Feynman stated that the double-slit experiment “...has in it the heart of quantum mechanics. In reality, it contains the only mystery,” and “nobody can give you a deeper explanation of this phenomenon than I have given; that is, a description of it.” We rise to the challenge with a novel alternative to the wavefunction-centered interpretations: instead of a quantum wave passing through both slits, we have a localized particle with non-local 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 a new approach to quantum mechanics using pre- and post-selection, weak measurements, deterministic and modular variables. We consider those properties of a single particle which 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 wavefunction which remains an ensemble property. We exercise this approach by analyzing a version of the double-slit experiment augmented with post-selection, showing only it, and not the wavefunction approach, can be accommodated within a time-symmetric interpretation, where interference appears even when the particle is localized. While the Heisenberg and Schrödinger pictures are equivalent formulations, nevertheless, the framework presented here has led to new insights, new intuitions and new experiments that were missed from the old perspective.
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