurements have been made to obtain values for the Poynting vector and from these measurements, sets of energy flow lines have been constructed This specific experiment used a weak electromagnetic source so that only one photon entered the apparatus at a time.
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