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Is the wave superposition necessary for the interference phenomenology?

Román Castañeda

Published Mar 28, 2022• 1 citation
Publisher

Abstract

The wave superposition is considered the phenomenological principle of light interference, as well as an accurate procedure to calculate the quantum probability of the buildup of single matter particle interference patterns.However, it cannot provide a unified phenomenological framework to explain both types of interference.In this paper, a unified framework is proposed which leads to a unique principle for interference of both light waves and single matter particles.It is shown that the term interference denotes the confinement of the light irradiance or the single matter particles in spatially structured Lorentzian wells, due to the geometric potential determined by the prepared non-locality at the mask plane.This new description does not resort to the assumption of wave superposition, so that the setup configuration plays the main role.

DOI
10.7149/opa.55.1.51090

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The wave superposition is considered the phenomenological principle of light interference, as well as an accurate procedure to calculate the quantum probability of the buildup of single matter particle interference patterns.However, it cannot provide a unified phenomenological framework to explain both types of interference.In this paper, a unified framework is proposed which leads to a unique principle for interference of both light waves and single matter particles.It is shown that the term interference denotes the confinement of the light irradiance or the single matter particles in spatially structured Lorentzian wells, due to the geometric potential determined by the prepared non-locality at the mask plane.This new description does not resort to the assumption of wave superposition, so that the setup configuration plays the main role.
Recently, the novel confinement principle in spatially-structured Lorentzian wells was reported to describe in a unified way the interference of classical waves and singular quantum particles in a causal framework in ordinary space. The phenomenology derived from this principle offers significant advantages over the conventional classical and quantum formalisms of interference founded on wave superposition. This paper presents a conceptual analysis of such a principle and its main implications indicating its fundamental differences from the standard descriptions.
Interference of light and material particles is described with a unified model which does not need to assume the wave-particle duality. A moving particle is associated with a region of spatial correlated points named coherence cone. Its geometry depends on photon or particle momentum and on the parameters of the experimental setup. The final interference pattern is explained as a spatial distribution of particles caused by the coherence cone geometry. In the present context, the wave front superposition principle, wave-particle duality and wave-collapse lose their meaning. Fits of observed single electron and single molecule interference patterns together with the simulation of expected near-field molecule interference (Talbot carpet) demonstrate the model validity.
Abstract In spite of its accurate prediction of the experimental outcomes of double-hole single particle interference, quantum mechanics does not provide a phenomenological description of the individual realizations of the experiment. By defining a non-locality function and considering the non-paraxial solution of the time-independent Schrödinger equation by the Green’s theorem, we introduce a geometrical potential which leads to an outstanding result. The geometric potential allows the description of spatially structured Lorentzian wells in the volume between the double-hole mask and the detector. The buildup of the interference patterns results from the confined propagation of single particles through these Lorentzian wells. The phenomenological implications of this description are discussed and illustrated by numerical examples, and its compatibility with quantum mechanical predictions is also shown. A further, non-trivial advantage of this model over the conventional formalism, is that the present quantum probability density can be exactly calculated both in the near and far field conditions.
Abstract Non-paraxial interference has recently been explained as light energy confinement in spatially structured Lorentzian wells. This theory describes, in the same way, single particle interference in ordinary space too. Such an alternative thought is discussed here in the framework of a quantum formalism, which introduces confinement operators and density matrices of space states for the first time. Therefore, Lorentzian wells are characterized as the base states of space, which are excited by the geometric potential to produce interference. Geometrical uncertainty and space entanglement are discussed as novel features that approach the proposed theory in the quantum context. This formalism provides insight into the role of space in interference.
The main goal of the present article is to elucidate the wave-particle duality problem by giving an unambiguous mathematical expression of the origin of the wave nature of particles. It is indicated that the wave nature of particles is originated from the multidimensional universe approach and under the one-dimensional universe assumption the wave nature vanishes. The one-dimensional universe assumption also gives a deterministic explanation for the double-slit experiment and answers how a single electron can interfere with itself. The locality paradox is also discussed. It is demonstrated that the same principle shows how a local measurement can determine the state of a distant system. The theoretical framework presented here may help us to understand various quantum physics phenomena. i.e., the superposition principle, wave function collapse, and entanglement.
Abstract Quantum interference plays a central role in the realm of quantum particles, revealing their wave‐like nature and probabilistic behavior. It relies on the concept of superposition, where the probability amplitudes of different processes that contribute to the given phenomenon interfere with each other. When combined, their phases can interfere either constructively or destructively. Quantum interference manifests in three distinct forms: optical interference, arising from the interaction of light waves and forming the basis for technologies such as lasers and optical filters; interference via atoms, which involves manipulating atomic states to control light–matter interactions and enables techniques like Stimulated Raman Adiabatic Passage and Electromagnetically Induced Transparency in quantum information processing; and interference of atoms with themselves, in which the matter waves of single atoms interfere with each other, as employed in precision measurements such as atom interferometry–a crucial tool for applications in quantum mechanics and precision navigation. These diverse forms of quantum interference have profound implications for numerous scientific disciplines, demonstrating that interference can involve particles beyond just photons.