纪念Einstein，纪念1905

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Einstein与其辉煌的1905。

我们固然不能要求每个人都知道或清楚地知道1905年究竟意味着什么，但在人类理论之路上，记住1905将使每个在这条路上行走的人受益无穷。

记住那些与自然博弈的人们吧，无论成功的，还是失败的。也许人们只能记住成功者的名字，甚至连他们也记不住，但与自然博弈的精神与兴趣是不以成败做论的。千千万万的博弈先锋们为人类创造了另一条生活之路——人类有这样一种生活，就是用自己的想像力、观察力、思考力同自然博弈，使自然看起来好似在按照自己所描述的那样存在——虽然人们知道自然永远不会是人们所描述的那样。

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关键词：Einstein Stein TEI 成功者 观察力 纪念 Einstein

版主是否贴几篇相关文章介绍爱因斯坦的成就，比如相对论、光电效应和布朗运动？

The 1905 Papers

In the first of three seminal papers that were published in 1905, Einstein examined the phenomenon discovered by Max Planck, according to which electromagnetic energy seemed to be emitted from radiating objects in quantities that were ultimately discrete. The energy of these emitted quantities, the so-called light-quanta, was directly proportional to the frequency of the radiation. This circumstance was perplexing because classical electromagnetic theory, based on Maxwell's equations and the laws of thermodynamics, had assumed that electromagnetic energy consisted of waves propagating in a hypothetical, all-pervasive medium called the luminiferous ether, and that the waves could contain any amount of energy no matter how small. Einstein used Planck's quantum hypothesis to describe visible electromagnetic radiation, or light. According to Einstein's heuristic viewpoint, light could be imagined to consist of discrete bundles of radiation. Einstein used this interpretation to explain the photoelectric effect, by which certain metals emit electrons when illuminated by light with a given frequency. Einstein's theory, and his subsequent elaboration of it, formed the basis for much of quantum mechanics. The second of Einstein's 1905 papers proposed what is today called the special theory of relativity. At the time Einstein knew that, according to Hendrik Antoon Lorentz's theory of electrons, the mass of an electron increased as the velocity of the electron approached the velocity of light. Einstein also knew that the electron theory, based on Maxwell's equations, carried along with it the assumption of a luminiferous ether, but that attempts to detect the physical properties of the ether had not succeeded. Einstein realized that the equations describing the motion of an electron in fact could describe the nonaccelerated motion of any particle or any suitably defined rigid body. He based his new kinematics on a reinterpretation of the classical principle of relativity, that the laws of physics had to have the same form in any frame of reference. As a second fundamental hypothesis, Einstein assumed that the speed of light remained constant in all frames of reference, as required by classical Maxwellian theory. Einstein abandoned the hypothesis of the ether, for it played no role in his kinematics or in his reinterpretation of Lorentz's theory of electrons. As a consequence of his theory Einstein recovered the phenomenon of time dilatation, wherein time, analogous to length and mass, is a function of the velocity of a frame of reference. Later in 1905, Einstein elaborated how, in a certain manner of speaking, mass and energy were equivalent. Einstein was not the first to propose all the elements that went into the special theory of relativity; his contribution lies in having unified important parts of classical mechanics and Maxwellian electrodynamics. The third of Einstein's seminal papers of 1905 concerned statistical mechanics, a field of study that had been elaborated by, among others, Ludwig Boltzmann and Josiah Willard Gibbs. Unaware of Gibbs' contributions, Einstein extended Boltzmann's work and calculated the average trajectory of a microscopic particle buffeted by random collisions with molecules in a fluid or in a gas. Einstein observed that his calculations could account for brownian motion, the apparently erratic movement of pollen in fluids, which had been noted by the British botanist Robert Brown. Einstein's paper provided convincing evidence for the physical existence of atom-sized molecules, which had already received much theoretical discussion. His results were independently discovered by the Polish physicist Marian von Smoluchowski and later elaborated by the French physicist Jean Perrin.

[此贴子已经被作者于2005-4-21 7:57:10编辑过]

从纯数学上说，Einstein并没有做出多么大的突破，但他给纯数学（当然只是数学的一部分）赋予了实在的物理内容（这里的“实在”意思是每一个物理量都是由某种观测的方法定义的，不可观测的物理量是没有物理意义的），并做出了精确度更高的预测（检验预测结论的前提是相关物理概念是可观测的）。

不管人们相不相信存在“绝对时间”，如果人们始终无法观测到绝对时间，绝对时间在物理学中就是需要舍弃的；不管人们相不相信“光速绝对不变”，如果人们始终无法观测到（真空中）光速的变化，“光速绝对不变”在物理学中就是需要保留的。

经济学在这条路上还要有许多准备工作要做，最困难的在于经济学家是在同人博弈，自然科学家是在与自然博弈。做出高精确度的预测，其前提还是每个经济学概念要在可观测的意义上定义。

“不管人们相不相信存在“绝对时间”，如果人们始终无法观测到绝对时间，绝对时间在物理学中就是需要舍弃的；不管人们相不相信“光速绝对不变”，如果人们始终无法观测到（真空中）光速的变化，“光速绝对不变”在物理学中就是需要保留的。”——我怎么觉得前后两个判断是矛盾的，后面应该是如果观察不到光速的不变，那么就要舍弃吧。

根据相对论，时间和光速都是有界限的。

罗默1676年测定了光传播的有限速率。17世纪以来人们就了解了光速的有限性。

然而后来人们发现光速是绝对不变的（广义相对论提出以前），狭义相对论中，光速是绝对的、不变的；而一维时间、三维空间分别是相对的，但四维时空（作为整体）是绝对的。

哦，原来如此，谢谢。你以前学物理的？

Einstein 论述的布郎运动对金融学的贡献也相当大,否则金融市场的有效性检验也就无法进行了.

Holmstrom将布朗运动引入委托代理模型，刻画了当存在非对称信息时代理人信息的特征。

Einstein 论述布郎运动，主要是证明了分子（运动）的存在，其数学模型可以清楚地描述布朗运动。虽然Boltzmann提出了热的统计力学，但这种统计力学假设的“分子及其分子运动”以前还没有确切的经验证据。

物理中的布朗运动，并不是小颗粒（如花粉）“自主”地运动，而是受到了周围大量分子的随机碰撞，而呈现出不规则的运动。

热的统计力学给热学第二定律以及相关的时间箭头一个比较清晰的统计学解释。

物理学的主要任务之一是给自然界以数学的描述，但数学并不是物理学，物理学也不是数学。经济学想走向以经验为基础的科学，其不可缺少的发动机就是数学。

许多人想谈经济学与其他学科的交叉，但前提是对两种学科都要有比较明确的了解。

在“交叉”这一领域里，个人感觉一个比较可能的方向是，对经济状态做出一个微分方程，这一方程考虑了我们感兴趣的经济的性质，但又不能太复杂。运用这一方程对“实际经济”做出“符合实际”的拟合。拟合的一个重要要求是，这个方程含有清晰的时间箭头（描述了一个不可逆的过程），并且能自然地得出“周期”与“突变”的结果。周期与突变也许是谁也不能否认的经济的特征，但非线性动力方程（混沌）可以将它们统一在一个方程里面，体现着随时间的演化。人们寻找这类方程的“恰当”形式，虽然非常困难，但也许是更“经济”的方法，因为数学本身就是用来研究的比较便宜的工具。

毕竟，人们在模拟动物身体斑点方面已经取得了相当的成功（当然要借助良好的计算机），非线性方程可以清晰地说明为什么体态（大致）处于两极的老鼠与大象肤色大都呈单色，而中间的斑马、金钱豹呈现出长纹与斑点；此外，为什么金钱豹的身体上是斑点，而尾巴上是条纹。

也有人认为人们之所以会有突发性心脏病以至猝死，是因为心脏的运动是个混沌的过程，每个人也许都会遭遇“蝴蝶效应”般地不测，虽然大多数时间里人们感觉的是心脏有节律的跳动。

交叉学科领域，“挥挥手式”、“动动口式”的论说时代应该已经过去，拿出“有力”的动力模型是研究价值所在。