反貼士搵笨大行動 1.3

無足夠資料 12

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中六時,我日校的同學中,有些在中五時和我一樣,都有補 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。

哪我為什麼在中六時,不去補 MC Chan 的物理班呢?

一方面,那時我覺得,只要足夠勤力,不補也沒有大所謂。另外,補習本身,就要花很多,我原本可以用來,研習的時間。

會考的兩年課程中,因為不開心,荒廢了第一年。所以,中五時的補習,是必須的。 但是,我在預科一開始的中六時,就立刻起步讀書,所以,我覺得我可能,毋須補習物理。

思前想後,結果,我在中六升中七的暑假,才去上 MC Chan 的物理班。那算是有點兒幸運,因為太多人報讀,不一定有學位給我。我第一次上他的課時,情形如我日校同學所述,真的連桌子之間的行人路,也放了椅子坐了人。好處是,那證明了導師真的很有型。壞處是,萬一有火警的話,一定傷亡慘重。

事後看來,我當年應該要中六開始時,就補 MC Chan 的物理。

理論上,只要花得足夠多時間研習,不補習也可以獲得,補習時獲得的知識。

實際上,這個講法,就有如:「雖然我住在十二樓,但是只有花足夠多的時間,用心行樓梯,我不乘搭升降機,也可以過到快樂的生活。」

(問:那你即是贊成補習?)

你這樣問沒有意思,因為,那就好像問我,贊不贊成看醫生。那要看情況而定,不能一概而論。

需不需要補習的一個指標是,你在日校專心聽課後,懂不懂做以往的公開試試題?

你可先參考本網誌的五篇文章:

無足夠資料

自我實現預言

天人天書

無足夠資料 4

無足夠資料 5.2

這五篇文章的主旨是,

  1. 「無知」即是「缺乏足夠資料」;

  2. 「無知」不是「愚蠢」。

需不需要補習的一個指標是,你在日校專心聽課後,懂不懂做以往的公開試試題?

如果你大部分試題也不懂做,那就代表了,你的日校導師,沒有提供足夠的資料給你,簡稱「無料到」。那樣,解決辦法是,找過另一位,可以提供足夠物理資料的導師。

記住,如果需要「補習」的話,重點不在於「補習」(額外上課),重點在於,你可以選擇導師。

而「選擇導師」的重點則在於「選擇」,而不在於「導師」。

有補習導師並不代表,你就會懂得做試題。

補習導師和日校導師一樣,可能提供不到足夠資料,即是「無料到」。補習導師和日校導師一樣,質素都是沒有保證的。「沒有保證」的意思是,如果補習無用,導師並不會賠償,你所損失的,大量金錢和時閶。

所以,「選擇導師」的重點在「選擇」,不在「導師」。

選擇對導師,才會有成果。

而「有料到」的導師極少,不易找到。以下是選擇導師的方法:

— Me@2020-03-31 04:28:23 PM

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2020.04.05 Sunday (c) All rights reserved by ACHK

Pier

d_2020_03_24__22_44_50_PM_

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

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} }

~~~

\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

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

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

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.

d_2020_02_22__16_02_00_PM_

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.

d_2020_02_22__18_12_54_PM_

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.

d_2020_03_11__20_28_27_PM_

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

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

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

Problem 2.2a

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.

(a) A boost with velocity parameter \displaystyle{\beta} in the \displaystyle{x^1} direction.

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

~~~

\displaystyle{ \begin{aligned} \begin{bmatrix} x^+ \\ x^- \end{bmatrix}  &= \frac{1}{\sqrt{2}}     \begin{bmatrix}        1 & 1 \\        1 & -1 \\     \end{bmatrix}     \begin{bmatrix} x^0 \\ x^1 \end{bmatrix}    \end{aligned}}

The matrix is its own inverse.

\displaystyle{ \begin{aligned} \begin{bmatrix} x^0 \\ x^1 \end{bmatrix}  &=  \frac{1}{\sqrt{2}}     \begin{bmatrix}        1 & 1 \\        1 & -1 \\     \end{bmatrix}  \begin{bmatrix} x^+ \\ x^- \end{bmatrix} \\   \end{aligned}}

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

Apply the result to the original transformation:

\displaystyle{ \begin{aligned} \begin{bmatrix} (x^0)' \\ (x^1)' \\ (x^2)' \\ (x^3)' \end{bmatrix}  &= \begin{bmatrix} \gamma&-\beta \gamma&0&0\\ -\beta \gamma&\gamma&0&0\\ 0&0&1&0\\ 0&0&0&1\\ \end{bmatrix} \begin{bmatrix} x^0 \\ x^1 \\ x^2 \\ x^3 \end{bmatrix} \\   \end{aligned}}

\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} \gamma&-\beta \gamma&0&0\\ -\beta \gamma&\gamma&0&0\\ 0&0&1&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}  \end{aligned}}

\displaystyle{ \begin{aligned}    \begin{bmatrix}        1  & 1 \\        1  & -1 \\     \end{bmatrix}  \begin{bmatrix} (x^+)' \\ (x^-)' \end{bmatrix}  &= \begin{bmatrix}       \gamma & -\beta \gamma \\       -\beta \gamma &\gamma       \end{bmatrix}     \begin{bmatrix}        1  & 1 \\        1  & -1 \\     \end{bmatrix}  \begin{bmatrix} x^+ \\ x^- \end{bmatrix}  \end{aligned}}

\displaystyle{ \begin{aligned} \begin{bmatrix} (x^+)' \\ (x^-)' \end{bmatrix}  &= \begin{bmatrix}        \gamma (1-\beta) & 0 \\        0 & \gamma (1+\beta) \\     \end{bmatrix}  \begin{bmatrix} x^+ \\ x^- \end{bmatrix}  \end{aligned}}

— Me@2020-02-27 07:14:19 PM

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2020.02.27 Thursday (c) All rights reserved by ACHK

Superposition always exists, 2

Decoherence means that the different components in the superposition do not interact with each other, but it does not mean that the components separate to form different macroscopic realities.

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Just like when a 100-soldier army’s marching gets interrupted, the decoherent soldiers do not form a single army anymore, because their actions become out of sync.

However, they do not become 100 armies either.

Instead, they form a group of 100 random people in the street.

Although now they are out of sync with each other, all original soldiers still exist, forming the (new) average result; all or most of them have become part of the environment.

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But it is an analogy only. It has an important distinction.

In quantum superposition, we discuss the relationships between different component states of the superposition. Those states exist not in physical space, but in a mathematical space.

In the army analogy, we discuss the relationships between the actions between different material items (solders in this case). Those material items exist in physical space.

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The unselected eigenstates do not cooperate with other particles to form macroscopic realities.

Although the spirit of the statement is correct, the statement itself is incorrect in multiple senses.

First, an eigenstate is a quantum state. It interferes with other eigenstates, not other particles.

Second, although the “unselected” eigenstates seem to disappear, they actually still exist; they entangles with the environment, which includes the apparatus and measurement devices of that experiment.

— Me@2013.01.01

— Me@2020-02-26 06:49:46 AM

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In “decoherence means that the different components do not interact with each other”, the meaning of “interact” is not defined yet.

The word should probably be “interfere”, instead of “interact”.

— Me@2020-02-25 10:44:23 PM

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interference ~ superposition with pattern

Decoherence means that the phase differences between different components in a superposition are not constants anymore. It does not mean that there is no superposition anymore.

Superposition is always there.

What disappears is the interference pattern, not the superposition.

— Me@2019-09-20 06:48:55 AM

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2020.02.26 Wednesday (c) All rights reserved by ACHK

Light, 2

Buddha 3 | 無額外論 6

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Whoever follows the principles is the Light.

— Me@2011.08.24

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The tricky part is that it is hard to know the principles, but feasible, as long as you are willing to pay the price.

— Me@2020-02-25 06:15:08 PM

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2020.02.25 Tuesday (c) All rights reserved by ACHK

機遇創生論 1.3

這段改編自 2010 年 4 月 18 日的對話。

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你可以花一生的時間,去令到自己受歡迎;但是,你的喪禮將會有多少人出席,還要視乎當日的天氣。

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萬事俱備,只欠東風時,就應該立刻離開,讓東風做事,不要阻礙東風。

亦即是話,一件事情的發展結果,受眾多因素影響。有些你控制得到,有些你控制不到。你既要盡力處理,你控制得到的部分,亦同時要盡力去忽略,你控制不到的部分。

千萬不要干涉,大自然的內政,因為,那只會弄巧反拙。

例如,如果你想受人歡迎,你可以做的,就是認真工作,善待自已,以誠待人等。最終會不會受歡迎,那不在你控制範圍。

試想想,如果你企圖保證,自己受歡迎的話,情形會怎樣?

情形就是,你會不斷地提醒他人,你自己的存在。那只會為他人,帶來極大的滋擾。那反而會令你討厭。

原理上,你就應該化成磁鐵,盡其在我地,增加自身的吸引力。重點是,你只可以吸引,而不能拉扯。

正如磁鐵一樣,它只能吸引磁性物質。其他東西,並不會受其吸引。

題外話:而更重要的問題是,為什麼要追求「受歡迎」呢?「受歡迎」的好處,真的大於壞處嗎?

而「不要干涉大自然的內政」,並不代表,「種子論」是「被動」、「消極」的。或者說,那是有意義的「被動」和有策略的「消極」。

那並不是負面意思下的被動消極,原因是「種子論」的行動三部曲,其實也相當上進積極。

第一部,要盡你自己的能力,獲取最多的情報,有關哪裡的土壤,最有機會讓農作物茁壯成長。然後,在那些範圍播種。沒有種子,就不可能有果實。 

第二部,有種子,亦不一定會果實。所以,你要積極不做事,積極去等待。除了定期的灌溉和施肥等工序外,並沒有任何行動,令你可以保證某單一棵植物,一定開花結果。

第三部,而要訓練到自已,習慣在適當的地方和時間,去「積極不做事,積極去等待」的技巧是,先做其他東西,同時在其他土壤播種。

而這正正回應了第一部:正正是因為,在某一指定地方有成果的機會極細,你要在最多的土壤,灑下最多的機遇種子;而底線是,不要多到自己管理不到。

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一件事情的發展結果,受眾多因素影響。有些你控制得到,有些你控制不到。你既要盡力處理,你控制得到的部分,亦同時要盡力去忽略,你控制不到的部分。

While we are free to choose our actions, we are not free to choose the consequences of those actions. Consequences are governed by natural law.

— The 7 Habits of Highly Effective People

— Stephen R. Covey

那只是理論比喻。執行「種子論」的真正難度在於,有時,在事情完結前,很難去分清該事件中的哪些部分,是「可控部分」,而哪些部分,卻是「不可控部分」。

亦即是話,「謀事在人,成事在天」之中,哪些部分而要由「你」去「謀」,而哪些地方是由「天」去「成」,事前不一定知道。

所以,那不會有公式答案,只能靠自己或他人的學術知識和實際經驗。

Grant me the serenity to accept the things I cannot change,

the courage to change the things I can change,

and the wisdom to distinguish the two.

「經驗」的近義詞,是「錯誤」。它們不同義的地方,在於「經驗」可以累積,「錯誤」不一定可以累積。

「種子論」的重點,並不是給予你,一條必勝的方程式。

「種子論」的重點是,令你知道,無論如何,你也會遇到無數次的失敗;那是正常不過的事。「種子論」的重點是,令你不再害怕失敗,從而,你會勇於嘗試,敢於超大量地犯錯。

「種子論」的重點是,重複犯同一個錯誤本身,並不能提高成功的機會率。

「種子論」所要求的「不斷犯錯」是,每次也是「新的錯誤」。「新錯誤」的意思,並不只是相對於你來說是「新」,而是相對全人類來說,都是「新」。

別人犯過的錯誤,你也不可以再犯。

一千萬次的失敗,可以兌換一次的成功。

而一次的成功,卻可以兌換一千萬次的應用。

— Me@2020-02-24 10:52:08 PM

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2020.02.24 Monday (c) All rights reserved by ACHK

scmutils, 2.3.2

Scheme Mechanics Installation for GNU/Linux

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Steps:

1. The following steps are tested in Ubuntu 18.04. Prepare Ubuntu 18.04 if you can.

Note: Since the installation of the library scmutils requires the root access of your Linux system, please do NOT use it on your working computer. Instead, create an isolated virtual machine to use it.

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2. 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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3. Go to the post titled “scmutils, 2.3” to download

scmutils-20160827-x86-64-gnu-linux

4. Although the official installation guide advises you to install “MIT/GNU Scheme system” before installing scmutils, you do NOT need to install “MIT/GNU Scheme system” at all.

5. Unzip the file scmutils-20160827-x86-64-gnu-linux.

In the following, if you need to copy any commands or programming codes, remember that any number on the left of the vertical green line is NOT part of the code.

6. Run the command

tar xzf scmutils-20160827-x86-64-gnu-linux.tar.gz

to further extract the file.

-x — extract files from an archive;
-f — specify the archive’s name;
-v — show a list of processed files.

— Wikipedia on tar (computing)

Then two folders will be created: bin and scmutils.

7. Run the command

cd bin

to go into the folder.

You will see a file called mechanics.

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8.1 Run the command

mechanics

You will get the error

mechanics: command not found

8.2 Instead, you should run the command

./mechanics

to specify that the file mechanics is actually in the current folder.

You will get the error

./mechanics: line 16: exec: xterm: not found

It is because your Linux system has not the program xterm yet.

8.3 Run the following command to install it.

sudo apt-get install xterm

8.4 Run the command again:

./mechanics

There will be an xterm window popup, but with an error message inside:

d_2020_02_22__17_08_35_PM_

That means you should move the two folders, bin and scmutils, to the pre-defined locations.

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9.1 Run the command to move the folder scmutils to its pre-defined location:

mv scmutils /usr/local/

You will get the error

mv: cannot move 'scmutils' to '/usr/local/scmutils': 
Permission denied

9.2 Try again by

sudo mv scmutils /usr/local/

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10.1 Go inside the folder bin.

10.2 Move its content to the pre-defined location by this command:

sudo mv mechanics /usr/local/bin/

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11. Run the command

mechanics

Then you will see the Edwin window is opened. That means, in theory, you system has successfully installed the scmutils library. You can use it within the Edwin window if you like.

However, in practice, it is difficult, because it provides no syntax-highlighting. Also, you cannot use mouse in the Edwin window, so if you want to copy and paste a command or a series of commands, there will be no obvious way to achieve that.

So I suggest you to use the standard Emacs as the editor instead.

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12.1 If you do not know Emacs, learn its basics.

12.2 Also, learn how to open Emacs’ initialization file, which has the filename

.emacs

After opening the file, you will see that it is just a text file.

12.3 Go to the end of the .emacs file. Add the following code:

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

12.4 Save the file. Close Emacs. Then re-open Emacs.

12.5 Within Emacs, type the command

M-x mechanics

M-x means that while the Alt key is pressed down, press also x. Then type the word mechanics.

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12.6 Type the command

(+ 1 1)

to test the system.

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13. If you want to access your last command without re-typing it, type the command

M-p

d_2020_02_22__18_19_31_PM_

— Me@2020-02-22 06:25:47 PM

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2020.02.22 Saturday (c) All rights reserved by ACHK

Unitarity, 2

Just as in the definition of a function in mathematics, two x values can map to the same y value, but one x value cannot map to two y values; the future is unique in classical physics.

In quantum mechanics, the uniqueness is not of the measurement results, but of the set of probabilities of the results.

— Me@2018-02-03 11:29:18 AM

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With respected to a known state, the future is unique in classical physics.

In quantum mechanics, the set of probabilities is encoded in the wave function.

— Me@2020-02-21 06:25:52 PM

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2020.02.22 Saturday (c) All rights reserved by ACHK