论文标题
布朗运动历史上的速度概念 - 从物理到数学再到背部
The concept of velocity in the history of Brownian motion -- From physics to mathematics and back
论文作者
论文摘要
植物学家罗伯特·布朗（Robert Brown）于1827年首次观察到了对布朗运动的兴趣：这种现象首先是在1900年代被物理学家理论上观察到的，最终由1920年代的数学家建模，同时仍以物理理论的发展。因此，布朗运动现在是指自然现象，但也指的是理论。从今天的发现到今天，从1827年到1900年代后期的佩林实验。或从数学家的角度来看，从1920年代开始。在本文中，我们解决了跨越刚才提到的两个“半历史”的时期，以突出连续性，调查从物理学到数学的域移动，并调查后来物理理论的增强。我们利用布朗尼速度作为领先的概念来研究1905年至1934年的爱因斯坦，Smoluchowski，Langevin，Wiener，Ornstein和Uhlenbeck的作品以及实验结果。我们展示了布朗运动在1920年代如何成为数学家维也纳的研究主题，为什么他的模型是物理实验的理想化，ornstein和uhlenbeck添加了爱因斯坦的结果，以及维也纳，奥恩斯坦和uhlenbeck如何在同时矛盾的棕色棕色velocity上发展。
Interest in Brownian motion was shared by different communities: this phenomenon was first observed by the botanist Robert Brown in 1827, then theorised by physicists in the 1900s, and eventually modelled by mathematicians from the 1920s, while still evolving as a physical theory. Consequently, Brownian motion now refers to the natural phenomenon but also to the theories accounting for it. There is no published work telling its entire history from its discovery until today, but rather partial histories either from 1827 to Perrin's experiments in the late 1900s, from a physicist's point of view; or from the 1920s from a mathematician's point of view. In this article, we tackle the period straddling the two `half-histories' just mentioned, in order to highlight continuity, to investigate the domain-shift from physics to mathematics, and to survey the enhancements of later physical theories. We study the works of Einstein, Smoluchowski, Langevin, Wiener, Ornstein and Uhlenbeck from 1905 to 1934 as well as experimental results, using the concept of Brownian velocity as a leading thread. We show how Brownian motion became a research topic for the mathematician Wiener in the 1920s, why his model was an idealization of physical experiments, what Ornstein and Uhlenbeck added to Einstein's results, and how Wiener, Ornstein and Uhlenbeck developed in parallel contradictory theories concerning Brownian velocity.
