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arXiv:2604.22481

Double Slit Experiment in the Heisenberg Picture of Quantum Mechanics

Vlatko Vedral

quant-phSubmitted Apr 24, 2026• Announced Apr 27, 2026• 0 citations
arXivHTMLPDF

Abstract

We present the standard double slit experiment with non-relativistic particles in the Heisenberg Picture of quantum mechanics. Our motivation is threefold. First and foremost, and contrary to some claims in the literature, we show that there is no need to talk about non-locality when explaining the interference fringes. Secondly, we emphasise the fact that even in the non-relativistic regime, and in order to preserve locality, we should define the position and momentum observables of a particle as functions of both space and time (and not just time). Thirdly, our presentation compares the projective measurements in the Heisenberg picture with the "Church of the Larger Hilbert Space", the latter of which is seldom discussed in the Heisenberg picture of quantum mechanics.

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We present the standard double slit experiment with non-relativistic particles in the Heisenberg Picture of quantum mechanics. Our motivation is threefold. First and foremost, and contrary to some claims in the literature, we show that there is no need to talk about non-locality when explaining the interference fringes. Secondly, we emphasise the fact that even in the non-relativistic regime, and in order to preserve locality, we should define the position and momentum observables of a particle as functions of both space and time (and not just time). Thirdly, our presentation compares the projective measurements in the Heisenberg picture with the "Church of the Larger Hilbert Space", the latter of which is seldom discussed in the Heisenberg picture of quantum mechanics.
]. 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.
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 Schrödinger 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.
We develop an approach to quantum interference phenomenon which makes the characteristics of the problem more conspicuous and brings out more physical concepts. We do this by discussing the idea of deterministic quantum experiments using the Heisenberg picture. The variables that are relevant for describing interference are modular variables. These variables obey non-local equations of motion and can be used to follow the time evolution of a system without disturbing it. 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). While the Heisenberg picture and the Schrodinger pictures are equivalent formulations of quantum mechanics, nevertheless, the results discussed here support a new approach to quantum mechanics which has led to new insights, new intuitions, new experiments, and even the possibility of new devices that were missed from the old perspective.
The double-slit experiment has stood for a century as the paradigmatic demonstration of quantum superposition: the standard interpretation holds that a particle passes through both slits simultaneously, existing in a superposition of two spatially separated states. This paper proposes a physically distinct alternative: the particle's matter wave — a real physical wave propagating through space in accordance with de Broglie's relation λ = h/p — passes through both slits, while the particle itself (matter) remains in an undetermined state until a constructive interference maximum is formed at the detection screen. The particle does not simultaneously occupy two locations; the wave does. This distinction eliminates the need for superposition as an ontological commitment while fully reproducing the observed interference pattern. We further show that the disappearance of the interference pattern upon which-path measurement is explained without invoking wavefunction collapse: the measurement interaction redirects the matter wave to a single-slit geometry, eliminating the two-wave interference condition. Three experimentally testable predictions distinguish this framework from the standard interpretation: (1) weak-measurement trajectory reconstruction should reveal single particle paths inconsistent with simultaneous two-slit passage; (2) diffraction fringe spacing should depend on the mass density of the slit material, because denser slit edges generate a steeper refractive-index gradient for the matter wave; (3) the fringe pattern should exhibit a density-dependent phase shift measurable with current matter-wave interferometry technology. This reinterpretation requires no new mathematical formalism — the Schrödinger equation and Born's rule are retained — but replaces the ontological claim of simultaneous multi-location existence with the physically consistent picture of matter-wave propagation through an undetermined-state particle.
Abstract The double-slit experiment is a classic experiment that presents the clearest manifestation of wave-particle duality, one of the fundamental principles of quantum mechanics. The double-slit experiment still remains the phenomenon that demonstrates wave-particle duality at the most fundamental level. This phenomenon quantitatively and conceptually demonstrates that microscopic objects can behave like both waves and particles at the same time. This article provides an in-depth analysis of the physical nature of dualism, the mechanism of formation of the interference pattern, and the impact of the act of observation on the dynamics of quantum systems. The need for a new perspective on this topic is due to the fact that the current uncertainty in the interpretation of quantum reality has not yet been completely eliminated, and the boundaries between classical and quantum behavior in microscopic objects are still being explored. The results presented here restructure the deep mechanisms of the interference picture, more clearly frame the relationship between observation and wavefunction collapse, and provide a quantum. Since the article attempts to provide a complete answer to the mechanism of the formation of wave-particle duality, extensive space is given to sections such as historical development, theoretical models, modern research, etc. New approaches to this phenomenon have been developed using modern research and string theory. As a result, a new mathematical expression has been proposed that explains the reasons for the initial emergence of wave-particle duality, and is also important for string theory. The article explains the measurement problem with a more effective physical structure and ontological model.
We propose a pedagogical presentation of measurement in the de Broglie-Bohm interpretation. In this heterodox interpretation, the position of a quantum particle exists and is piloted by the phase of the wave function. We show how this position explains determinism and realism in the three most important experiments of quantum measurement: double-slit, Stern-Gerlach, and EPR-B. First, we demonstrate the conditions in which the de Broglie-Bohm interpretation can be assumed to be valid through continuity with classical mechanics. Second, we present a numerical simulation of the double-slit experiment performed by Jönsson in 1961 with electrons. It demonstrates the continuity between classical mechanics and quantum mechanics. Third, we present an analytic expression of the wave function in the Stern-Gerlach experiment. This explicit solution requires the calculation of a Pauli spinor with a spatial extension. This solution enables us to demonstrate the decoherence of the wave function and the three postulates of quantum measurement. Finally, we study the Bohm version of the Einstein-Podolsky-Rosen experiment. Its theoretical resolution in space and time shows that a causal interpretation exists where each atom has a position and a spin.