主题：从狭义相对论公式看当物体超光速的时候，是否是会时光倒流？ -- 思想的行者

for the reasons said many times, I am going to write the way I have been writing, sorry for the "dark side" of it, using a lot of rough analogies to get the key & basic concepts/"model" across.

1.

德布罗意物质波 has no media or "介质" in terms of

macroscopic physics;

for classic/macroscopic waves, we normally can figure out the physics wave equations associated with them, partially by figuring out the physics of "介质" involved.

2.

德布罗意物质波 is still a 物质波

but the 物质 here is in terms of "mesoscopic and/or microscopic" physics, where "介质" is difficult to define in general, except for specific situations or applications such as "晶格/laatice viberations/晶格振动"/ phonon etc.

[PDF]

晶格振动的量子化－声子

staff.ustc.edu.cn/~zhaojin/courseware/chap10.pdf

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引入简正坐标，用分析力学的方法重新处理晶格振动问题. 将分析力学中的哈密顿量 ..... (1)离子-离子相互作用引起的晶格振动--声子(phonon);. (1)离子-离子相互作用 ...

3

薛定谔(Schroedinger): how to model 德布罗意物质波?

1).

测不到"介质"

obviously, at his time, that was a huge challenge for humanity as a whole.

roughly speaking, his logic of guessing/modeling of 德布罗意物质波 is very logic and intuitive:

since it's hard to figure out the general "media/介质" of 德布罗意物质波, 薛定谔 starts with/or goes back to the original 色散關係 of 德布罗意物质波

2)

"测"色散關係

物质波是"概率波", and we are talking about physics, not "social science", if 测不到"介质", then how about 测 some kind of "form" related to 粒子 in terms of "动量为p=mv，能量为E"?

色散關係 is basically about the following concept

"德布罗意是把光的这个波粒二象性的事实加以推广，提出一切微观粒子都具有波动性的大胆假设，并论证了一个动量为p=mv，能量为E的自由的粒子，相当于一个波长为λ=h/p、频率为ω=E/h、沿粒子运动方向传播的平面波（h=6.6260755×10-34Js 是普朗克常量）";

dispersion relation

roughly speaking it is about relationship between 波数/波长 & 频率

4.

basic PDE modeling of wave function in general:

"回到波动方程，举个最简单的例子，平面波函数Ａ＊exp[i＊(w＊t＋k＊x)]。相信您学过傅里叶变换，理解为什么考虑平面波一般就够了。平面波函数对时间求个导数，哇塞，出来一个 i，进入虚数时空了！对空间位移求导，也能出 i，太神奇了。其实不光物理，工程也一样。随手翻开一本数字信号处理就会发现，Mama Mia！"

basically & roughly speaking,

波动方程 (such as those with "正弦波"解)对空间位移求导/微分: we are going after 波数/波长, similarly, if we do it a couple of times, we are going after pattern/ratios of 波数/波长 ;

波动方程 (such as those with "正弦波"解) 对时间求个导数/微分: we are going after

频率, & and if we do it a couple of times, we are going after the pattern/ratios of 频率;

and with all that, we are going after

色散關係 of "物质波", 方向正确?

with pattern or metrics of 色散關係 modeled and calculated, we then go to lab, play with a few atoms, such as 氢原子光谱: omg, 薛定谔=伟光正, global, at humanity level, 坐标系变换不变(:).

I had a post about 哈密顿 modeling and its apps in QM modeling of 德布罗意物质波.

5.

德布罗意物质波是"概率波":

again, roughly speaking, if in many cases, 德布罗意物质波 has no "介质"(or 介质 we can measure in the lab), then it is not really 傳播, with no 能量: in that sense, 德布罗意物质波 is a "phase wave" or travelling as 相位波 with 动量 & 概率;

here comes all the "complex numbers" related to 相位波, 超光速 etc;

"相位波"超光速 is real in terms of

"量子计算与量子逻辑门 操作上为所有可能的幺正变换，因而，对态的操作应是幺正的、 可逆的，无能量的"

6.

自旋, dirac equation, QFT, etc

as posted before about Berry相位, "相位波/field" is still 物质波/field, possibly related to 自旋 and atom (自旋 based) interactions with the global "heatbath" in terms of QFT , etc

POV is critical to 量子计算与量子逻辑门, not sure where China(or USTC) is in that area, likely very behind.

可观测量视为正算子测度，并深入探索而得到量子测量理论

7.

科学=logic+实证+預測

量子力学(& 量子场论) is the best we have ever had as a 科学, at this stage of humanity, period.

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[DOC]

3. PlaneWave-1

www.ss.ncu.edu.tw/~cjpan/wave/3.%20PlaneWave-1.doc

這就是dispersion relation(色散方程式)，由dispersion relation來規範波在介質中的傳播，如果波在某介質下能傳播，就一定要滿足dispersion relation 其中k規範， ...

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哈密顿力学表述形式长驱直入量子力学 - 西西河

www.cchere.com/article/3871187

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2013年4月28日 - 哈密顿力学表述形式长驱直入量子力学 [ 晓兵 ] 于:2013-04-28 ... 赵凯华. (北京大学物理学院，北京l00871). PDF]. 创立量子力学的睿智才思.

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几何相位与量子相变| Yin Zhangqi's Blog

zqyin.wordpress.com/2007/04/26/几何相位与量子相变/

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2007年4月26日 - Berry相位，又称为几何相位，是系统的哈密顿绝热的沿着闭合的参数回路周期性的变化时，在波函数上引入的附加相位。几何相位与系统的Hilbert ...

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POV, 正算子测度

本书是Springer《物理学讲义》丛书新系列第31卷。书中利用量子理论的概率结构，用运算量子物理学给出量子力学一个系统表述。书中把可观测量视为正算子测度，并深入探索而得到量子测量理论，从而应用它来解决长期存在于量子力学基础中的哲学概念，并解释其中的疑难问题，而且使许多量子力学中最新的基本实验也获得圆满分析。

量子力学研究领域的高年级大学生、研究生和科研人员；物理学的哲学家及算子测度的数学工作者。

此书为英文版！