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National Meeting on Optics and Andean and Caribbean Conference on Optics and its Applications (ENO-CANCOA)

Geometric Uncertainty in Non-Paraxial Interference

Laura Bravo, Daniel Peláez, Valentina López, Samuel Huertas, Román Castañeda

Published Jun 12, 2024• 0 citations
Publisher

Abstract

A new type of indetermination is discussed in the framework of the exact (non-paraxial) and generalized description of interference in ordinary space for light, photons and matter particles. This description is based on the novel phenomenological principle of confinement in geometric states of space. It is shown that space states with vertices within a sphere of diameter no greater than a fixed value must be ground states of space, which can be represented by a single ground state with vertex at any point of this sphere. This geometric uncertainty differs from Heisenberg's uncertainty which was established for matter particles and deals with dynamical quantities. However, it is shown that geometric uncertainty establishes limitations for Heisenberg's uncertainty.

DOI
10.1109/eno-cancoa61307.2024.10751112

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A new type of indetermination is discussed in the framework of the exact (non-paraxial) and generalized description of interference in ordinary space for light, photons and matter particles. This description is based on the novel phenomenological principle of confinement in geometric states of space. It is shown that space states with vertices within a sphere of diameter no greater than a fixed value must be ground states of space, which can be represented by a single ground state with vertex at any point of this sphere. This geometric uncertainty differs from Heisenberg's uncertainty which was established for matter particles and deals with dynamical quantities. However, it is shown that geometric uncertainty establishes limitations for Heisenberg's uncertainty.
In this article, a novel meaning for the notion of uncertainty is discussed, within the framework of the non-paraxial interference theory based on confinement in geometric states of space. This novel meaning refers to the fact that, for any set of space states whose vertices are distributed in an arbitrary array of size less than λ 10, both the excitation provided by the geometric potential and the positions of the vertices of the states are completely uncertain, such that the complete set is represented by the Lorentzian well of an individual ground state of space, with vertex at any of the points of the array, even if the set is under the maximum prepared non-locality (i.e., under a strong geometric potential). It is shown that the geometric uncertainty is different but compatible with the Heisenberg uncertainty principle. In fact, geometrical uncertainty establishes both the upper limit of momentum uncertainty and the lower limit of position uncertainty in the Heisenberg principle.
Non-paraxial interference in ordinary space has been described as the confinement of light, photons, and matter particles in geometric states of space, which are realized as spatially structured Lorentzian wells in the setup volume. Michelson interference is discussed in this framework by regarding the space states dependence from lengths of interferometer arms. It is optically equivalent to considering the space state vertices distributed in a three-dimensional region before the detector plane. This description is potentially relevant in devices where light comes from three-dimensional distributions of points, for instance, the outputs of waveguide arrays in optical or integrated photonics elements.
An exact and exhaustive phenomenology of interference in ordinary space describes it in terms of confinement in geometric states of space. Under high prepared non-locality, such space states exhibit spatial entanglement, a behavior not reported in the standard interference formalism of optics and quantum mechanics. In this paper, the fundamental theoretical features of the spatial entanglement of geometric states of space are discussed and illustrated with numerical simulations of non-paraxial Young interference.
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.
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.
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.