Finally making sense of the double-slit experiment

Abstract

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.Heisenberg picture | two-state vector formalism | modular momentum | double slit experiment B eginning with de Broglie (1), the physics community embraced the idea of particle-wave duality expressed, for example, in the double-slit experiment. The wave-like nature of elementary particles was further enshrined in the Schrödinger equation, which describes the time evolution of quantum wave packets.It is often pointed out that the formal analogy between Schrödinger wave interference and classical wave interference allows us to interpret quantum phenomena in terms of the familiar classical notion of a wave. Indeed, wave-particle duality was construed by Bohr and others as the essence of the theory and, in fact, its main novelty. Even so, the foundations of quantum mechanics community have consistently raised many questions (2-5) centered on the physical meaning of the wave function.From our perspective and consistent with ideas first expressed by Born (6) and thereafter extensively developed by Ballentine (7, 8), a wave function represents an ensemble property as opposed to a property of an individual system.What then is the most thorough approach to ontological questions concerning single particles (using standard nonrelativistic quantum mechanics)? We propose an alternative interpretation for quantum mechanics relying on the Heisenberg picture, which although mathematically equivalent to the Schrödinger picture, is very dif...

The Two-Time Interpretation and Macroscopic Time-Reversibility

“…At the heart of this reformulation lies a (dynamically) nonlocal ontology based on a time-symmetric set of deterministic operators [14,15]. A merger of these ideas into the TTI is in progress.…”

Interaction-Free Effects Between Distant Atoms

“…The contradiction, however, is only apparent. Within the TSVF, the information provided by the two boundary conditions about the quantum values prevailing between them is complementary [52][53][54]. Using this formalism and the time-dependent definition of weak values:…”

“…This time-symmetric formulation of the paradox may gain further insights when examined within the recently formulated time-symmetric Heisenberg framework [53,54]. Within this formulation, Alice's atom has a deterministic operator with regard to its energy (i.e., when projecting on the atom's energy she finds an excited state with certainty), yet it also has a nonlocal deterministic operator sensitive to the relative phase between |e A |g B and |g A |e B .…”

“…In other words, the initial (entangled) state of the system suggests that the operator σ A y σ B x is a deterministic operator, while the final strong measurements disentangle the state, giving rise to σ A z and σ B x as the set of deterministic operators. This kind of complementarity between future and past is discussed in detail in [52][53][54].…”

“…We find it more natural to assign this property to each of the atoms individually (this was recently supported by [64]). In a recent series of papers [52][53][54], we have further advocated this view, based on a realistic and deterministic account of QM relying on the combination of two boundary conditions. For a related discussion on this topic see [65,66].…”