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Revista de la Academia Colombiana de Ciencias Exactas Físicas y Naturales

Confinement and spatial entanglement: phenomenology of a new interference principle

Román Castañeda

Published Nov 21, 2022• 2 citations
Publisher

Abstract

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.

DOI
10.18257/raccefyn.1695

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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.
We elaborate an interpretation of quantum physics founded on the hypothesis that quantum particles are conceptual entities playing the role of communication vehicles between material entities composed of ordinary matter which function as memory structures for these quantum particles. We show in which way this new interpretation gives rise to a natural explanation for the quantum effects of interference and entanglement by analyzing how interference and entanglement emerge for the case of human concepts. We put forward a scheme to derive a metric based on similarity as a predecessor for the structure of ‘space, time, momentum, energy ’ and ‘quantum particles interacting with ordinary matter ’ underlying standard quantum physics, within the new interpretation, and making use of aspects of traditional quantum axiomatics. More specifically, we analyze how the effect of non-locality arises as a consequence of the confrontation of such an emerging metric type of structure and the remaining presence of the basic conceptual structure on the fundamental level, with the potential of being revealed in specific situations.
Recent works in foundations of quantum (field) theory and relativistic quantum information try to better grasp the interplay between the structure of quantum correlations and the constraints imposed by causality on physical operations. Chapter 1 is dedicated to the study of the conceptual implications of quantum nonlocality, a concept that subsumes that of entanglement in a certain way. We detail the recent information-theoretic approaches to understanding the structure of nonlocal correlations, and the issues the latter raise concerning the ability of local observers to isolate a system from its environment. Chapter 2 reviews in what sense imposing Poincare invariance affects entanglement detection and quantification procedures. This invariance ultimately forces a description of all quantum systems within the framework of quantum field theory, which leads to the impossibility of localized finite-energy states and to the divergence of all entanglement measures for local observers. We provide a solution to these two problems by showing that there exists a generic equivalence between a finite spatial resolution of the measurement apparatus and the exclusion of high-energy degrees of freedom from the definition of the observed system. This equivalence allows for an epistemic interpretation of the standard quantum formalism describing nonrelativistic localized systems and their correlations, hence a clarification of the origin of the finite measures of entanglement between such systems. Chapter 3 presents a recent theoretical framework that predicts the existence of correlations with indefinite causal order. In analogy to the information-theoretic approaches to nonlocal correlations, we introduce some principles that constrain the structure of such correlations, which is a first step toward a clear understanding of their physical origin.
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.
This work presents a minimal reinterpretation of quantum entanglement based solely on the causal structure inherent in relativistic spacetime. No new physical entities, parameters, or modifications to existing theories are introduced.The discussion remains entirely within the established frameworks of general relativity and quantum mechanics, with particular emphasis on Lorentz invariance and relativistic causality. The central idea is that the causal structure of spacetime is unique and invariant, while spatial separation corresponds to different references (foliations) to this structure rather than its duplication.Within this viewpoint, quantum entanglement is understood as a local readout of correlations already encoded in a shared causal structure, without invoking nonlocal influences or superluminal information transfer. This document is intended as a conceptual clarification and archival record rather than a proposal of a new theory.It is provided to preserve a logically consistent interpretation that may be of interest for future foundational discussions.
Abstract: The exact nature of non-locality and entanglement is still a matter of an ongoing controversy. Especially, the concept of non-locality as postulated by the orthodox Copenhagen quantum mechanics is claiming to reflect any non-locality in the quantum realm. Attention should be called to the obvious but very disconcerting fact that the concept of non-locality cannot contradict the theory of special relativity, as long as the same is not refuted theoretically or by experiments. Another way of expressing the peculiar situation is, under conditions of the special theory of relativity it remains rather discomforting to alter the properties of a distant system instantaneously (i. e. no light signal can travel) by acting on a local system. The purpose of this publication is to solve the problem of non-locality and entanglement from the standpoint of the special theory of relativity.