{"title":"Aharonov–Bohm Effect as a Diffusion Phenomenon","authors":"Charalampos Antonakos, Andreas F. Terzis","doi":"10.1007/s10701-024-00786-2","DOIUrl":null,"url":null,"abstract":"<div><p>This paper presents a hydrodynamical view of the Aharonov–Bohm effect, using Nelson’s formulation of quantum mechanics. Our aim is to gain a better understanding of the mysteries behind this effect, such as why in the prototype Aharonov–Bohm system with a cylinder the motion of a particle is affected in a region where there is no magnetic field. Our main purpose is to use Nelson’s formulation to describe the effect and demonstrate that it can be explained by the direct action of the current surrounding the magnetic field region. Although conventional theories try to present vector potentials as more physically significant than magnetic fields, our purpose is to demonstrate that such debate regarding the comparison between vector potentials and magnetic fields should not exist at all; within our context, magnetic fields and vector potentials serve as tools for finding other fundamental hydrodynamical quantities that arise from the interaction between the quantum background fields described by Nelson’s quantum theory, and thus, play a secondary role at the explanation of this phenomenon. So, in this paper, we do not intend to participate in a debate regarding whether we should give a local (based on e/m forces and e/m fields) or non-local (based on vector potentials) description of the phenomenon. Finally, we investigate the relationship between hidden variables and quantum fluctuations, their role in this phenomenon and their connection with the gauge transformation of the vector potential, that plays a leading role in quantum AB systems.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Foundations of Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10701-024-00786-2","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
This paper presents a hydrodynamical view of the Aharonov–Bohm effect, using Nelson’s formulation of quantum mechanics. Our aim is to gain a better understanding of the mysteries behind this effect, such as why in the prototype Aharonov–Bohm system with a cylinder the motion of a particle is affected in a region where there is no magnetic field. Our main purpose is to use Nelson’s formulation to describe the effect and demonstrate that it can be explained by the direct action of the current surrounding the magnetic field region. Although conventional theories try to present vector potentials as more physically significant than magnetic fields, our purpose is to demonstrate that such debate regarding the comparison between vector potentials and magnetic fields should not exist at all; within our context, magnetic fields and vector potentials serve as tools for finding other fundamental hydrodynamical quantities that arise from the interaction between the quantum background fields described by Nelson’s quantum theory, and thus, play a secondary role at the explanation of this phenomenon. So, in this paper, we do not intend to participate in a debate regarding whether we should give a local (based on e/m forces and e/m fields) or non-local (based on vector potentials) description of the phenomenon. Finally, we investigate the relationship between hidden variables and quantum fluctuations, their role in this phenomenon and their connection with the gauge transformation of the vector potential, that plays a leading role in quantum AB systems.
本文采用纳尔逊的量子力学公式,从流体力学的角度阐述了阿哈诺夫-玻姆效应。我们的目的是更好地理解这一效应背后的奥秘,例如为什么在带有圆柱体的阿哈诺夫-玻姆系统原型中,粒子的运动会在没有磁场的区域受到影响。我们的主要目的是使用纳尔逊公式来描述这种效应,并证明它可以用磁场区域周围电流的直接作用来解释。虽然传统理论认为矢量势比磁场更具物理意义,但我们的目的是要证明,关于矢量势和磁场之间比较的争论根本就不应该存在;在我们的语境中,磁场和矢量势只是用来寻找其他基本流体力学量的工具,而这些基本流体力学量是由纳尔逊量子理论描述的量子背景场之间的相互作用产生的,因此,在解释这一现象时起着次要作用。因此,在本文中,我们不打算参与关于我们应该对这一现象进行局部(基于电子/米力和电子/米场)描述还是非局部(基于矢量势)描述的争论。最后,我们研究了隐变量和量子波动之间的关系、它们在这一现象中的作用以及它们与矢量势的规规变换之间的联系,后者在量子 AB 系统中起着主导作用。
期刊介绍:
The conceptual foundations of physics have been under constant revision from the outset, and remain so today. Discussion of foundational issues has always been a major source of progress in science, on a par with empirical knowledge and mathematics. Examples include the debates on the nature of space and time involving Newton and later Einstein; on the nature of heat and of energy; on irreversibility and probability due to Boltzmann; on the nature of matter and observation measurement during the early days of quantum theory; on the meaning of renormalisation, and many others.
Today, insightful reflection on the conceptual structure utilised in our efforts to understand the physical world is of particular value, given the serious unsolved problems that are likely to demand, once again, modifications of the grammar of our scientific description of the physical world. The quantum properties of gravity, the nature of measurement in quantum mechanics, the primary source of irreversibility, the role of information in physics – all these are examples of questions about which science is still confused and whose solution may well demand more than skilled mathematics and new experiments.
Foundations of Physics is a privileged forum for discussing such foundational issues, open to physicists, cosmologists, philosophers and mathematicians. It is devoted to the conceptual bases of the fundamental theories of physics and cosmology, to their logical, methodological, and philosophical premises.
The journal welcomes papers on issues such as the foundations of special and general relativity, quantum theory, classical and quantum field theory, quantum gravity, unified theories, thermodynamics, statistical mechanics, cosmology, and similar.