Comment on Backow in relativistic wave equations Maximilien Barbier1 Christopher J. Fewster2 Arseni Goussev3 Gregory Morozov1 and Shashi C. L. Srivastava45

2025-04-27 0 0 122.55KB 2 页 10玖币

侵权投诉

Comment on “Backﬂow in relativistic wave equations”

Maximilien Barbier1, Christopher J. Fewster2, Arseni Goussev3, Gregory Morozov1, and

Shashi C. L. Srivastava4,5

1Scottish Universities Physics Alliance, Institute of Thin Films, Sensors and Imaging, University of the

West of Scotland, Paisley PA1 2BE, Scotland, UK

2Department of Mathematics, University of York, York YO10 5DD, UK

3School of Mathematics and Physics, University of Portsmouth, Portsmouth PO1 3HF, UK

4Variable Energy Cyclotron Centre, 1/AF Bidhannagar, Kolkata 700064, India

5Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai - 400094, India

The stated goal of Ref. [1] is to argue that “the phenomenon of backﬂow is a common feature

of various physical system[s], quantum and classical, described by the linear wave equations”.

The authors challenge a perceived view that “backﬂow is inseparably connected with quantum

theory”. In particular, the authors strongly oppose statements in the literature that backﬂow is

a “peculiar quantum eﬀect”, an “intriguing quantum-mechanical phenomenon”, a “surprising

and clearly nonclassical eﬀect”, a “classically impossible phenomenon”, and a “generic purely

quantum phenomenon”.

It appears that the authors of [1] have misunderstood the purpose of the statements to which

they object. To explain, we must distinguish two mathematically inseparable, but physically

distinct phenomena: backﬂow (B) and quantum backﬂow (QB). In more detail:

(B) Backﬂow. This is a general wave phenomenon, which may be deﬁned, quoting [1], as “the

counterintuitive behavior of the ﬂow of some quantity (energy, probability, etc). Namely,

in some regions of space the direction of the ﬂow is opposite with respect to the direction

of all its constituent elementary waves.” As the authors correctly state, B is “a common

feature of various physical system[s], quantum and classical, described by the linear wave

equations” [1]. This statement is not subject to doubt and, to our knowledge, has never

been challenged.

(QB) Quantum backﬂow [2, 3]. This is the phenomenon of backﬂow speciﬁc to quantum

particles such as electrons, which concerns the following question: Can the position prob-

ability density of a particle ﬂow to the left if the particle’s momentum points to the right?

Consider a free quantum particle moving in one dimension and suppose that, in the initial

state, the measured value of momentum would be positive with probability 1. Is it possible

that the probability of ﬁnding the particle in the left-hand half-line is higher at a later time

than it is initially? In classical particle mechanics, the answer to this question is negative.

In quantum mechanics, it is positive. This is why numerous authors have referred to QB

as a “peculiar quantum eﬀect”, “intriguing quantum-mechanical phenomenon”, “surpris-

ing and clearly nonclassical eﬀect”, “classically impossible phenomenon”, and “generic

purely quantum phenomenon”. Such phrases concern the contrast between the classical

and quantum dynamics of particles.

QB arises, of course, because quantum mechanics describes particle mechanics using a wave

equation. For exactly the same reason, quantum particles exhibit diﬀraction and interference

arXiv:2210.05368v1 [quant-ph] 11 Oct 2022

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

CommentonBackowinrelativisticwaveequations"MaximilienBarbier1,ChristopherJ.Fewster2,ArseniGoussev3,GregoryMorozov1,andShashiC.L.Srivastava4,51ScottishUniversitiesPhysicsAlliance,InstituteofThinFilms,SensorsandImaging,UniversityoftheWestofScotland,PaisleyPA12BE,Scotland,UK2DepartmentofMathematics,Un...

展开>> 收起<<

Comment on Backow in relativistic wave equations Maximilien Barbier1 Christopher J. Fewster2 Arseni Goussev3 Gregory Morozov1 and Shashi C. L. Srivastava45.pdf

共2页,预览1页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Comment on Backow in relativistic wave equations Maximilien Barbier1 Christopher J. Fewster2 Arseni Goussev3 Gregory Morozov1 and Shashi C. L. Srivastava45

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: