Boundary Interactions in Pilot-Wave Hydrodynamics

这个项目是对“行走液滴”系统的实验和理论研究，在这个系统中，一个毫米大小的液滴在振动的液浴中反弹，当它撞击流体表面时产生的波与共振相互作用推动。行走的液滴表现出几个先前被认为是微观量子领域独有的特征。该项目的结果将是对行走液滴系统作为微观行为模拟的潜力和局限性的关键评估。虽然行走的液滴系统在十年前才被发现，但微观量子粒子运动的类似概念在20世纪20年代就被先锋物理学家路易斯·德布罗意提出了。德布罗意设想微观粒子与他称之为“导波”的共振运动。从这个概念出发，德布罗意推导出了一系列方程，这些方程成为现代量子理论的基石，并正确地预测了电子衍射现象，为此他获得了诺贝尔奖。尽管取得了早期的成功，但先导波的概念被一种观点所掩盖，即量子力学的统计预测是对微观尺度上物理现实的完整描述，没有任何额外的物理结构的作用。这个项目重新审视了这些相互竞争的模型，并提出了一个问题，即由德布罗意（de Broglie）构想并在游动液滴系统中实现的混沌导波动力学是否可能成为量子统计学的基础。如果答案是肯定的，那么微观领域的主流观点将需要彻底修正，这将对科学哲学产生深远的影响。pi设计了一种行走液滴装置，由一款免费的智能手机应用程序控制，制造成本不到60美元。pi使用行走液滴实验进行各种科学推广活动。这个项目将质疑并告知现代物理学的哲学基础。弹跳液滴系统以粒子与其导波之间的共振相互作用为特征，是一种丰富的新动力系统，它扩展了经典系统的范围，包括以前被认为是微观领域独有的特征。此外，它是20世纪20年代由路易·德布罗意提出的导航波动力学的第一个宏观实现，他在他的双解理论中设想了微观量子粒子与导波共振运动。这项研究建立在先前的工作基础上，这些工作已经产生了最精确的弹跳跌落实验系统和最复杂的理论模型。理论与实验相结合，为该水动力导波系统的动力学和稳定性提供了预测能力。该项目将应用这些完善的实验和理论工具来重新审视涉及边界相互作用的关键流体力学量子模拟系统，包括受限几何中的运动和单粒子衍射和干涉。该项目还将研究几个新的模拟系统，包括步行者在离散台阶上的折射，其中修改的斯涅尔定律被遵守，以及圆形障碍物的散射，其中类似于电磁自感的特性出现。量子海市蜃楼、卡皮察-狄拉克效应和布拉格散射的流体力学类似物也将被探讨。这类问题将导致对导波流体力学的更好理解，并添加到不断增长的流体力学量子类似物列表中。为了提供在宏观尺度上观察和理解导波动力学的机会，弹跳液滴系统邀请对德布罗意的导波力学进行批判性的回顾，并检查其作为现实主义量子动力学基础的可行性。

This project is an experimental and theoretical investigation of the "walking droplet" system, in which a millimeter-size droplet bounces across a vibrating fluid bath, propelled by a resonant interaction with the waves created when it strikes the fluid surface. The walking droplet exhibits several features previously thought unique to the microscopic quantum realm. The outcome of this project will be a critical assessment of the potential and limitations of the walking droplet system as an analog for microscopic behavior. Although the walking droplet system was discovered only a decade ago, a similar conception for the motion of microscopic quantum particles was formulated in the 1920s by pioneering physicist Louis de Broglie. De Broglie envisioned microscopic particles moving in resonance with what he called a "pilot wave." Working from this conception, de Broglie deduced a number of equations that became the cornerstones of modern quantum theory, and correctly predicted the phenomenon of electron diffraction, for which he received the Nobel Prize. Despite this early success, the pilot wave concept was overshadowed by the viewpoint that the statistical predictions of quantum mechanics stand alone as a complete description of physical reality on the microscopic scale, with no role for any additional physical structure. This project revisits these competing models, and asks whether chaotic pilot-wave dynamics, of the form conceived by de Broglie and now realized in the walking droplet system might plausibly underlie quantum statistics. If the answer is yes, then the prevailing view of the microscopic realm will require drastic revision, with deep implications for the philosophy of science. The PIs have designed a walking droplet apparatus, controlled by a free smartphone app, which can be built for less than $60. The PIs have used the walking droplet experiment for a variety of science outreach activities. This project will both question and inform the philosophical foundations of modern physics. The bouncing drop system, characterized by a resonant interaction between a particle and its guiding wave, is a rich new dynamical system that extends the range of classical systems to include features previously thought to be exclusive to the microscopic realm. It is, moreover, the first macroscopic realization of a pilot-wave dynamics of the form that was postured in the 1920s by Louis de Broglie, who, in his double-solution theory, envisaged microscopic quantum particles moving in resonance with a guiding wave. This study builds upon prior work that has yielded both the most refined bouncing-drop experimental system in operation and the most sophisticated theoretical models. Together the theory and experiments provide predictive power for the dynamics and stability of this hydrodynamic pilot-wave system. This project will apply these refined experimental and theoretical tools to revisit key hydrodynamic quantum analog systems involving boundary interactions, including motion in confined geometries and single-particle diffraction and interference. The project will also examine several new analog systems, including refraction of walkers across discrete steps, where a modified Snell's Law is obeyed, and scattering from circular obstacles, where a property akin to electromagnetic self-induction arises. Hydrodynamic analogs of the quantum mirage, Kapitza-Dirac effect, and Bragg scattering will also be explored. This class of problems will lead to a better understanding of pilot-wave hydrodynamics, and add to the growing list of hydrodynamic quantum analogs. In providing the opportunity to observe and understand pilot-wave dynamics on a macroscopic scale, the bouncing droplet system invites a critical revisitation of de Broglie's pilot-wave mechanics, and an examination of its viability as the basis for a realist quantum dynamics.