Friday, April 10, 2015

white sr maxwell assumption of homogeneity (no preferred origin) and isotropic (no preferred direction) of space

路径依赖
right now, assume both 乙肝，丙肝 are treatable, then it is not 路径依赖;

if 丙肝 is not treatable, and you get it, then your life, luck are all 路径依赖: you get 乙肝, you are ok; you get 丙肝, you are done this life.

热统计物理学，时间有方向，路径依赖，初试点或条件很重要，生死攸关

but there is this theoretical argument, that if we make

旋转变换_百度百科

baike.baidu.com/view/2028050.htm 轉為繁體網頁

简称旋转。欧氏几何中的一种重要变换.即在欧氏平面上(欧氏空间中)，让每一点P绕一固定点(固定轴线)旋转一个定角，变成另一点P′，如此产生的变换称为平面上( ...

缺少字詞： ~~isotropic~~

chap07邻域运算_百度文库

wenku.baidu.com/view/101a3f8583d049649b665809 轉為繁體網頁

2010年11月2日 - ... 和，拉普拉斯算子可以简化为：有几种不同的模板计算形式： Laplacian算子也是各向同性（isotropic）的，考虑坐标旋转变换，设旋转前坐标为，旋转 ...

Laplace算子的旋转不变性的证明| NARUTOACM

www.narutoacm.com/archives/laplace-rotation-invariant/ 轉為繁體網頁

2013年1月1日 - 所谓算子可看成一种变换，作用在函数上，生成另一个函数。 ... 好的滤波器模版应当是各向同性的(isotropic)，即具有旋转不变性(rotation invariant)。

https://www.physicsforums.com/search/632980/

am going to give an answer that's probably more difficult than necessary. Classicaly, two frames are inertial if observer in each frame can agree on Newton's Laws (law of inertia, f=ma, action/reaction). Turns out that they must be moving at constant speed relative to each other. If you are in an accelerated frame, then newton's laws won't hold. The first one, for example, would break down, because object would have acceleration without force (there is an ambient force due to the fact that the observer is accelerating). The problem is how do we jump from one frame to another so that measurements in each frame agree. By simple assumption of homogeneity (no preferred origin) and isotropic (no preferred direction) of space one can prove that there are three kinds of transformation possible: one with a speed minimum, one with a speed maximum (Lorentz), and one with neither (Galileon). The first kind turns out to violate causality. And the third kinds turns out to be invalid because some other law of physics is not invariant under it (Maxwell's Eqn). So one conclude that the second one to be correct and the third one to be a limiting case of it (limit as the speed limit goes to infinity). And for all law (included EM) to be correct, this speed limit must be the speed at which EM disturbance travel in vaccum, i.e. the speed of light. Arriving at this conclusion requires 5 assumptions: 1) all Law of physics is invariant when you go from one inertial frame to another. 2) the transformation from one frame to another is linear 3) spacetime is homogeneous 4) spacetime is isotropic 5) Causality is preserved. I like this derivation better because the speed limit turn out to be a result, not an assumption. And the 5 assumptions above are more "obvious", "trivial", and "intuitive". In short, inertial frame are frames that moves at constant speed with respect to each other. And by assuming the 5 assumptions above, and using some group theory and linear algebra. One arrive at the Lorentz transformation which has stand the tests of experiments

Reference https://www.physicsforums.com/threads/what-is-an-inertial-reference-frame.11148/

Maxwell's equations - Wikipedia, the free encyclopedia

en.wikipedia.org/wiki/Maxwell's_equations

Wikipedia

For the history of the equations, see History of Maxwell's equations. ..... For homogeneous materials, ε and μ are constant throughout the material, while for ... For isotropic materials, ε and μ are scalars, while for anisotropic materials (e.g. due to ...

‎Gauss's law - ‎Ampère's law - ‎Gauss's law for magnetism - ‎Current density

[PDF]EM Waves, Wave Propagation in Linear/Homogeneous ...

web.hep.uiuc.edu/home/serrede/P436/Lecture.../P436_Lect_06.pdf

o μ = magnetic permeability of free space = 4π × 10. −7. Henrys/m. Thus, Maxwell's equations for theE and B fields inside this linear, homogeneous and isotropic.

[PDF]Chapter 1 Electromagnetic Theory ² Maxwell's Equation

www.colorado.edu/...fa05/Chapter1.pdf

University of Colorado Boulder

The electromagnetic theory of optics begins with Maxwell's equation. ..... We have seen how plane wave propagate in vacuum or in isotropic homogeneous.

[PDF]Lesson 9 - NICADD

nicadd.niu.edu/~piot/phys_630/Lesson9.pdf

medium then Maxwell's equations simplify to. • For now on we consider non-magnetic media (M=0) and ... Linear, homogeneous, isotropy, nondispersive media.

[PDF]Electromagnetic Waves in Homogeneous Media - MIT

web.mit.edu/.../Lec02_Waves-v11....

Massachusetts Institute of Technology

therefore solution is any function with identical dependencies on space and time (up to a constant). Maxwell's Equations in linear isotropic homogeneous ...