第一种方法其实就是解释迈-莫试验用往返平均时间把速度v的一级项给“平均”掉的结果，所以我才说如此解释迈-莫试验很弱智！留下的二级教应后就你说我“收缩”我说你“收缩”，弄得整个物理学界打大架已经百年了。

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    第二种方法是将两个毫不相关而且也根本就不是同一光信号速度却用σ连接起来，这哪里是搞物理科学？而简直是一种公然的神学欺骗行为！

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第三种方法与我的方法有何区别？容我再重新转贴过来请看清楚些﹕

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原贴地址：http://club.xilu.com/hongbin/msgview-950451-104915.html

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相对论误导科学走斜路，道是非曲折待历史见证；引力场以太旧貌焕新颜，作定海神柱将扭转乾坤。持一份平和心态闯科海，能生命当歌也荣辱以乐；唯真理艰难求索胸怀广，可气吞山河再平展时空。

不管中文的英文的，不管是伽利略的、洛仑兹的抑或爱因斯坦的变换，不管数学推导对错与否，一律都是伪科学！
道理很简单：都是基于“惯性系平权轮”的结果！

彻底推翻“惯性系平权轮”紧紧把握挑战相对论物理学会会长的“明确时空观”，恢复物理科学本来面目，自然会使20世纪为止的人类“普通物理学”画上圆满句号，走进《高等物理学》阶段！

沉舟侧畔千帆过病树前头万木春！
……
努力吧朋友，曙光就在前头！

倒相对论学者们，一齐喊口号：让相对论患者们都必须要老老实实的“站队”！
然后再讨论问题。
“站队”，就是我们挑战制胜的操作法宝！

要知道：一“站队”，相对论患者就懵，最害怕“站队”，所以他们无例外都不敢“站队”！

否则，因为人类语言文字本身逻辑恶性循环，他们总会振振有词。

一“站队”，就没词了！

希望朋们喜欢。

4. Lorentz Transformations

(你粘贴过的为何还让别人做？)

That is what happens in the primed frame. What happens in the unprimed frame? The light starts at some time and travels to the final point at time . Since the light travels at , and the photodetector is moving away from the flash at velocity , and the length of the separation is in this reference frame, the time it takes is given by

At the end of the experiment, the flash bulb has moved a distance from the origin, and the photodetector is a distance beyond that, so

Our goal is to obtain equations relating the coordinates and to and . We already have three equations, but we have five unknowns: , , , , and . We need two more equations. Fortunately, since the initial flash was at , we can use the time dilation relation

and the Lorentz contraction relation

to find the desired relationships. From here on out it is all algebra.

First, combine equations (E) and (C) to find a relation for :

That was relatively easy.

Much harder is finding the expression for . We start by solving equation (A) for :

We then use (D) to substitute for and (E) to solve for :

We now solve (B) for , yielding

If we now substitute equation (C) for , we have an expression for exclusively in terms of and , namely

We have the transformation properties of and in the two coordinate systems. What we have not been careful about is the transformations of the other coordinates and . Since the motion is only in the direction, it is not surprising that these coordinates are not affected by Lorentz transformations. So the full equations for the Lorentz transformations are given by

These equations will be discussed at some length in the next lecture.

fuj0

4. Lorentz Transformations

We are now prepared to deal with the problem of how to relate an arbitrary and coordinate in an unmoving frame to an arbitrary and coordinate in a moving frame. For this we imagine an experiment in which we get rid of the mirror altogether, and simply have the flash bulb at and the photodetector at . The flash bulb flashes at an arbitrary time at , and the light is received at time at . By choosing the initial flash time carefully, it is possible to arrange an arbitrary time at which the light is received. Since the light travels at speed , we have

That is what happens in the primed frame. What happens in the unprimed frame? The light starts at some time and travels to the final point at time . Since the light travels at , and the photodetector is moving away from the flash at velocity , and the length of the separation is in this reference frame, the time it takes is given by

At the end of the experiment, the flash bulb has moved a distance from the origin, and the photodetector is a distance beyond that, so

Our goal is to obtain equations relating the coordinates and to and . We already have three equations, but we have five unknowns: , , , , and . We need two more equations. Fortunately, since the initial flash was at , we can use the time dilation relation

and the Lorentz contraction relation

to find the desired relationships. From here on out it is all algebra.

First, combine equations (E) and (C) to find a relation for :

That was relatively easy.

Much harder is finding the expression for . We start by solving equation (A) for :

We then use (D) to substitute for and (E) to solve for :

We now solve (B) for , yielding

If we now substitute equation (C) for , we have an expression for exclusively in terms of and , namely

We have the transformation properties of and in the two coordinate systems. What we have not been careful about is the transformations of the other coordinates and . Since the motion is only in the direction, it is not surprising that these coordinates are not affected by Lorentz transformations. So the full equations for the Lorentz transformations are given by

These equations will be discussed at some length in the next lecture.