We address the problem of interference using the Heisenberg picture and highlight some new aspects through the use of pre-selection, post-selection, weak measurements and modular variables. We present a physical explanation for the different behaviors of a single particle when the distant slit is open or closed; instead of having a quantum wave that passes through all slits, we have a localized particle with non-local interactions with the other slit(s). We introduce a Gedanken experiment to measure this non-local exchange. While the Heisenberg and Schrodinger pictures are equivalent formulations of quantum mechanics, nevertheless, the results discussed here support a new approach to quantum mechanics which has lead to new insights, new intuitions, new experiments and even the possibility of new devices that were missing from the old perspective.
Tollaksen, Jeff, Yakir Aharonov, Aharon Casher, Tirzah Kaufherr, and Shmuel Nussinov. "Quantum interference experiments, modular variables and weak measurements." New Journal of Physics 12.1 (2010): 013023. doi: 10.1088/1367-2630/12/1/013023
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