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.
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.
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 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 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 propose a quantum framework where cavity-induced nonlocal stochastic quantized momentum transfer governs double-slit interference of single eelectrons, replacing self-interference, wavefunction collapse, and Schrödinger’s wavefunction description. Using Heisenberg’s operator formalism, we model the electron’s interaction with the double slit as a quantized field potential. This approach explains interference via discrete momentum transfer through stochastic cavity modes. We explore its role as a non-local hidden-variable mechanism, predicting deviations in Bell violation, and finer discrete interference fringes in short cavity-mode wavelength regimes, opening new avenues for experimental verification. Our new interpretation of quantum dynamics sheds light on long-standing debates about quantum reality, hidden variables, wave-function superposition and Schrödinger’s cat, the illusion of self-interference of a single electron, and instantaneous wavefunction collapse misconception in the measurements. Our theory possesses the deterministic description of an electron a stochastic yet nonlocal hidden variable characteristic of the quantized cavity modes. It meets Einstein’s desire for a more complete theory and bridges the gap between physical reality and the incomplete conventional quantum theory that requires confusing Copenhagen or many-world interpretations.
In a new approach to explain double-slit interference "from the single particle perspective" via "systemic nonlocality" , we answer the question of how a particle going through one slit can "know" about the state of the other slit. We show that this comes about by changed constraints on assumed classical sub-quantum currents, which we have recently employed [1] to derive probability distributions and Bohm-type trajectories in standard double-slit interference on the basis of a modern, 21st century classical physics. Despite claims in the literature that this scenario is to be described by a dynamical nonlocality that could best be understood in the framework of the Heisenberg picture [2], we show that an explanation can be cast within the framework of the intuitively appealing Schrödinger picture as well. We refer neither to potentials nor to a "quantum force" or some other dynamics, but show that a "systemic nonlocality" may be obtained as a phenomenon that emerges from an assumed sub-quantum kinematics, which is manipulated only by changing its constraints as determined by the changes of the apparatus. Consequences are discussed with respect to the prohibition of superluminal signaling by standard relativity theory.
Abstract For about a century, physicists have been debating over the behavior of particles on a microscopic scale. Although the principle of the wave-particle duality is accepted in the scientific community, many experiments with puzzling results are still challenging quantum mechanics until now, such as the double slit experiment, entanglement, interferences of a single electron, or delayed choice quantum eraser. In this article, we shall bring forth explanations for some of these experiments. Unlike standard quantum mechanics (SQM) built by Schr¨odinger1 and P.Dirac2 which considers that the wave function is an abstract mathematical tool, our model takes up the concept of the pilot wave once initiated by physicists De Broglie and D.Bohm,3 who suggested that the wave associated to a quantum object has a real existence and that it is not simply a wave of probability. We shall discuss how this old-new conception of reality renders quantum mechanics ultimately less mysterious than it seems.