Finally making sense of the double-slit experiment

Yakir Aharonov, Eliahu Cohen, Fabrizio Colombo, Tomer Landsberger, Irene Sabadini, Daniele C. Struppa, Jeff Tollaksen

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


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 preand 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.

Original languageEnglish
Pages (from-to)6480-6485
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number25
StatePublished - 20 Jun 2017
Externally publishedYes

Bibliographical note

Funding Information:
Y.A., D.C.S., and J.T. acknowledge support, in part, from the Fetzer Franklin Fund of the John E. Fetzer Memorial Trust. Y.A. acknowledges support from Israel Science Foundation Grant 1311/14, Israeli Centers of Research Excellence "Circle of Light," and the German-Israeli Project Cooperation (DIP). E.C. was supported by the European Research Council Advanced Grant Nonlocality in Space and Time. Funding for this research was provided by the Institute for Quantum Studies at Chapman University. This research was also supported, in part, by the Perimeter Institute for Theoretical Physics. Research at the Perimeter Institute for Theoretical Physics is supported by the Government of Canada through the Department of Innovation, Science and Economic Development and the Province of Ontario through the Ministry of Research and Innovation.


  • Double slit experiment
  • Heisenberg picture
  • Modular momentum
  • Two-state vector formalism


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