# Pier

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

.

.

# Problem 2.2b

A First Course in String Theory

.

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

.

.

# Logical arrow of time, 7.2

Microscopically, there is no time arrow.

— Me@2011.06.23

.

No. There is weak force.

— Me@2011.07.22

.

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

.

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

.

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

.

.

~ 愚蠢化

— Me@2011.06.23

.

.

# 機遇創生論 1.4

.

1. 不懂道理

2. 懂道理但缺乏足夠情報

「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。

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

「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。

— Me@2020-03-19 09:34:39 PM

.

.

# scmutils, 3

Structure and Interpretation of Classical Mechanics

Scheme Mechanics Installation for GNU/Linux

.

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.

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

.

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

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"
))




(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)))

(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)
(comint-send-input)))
(windmove-up)
)

(defun cxce ()
(interactive)
(save-buffer)
(windmove-down)
(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.

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

.

.

# 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.

.

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.

.

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.

.

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.

.

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

— Hacker News

.

.

2020.03.07 Saturday ACHK

# 反貼士搵笨大行動 1.2

.

「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。

「咦，你識佢呀？」（你認識他嗎？）我的學生問。

.

— Me@2020-03-04 11:18:52 PM

.

.