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Proc Natl Acad Sci U S A. 2017 Jun 20;114(25):6480-6485. doi: 10.1073/pnas.1704649114. Epub 2017 May 31.

Finally making sense of the double-slit experiment.

Author information

Institute for Quantum Studies, Chapman University, Orange, CA 92866;
Schmid College of Science and Technology, Chapman University, Orange, CA 92866.
School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel.
H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom;
Dipartimento di Matematica, Politecnico di Milano, 9 20133 Milan, Italy.
Institute for Quantum Studies, Chapman University, Orange, CA 92866.


Feynman stated that the double-slit experiment "…has in it the heart of quantum mechanics. In reality, it contains the only mystery" and that "nobody can give you a deeper explanation of this phenomenon than I have given; that is, a description of it" [Feynman R, Leighton R, Sands M (1965) The Feynman Lectures on Physics]. We rise to the challenge with an alternative to the wave function-centered interpretations: instead of a quantum wave passing through both slits, we have a localized particle with nonlocal interactions with the other slit. Key to this explanation is dynamical nonlocality, which naturally appears in the Heisenberg picture as nonlocal equations of motion. This insight led us to develop an approach to quantum mechanics which relies on pre- and postselection, weak measurements, deterministic, and modular variables. We consider those properties of a single particle that are deterministic to be primal. The Heisenberg picture allows us to specify the most complete enumeration of such deterministic properties in contrast to the Schrödinger wave function, which remains an ensemble property. We exercise this approach by analyzing a version of the double-slit experiment augmented with postselection, showing that only it and not the wave function approach can be accommodated within a time-symmetric interpretation, where interference appears even when the particle is localized. Although the Heisenberg and Schrödinger pictures are equivalent formulations, nevertheless, the framework presented here has led to insights, intuitions, and experiments that were missed from the old perspective.


Heisenberg picture; double slit experiment; modular momentum; two-state vector formalism

Conflict of interest statement

Conflict of interest statement: Y.A. is a visiting scholar at Perimeter Institute, and has received funding from reviewer N.T.’s institution, Perimeter Institute.

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