时空中的量子力学：物理光学的费曼路径振幅描述、德布罗意物质波与夸克和中微子味振荡

波函数作为相干轨迹系综的解释

Interpretation of wave function by coherent ensembles of trajectories

本文基于德布罗意、薛定谔、狄拉克和费曼的思想，引入时空中的相干轨迹系综来修正波函数的系综解释，从而避免测量坍缩悖论，并指出依赖单量子比特代表整个波函数的量子计算或密码学方法将失效。

Droplets moving on a fluid surface: interference pattern from two slits

The Feynman path integral approach for solving the motion of a droplet along a silicon oil surface is developed by replacing the Planck constant by a surrogate parameter. The latter is proportional to the surface tension of the silicon oil multiplied by the area of the thin air film, separating the droplet from the oil, and by the half-period of the Faraday oscillations. It is shown that the Navier-Stokes equation together with the mass conservation equation can be reduced to the Schrödinger equation when the surrogate parameter replaces the Planck constant. The Feynman path integral underlyin…

量子力学的Vlasov-Bohm方法用于统计系统

A Vlasov-Bohm approach to Quantum Mechanics for statistical systems

本文提出利用Vlasov-Bohm方法对经典非相对论系统进行量子化，通过玻姆量子势构建平均场理论，与量子力学在随机相近似下一致。

通往量子力学的第三条路是被遗忘的第一条路

The third way to quantum mechanics is the forgotten first

量子力学可以用三种方式表述，海森堡、薛定谔和费曼分别是这样做的。最后，我们在格雷戈尔·文策尔（Gregor Wentzel）的一篇论文中发现了一个未知的（即被遗忘的）先驱，该论文发表于海森堡和薛定谔的著名著作之前，与L.德布罗意。在这篇论文中，人们可以找到基本公式和它们的解释，因为它们在20年后被费曼采用。我们认为，文策尔的工作被遗忘的原因有几个：（一）薛定谔方程是简单得多处理（文策尔本人有助于其发展以同样的方式作为L.布里渊和H.克拉默斯没有）。(II)第一次申请被海森堡和克拉默斯拒绝。(III)Wentzel使用的近似法太天真，失败了。尽管如此，文策尔奠定的基础是健全的，正如费曼的工作所表明的那样。因此，温策尔被认为是量子力学的创始人之一。

Intrinsic periodicity: the forgotten lesson of quantum mechanics

Wave-particle duality, together with the concept of elementary particles, was introduced by de Broglie in terms of intrinsically "periodic phenomena". However, after nearly 90 years, the physical origin of such undulatory mechanics remains unrevealed. We propose a natural realization of the de Broglie "periodic phenomenon" in terms of harmonic vibrational modes associated to space-time periodicities. In this way we find that, similarly to a vibrating string or a particle in a box, the intrinsic recurrence imposed as a constraint to elementary particles represents a fully consistent quantizatio…

First observation of antimatter wave interference

In 1924 Louis de Broglie introduced the concept of wave-particle duality: the Planck constant $h$ relates the momentum $p$ of a massive particle to its de Broglie wavelength $λ=h/p$. The superposition principle is one of the main postulates of quantum mechanics; diffraction and interference phenomena are therefore predicted and have been observed on objects of increasing complexity, from electrons to neutrons and molecules. Beyond the early electron diffraction experiments, the demonstration of single-electron double-slit-like interference was a highly sought-after result. Initially proposed b…

双时间相对论性玻姆模型的结果

Consequences of a Two-Time Relativistic Bohmian Model

本文提出一种引入独立时间参数的双时间相对论性玻姆模型，通过自由粒子颤动运动赋予费曼路径物理实在性，并导出不确定性原理的相对论性修正。

The theory of the double preparation: discerned and indiscerned particles

In this paper we propose a deterministic and realistic quantum mechanics interpretation which may correspond to Louis de Broglie's "double solution theory". Louis de Broglie considers two solutions to the Schrödinger equation, a singular and physical wave u representing the particle (soliton wave) and a regular wave representing probability (statistical wave). We return to the idea of two solutions, but in the form of an interpretation of the wave function based on two different preparations of the quantum system. We demonstrate the necessity of this double interpretation when the particles ar…

Double-slit and electromagnetic models to complete quantum mechanics

We analyze a realistic microscopic model for electronic scattering with the neutral differential delay equations of motion of point charges of the Wheeler-Feynman electrodynamics. We propose a microscopic model according to the electrodynamics of point charges, complex enough to describe the essential physics. Our microscopic model reaches a simple qualitative agreement with the experimental results as regards interference in double-slit scattering and in electronic scattering by crystals. We discuss our model in the light of existing experimental results, including a qualitative disagreement …

不确定性原理、不确定性关系与底层轨迹：费曼、纳尔逊、玻姆与持续卡茨-狄拉克动力学

Quantum Uncertainty and Particle Trajectories: From Heisenberg and Schrödinger to Constructive Dynamical Models

本文区分量子不确定性关系与广义不确定性原理，通过费曼路径、纳尔逊随机力学、玻姆力学及卡茨动力学证明不确定性关系不排除底层轨迹描述，从而驳斥其否定微观轨迹的本体论解读。

Space-time-hap: a coordinate system for the multiverse and its application to show that free choice is observer-dependent

This note proposes a paradigm and coordinate system that extends flat, four-dimensional Minkowski spacetime to a broader framework that identifies an event not only in space and in time, but also in terms of possible world, with a third category of coordinates called ``hap'' modelling contingency and counterfactuals. Semantically, hap is based on a Bohmian-like configuration space, in which initial conditions at a specific moment in time uniquely identify a trajectory. This framework can be used to support reasonings that rigorously distinguish between causal dependencies (through time), stati…