Monthly Archives: March 2020

Pier

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It was a picture I drawn in 1997. It was the summer holiday after my HKCEE public exam. It was a drawing trip with my school’s Art Club. The location was Sai Kung Pier.

As far as I remember, I haven’t drawn since then. Perhaps I do not like to draw alone. Hope that one day I could find my girlfriend finally so that I have someone to draw with.

— Me@2020-03-24 10:37:58 PM

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2020.03.26 Thursday (c) All rights reserved by ACHK

Problem 2.2b

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A First Course in String Theory

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2.2 Lorentz transformations for light-cone coordinates.

Consider coordinates \displaystyle{x^\mu = ( x^0, x^1, x^2, x^3 )} and the associated light-cone coordinates \displaystyle{x^\mu = ( x^+, x^-, x^2, x^3 )}. Write the following Lorentz transformations in terms of the light-cone coordinates.

(b) A rotation with angle \displaystyle{\theta} in the \displaystyle{x^1, x^2} plane.

\displaystyle{ \begin{aligned} \begin{bmatrix} c t' \\ x' \\ y' \\ z' \end{bmatrix} &= \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & \cos \theta & -\sin \theta & 0 \\ 0 & \sin \theta & \cos \theta & 0 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix} \begin{bmatrix} c\,t \\ x \\ y \\ z \end{bmatrix} \\ \end{aligned} }

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\displaystyle{ \begin{aligned} \begin{bmatrix} \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 & 0 \\ \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix} \begin{bmatrix} (x^+)' \\ (x^-)' \\ y' \\ z' \end{bmatrix} &= \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & \cos \theta & -\sin \theta & 0 \\ 0 & \sin \theta & \cos \theta & 0 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix} \begin{bmatrix} \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 & 0 \\ \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix} \begin{bmatrix} x^+ \\ x^- \\ y \\ z \end{bmatrix} \\ \begin{bmatrix} (x^+)' \\ (x^-)' \\ y' \\ z' \end{bmatrix} &= \frac{1}{2} \begin{bmatrix} \cos\theta + 1 & 1 - \cos\theta & -\sqrt{2} \sin\theta & 0 \\ 1 - \cos\theta & \cos\theta + 1 & \sqrt{2} \sin\theta & 0 \\ \sqrt{2} \sin{\theta} & -\sqrt{2} \sin{\theta} & 2 \cos{\theta} & 0 \\ 0 & 0 & 0 & 2 \\ \end{bmatrix} \begin{bmatrix} x^+ \\ x^- \\ y \\ z \end{bmatrix} \end{aligned} }

— Me@2020-03-22 10:16:09 PM

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2020.03.23 Monday (c) All rights reserved by ACHK

Logical arrow of time, 7.2

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Microscopically, there is no time arrow.

— Me@2011.06.23

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No. There is weak force.

— Me@2011.07.22

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Myth: The arrow of time is a consequence of CP-symmetry violation.

The weak nuclear interactions violate the CP symmetry which is equivalent to saying that they violate the T symmetry. Is it the reason why eggs don’t unbreak? Of course not. There are two basic ways to see why. First, the weak interactions much like all other interactions preserve the CPT symmetry – there is extensive theoretical as well as experimental evidence supporting this assertion. And the CPT symmetry would be enough to show that eggs break as often as unbreak. More precisely, eggs break as often as mirror anti-eggs unbreak. ;-)

— Myths about the arrow of time

— Lubos Motl

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Weak force’s T-symmetry-violation has nothing to do with the time arrow.

In other words, microscopic time arrow has nothing to do with the macroscopic time arrow.

— Me@2020-03-21 07:56:01 PM

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About T-violation and the arrow of time: the simple answer is that the weak interactions are perfectly unitary, even if they are not T-invariant. They don’t affect the entropy in any way, so they don’t help with the arrow of time.

A bit more carefully: if you did want to explain the arrow of time using microscopic dynamics, you would have to argue that there exist more solutions to the equations of motion in which entropy grows than solutions in which entropy decreases. But CPT invariance is enough to guarantee that that’s not true. For any trajectory (or ensemble of trajectories, or evolution of a distribution function) in which the entropy changes in one way, there is another trajectory (or set…) in which the entropy changes in precisely the opposite way: the CPT conjugate. Such laws of physics do not in and of themselves pick out what we think of as the arrow of time.

People talk about the “arrow of time of the weak interactions,” but ask yourself: in which direction does it point? There just isn’t any direct relationship to entropy.

— Sean Carroll

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2020.03.21 Saturday (c) All rights reserved by ACHK

機遇創生論 1.4

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這段改編自 2010 年 4 月 18 日的對話。

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你只能控制因，不能控制果。事情結果，除了受你的因以外，還受千百萬樣其他因素影響。所以，人生的大目標之中，很多也只有極細的成功機會率。

你唯一可以做的，就是透過嘗試掌握，最多的自然定律（道理）和具體資訊（世情／情報），去把成功的機會率，稍為提高一點。但記住，只可以提高一點，不會很多。

或者說，從來沒有必定成功的途徑，只有保證失敗的方法。而保證失敗的主要方法有：

  1. 不懂道理

  2. 懂道理但缺乏足夠情報

刪除必敗之道，就有成功之機。

這個大統一理論的成員，包括（但不止於）：

精簡圖：

種子論
反白論
間書原理
完備知識論

自由決定論

它們可以大統一的成因，在於它們除了各個自成一國外，還可以合體理解和應用。

而道理和情報之中，較為常用的，有「反白論」和「間書原理」。

「反白論」的意思是，現時的地球人間，極多的情況下，名義與實情都是相反的。

反白論 ～ 名實時常相反論

例如，真正的有利健康的食品，例如蘋果，你不會刻意標籤它，為「健康食品」。市面上，刻意標籤為「健康食品」的，通常也是人工製品，營養價値不及水果高，有時甚至有害。

又例如，小學畢業和中學畢業時，紀念冊也會寫「友誼永固」，正正是友誼不會永固，通常。長大後，仍然有聯絡的兒時同學，極端接近零。從來沒有「石頭永固」的口號，因為，石頭本身就永固。

再例如，通常國家名越長，包含越多形容詞，那個國家就越危險。國名中的形容詞，往往正正就是，那個國家沒有的東西。

As a rule of thumb, the more qualifiers there are before the name of a country, the more corrupt the rulers. A country called The Socialist People’s Democratic Republic of X is probably the last place in the world you’d want to live.

–- Paul Graham

又再例如，為什麼結婚時會「山盟海誓」？

正正是因為愛情關係，可說是眾多感情關係中，最不可靠的一種；正正是因為誓詞中的承諾，很多人也不能達到。不信的話，你可以查看，離婚率的高低。

又再又例如，

我認為，對我們來說，一個人，一個黨，一個軍隊，或者一個學校，如若不被敵人反對，那就不好了，那一定是同敵人同流合污了。如若被敵人反對，那就好了，那就證明我們同敵人劃清界線了。如若敵人起勁地反對我們，把我們說得一塌糊塗，一無是處，那就更好了，那就證明我們不但同敵人劃清了界線，而且證明我們的工作是很有成績的了。

「反白論」的應用在於，掌握以後，大大減少了，你被世人欺騙得到的比例。

而更上一層樓話，你更可以反世人之言而行。例如，你選擇工作時，再不會為了一個職位的名氣大而選它，因為「名氣大」通常代表「收入少」或者「不快樂」。否則，為什麼一份工作需要用「名氣大」作賣點呢？

你不會再考慮，一份工作的名氣大小。反而，你會先考慮其短期收入和長遠收入，再考慮自己的興趣。

— Me@2020-03-19 09:34:39 PM

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2020.03.21 Saturday (c) All rights reserved by ACHK

scmutils, 3

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Structure and Interpretation of Classical Mechanics

Scheme Mechanics Installation for GNU/Linux

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This post assumes that you have already installed the scmutils library and been able to open it using the standard editor Emacs.

If not, go to the bottom of this post to click the category scmutils, so that you can see all the posts in this scmutils series.

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Then go to the post “scmutils, 2.3.2” to follow the installation and setup instructions.

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After installing and setting up the scmutils library, you can start to use it.

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However, what if you want to close the Emacs editor? How to save your scheme program before closing Emacs?

By default, you cannot. So I have written a small program to help. Here is the installation instruction:

1. Go to the end of the .emacs file. Add the following code, if it does not already exist:


(defun mechanics()
  (interactive)
  (run-scheme
   "/usr/local/scmutils/mit-scheme/bin/scheme --library
/usr/local/scmutils/mit-scheme/lib"
  ))

2. Add the following code:


(fset 'set-working-dir
      (lambda (&optional arg) "Keyboard macro."
	(interactive "p")
	(kmacro-exec-ring-item
	 (quote ("(set-working-directory-pathname! 
                  \"~/Documents/\")\n" 0 "%d")) arg)))
 
(fset 'load-scm
      (lambda (&optional arg) "Keyboard macro."
	(interactive "p")
	(kmacro-exec-ring-item
	 (quote ("(load \"tt.scm\")" 0 "%d")) arg)))
 
(defun mechan ()
  (interactive)
  (split-window-below)
  (windmove-down)
  (mechanics)
  (set-working-dir)
  (comint-send-input)
  (windmove-up)			
  (find-file "~/Documents/tt.scm")
  (end-of-buffer)
  (windmove-down)
  (cond ((file-exists-p "~/Documents/tt.scm")
	 (interactive)
	 (load-scm)
	 (comint-send-input)))
  (windmove-up)
)
 
(defun cxce ()
  (interactive)
  (save-buffer)
  (windmove-down)
  (load-scm)
  (comint-send-input)
  (windmove-up)
)
 
(global-set-key (kbd "C-x C-e") 'cxce)

3. Close Emacs. Re-open it.

4. Type the command

M-x mechan

The command M-x means pressing the Alt key and x together. Then type the word mechan.

5. You will see the Emacs editor is split into two windows, one up and one down.

The lower window is the scheme environment. You can type a line of code and the press Enter to execute it.

The upper window is the editor. You can type multiple lines of code and the type

C-x C-e

to execute it. The command C-x C-e means pressing Ctrl and x together and then Ctrl and e.

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6. Your scheme code is saved to the following file

"~/Documents/tt.scm"

In case you need to backup your code, backup this file.

— Me@2020-03-10 10:59:45 PM

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2020.03.10 Tuesday (c) All rights reserved by ACHK

Bell’s theorem, 7

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dools on Nov 21, 2014

When I watched the Leonard Susskind lectures on quantum entanglements he said the whole “communicating faster than light” thing is a bit misleading. The analogy he gives if imagine you have two coins and you ask someone to turn them over so one is heads and the other tails then you give them to 2 people without them knowing which is which, then they go to opposite ends of the universe, and they look at their coins, they instantly know the state of the other coin purely by deduction.

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hasenj on Nov 21, 2014 [-]

That’s what Einstein argued for, and it’s what Bell’s inequality proves to not be the case.

I actually remember seeing a Youtube video of Susskind talking about how “FTL” communication is a hack to try to force the quantum state to conform with our notions about the world. (he didn’t phrase it this way though; just my interpretation).

I don’t know the context it was said, but it seemed to imply that there’s a way of thinking about quantum states completely independent of set theory and our classical notions, and this way of thinking should not require FTL communication between entangled particles.

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evanb on Nov 21, 2014 [-]

While GP’s example is not what happens in QM (Bell’s inequality shows that the state of the two coins is not predetermined-but-secret), it is akin to that example, in the sense that because each person gets a random (though correlated) bit, they cannot transmit information to one another.

Bell’s inequality is a statement about the possible strength of the correlation, rather than about information transmission.

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pfortuny on Nov 21, 2014 [-]

Exactly. It is important to note that there is no information exchange if you do not have any information at all.

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— You can’t get entangled without a wormhole (2013)

— Hacker News

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2020.03.07 Saturday ACHK

反貼士搵笨大行動 1.2

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幾個月後，考了物理科後的一晚，我和馬同學於電話傾談。他說他在見到試題時，十分生氣，因為不如傳說中的所謂「5 題貼中 4 題」。（根本就一題也沒有貼中，除非「貼中」的定義，就只是「同一課題」而已；例如，貼「力學」題目，又真是出了「力學」題目。）

我則不會有那樣的期望。我回答他說：「如果他真的可以貼中題目，他在平時又何須那麼用心去授課？他又何須在聖誕假和農曆年假中，再要不斷的補課呢？」

他：「真希望思考可以像你那麼成熟。那不是反話。那是我真正覺得。」

幾個月後，我有幸升到預科中六，打算再參加 Ken Chan 的補習班。他在我中五時，沒有同時開中六的課程。我估計，那是因為高考班的市場，只有會考班的五分之二。但是，在我中五後，傳說他會開中六班。所以，我打算去問一問，本來。

不幸，該補習社的負責人，在那時（1997 年的暑假）因涉嫌無牌經營補習社，被警方的重案組拘捕了。結果，我不了了之，中六時沒有再補物理。

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在我參加 Ken Chan 補習班的年代，在他的筆記中，每題 MC 題目方格的底部，都會有一句署名，大概是

This question set is prepared by Ken Chan. Please contact Ken Chan if you want to use it in your class.

我也不記得確實在哪時，但大概是在 1996 年底，他說：「最近的筆記，可能署名不是我，而是 MC Chan。我的手提電腦中了毒，所以需要問他借筆記。」

幾個月後，1997 年初，補習課程的尾聲時，Ken Chan 說：「今年我無開 intensive course（臨近正式公開試時的精修密集班），如果需要的話，你可以找市面上另一位導師。」

那另一位導師，因為在另一間補習社任教，Ken Chan 所以不好意思，直接開名介紹，唯有暗示：

「我係 Long Ques 陳，你估吓另一位係邊個。」

「Long Ques」即是長題目。相反就是「MC」，即 multiple choices（多項選擇題）。他所暗示的，其實就是 MC Chan。

Ken Chan 竟然會介紹其他導師，其實我有一點意外。他願意介紹的，必定和他的水平相當。但是，Ken Chan 對我來說是，半人半神。難以想像有另一個物理的半人半神。

在大約十年後，2007 年時，我是一位日校的數學教師。數學問題外，有空時，我也時常答學生物理問題。有一次，我向給有幾位學生解釋物理時，有一位學生突然講：「好似 Ken Chan 呀！」

她的意思是，我解釋物理時的說話風格，與 Ken Chan 的，十分相似。由於法例所限，日校教師不可介紹補習導師，所以，我沒有回應。我只能在心裡說：「梗係以啦，好細個嗰陣，係佢學生吖嘛。」（當然相似啦，因為我小時候是他學生。）

另一次那位學生問我物理。那份筆記我揭到封面看一看，原來是 Ken Chan 班的筆記。我感格外親切。

「咦，你識佢呀？」（你認識他嗎？）我的學生問。

又由於法例所限，我再沒有回應。但她再講多一句：「佢仲有個呀哥 MC Chan。」（他還有一個哥哥 MC Chan。）

雖然我不知其真假，但我覺得十分有可能，因為，那解釋了為何 Ken Chan 會信任他。

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中六時，我日校的同學中，有些在中五時和我一樣，都是補 Ken Chan 的物理班。升上中六後，他們大部分也補 MC Chan 的物理班。我在中六時則沒有補習。

— Me@2020-03-04 11:18:52 PM

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2020.03.07 Saturday (c) All rights reserved by ACHK