Dimension 1.1

這段改編自 2010 年 4 月 3 日的對話。

(安:你上次電郵了一段有關「dimension(次元)」的短片給我,內容講述何謂「第四個次元」或以上。但是,你在電郵中又提及,那段短片的講法不盡正確,有所遺漏。它錯在哪裡呢?)

「量數」(counting number)不同於「序數」(ordering number)。以下請留意,「一個」(one)和「第一」(first)的分別;「二個」(two)和「第二」(second)的分別;如此類推。

「點」是零次元;「線」是一次元;「面」是二次元;「立體」是三次元。「時間」,在物理的「相對論」中,可以看成「第四個次元」。「三次元空間」加「一次元時間」,形成我們宇宙的「四次元時空」。

該段影片的錯處是,它假設了,「第四個次元」一定是「時間次元」。它彷彿不知道,在理論上,「第四個次元」可能都是「空間次元」。所以,那段影片有「以偏概全」之嫌。

雖然,根據現時的實驗結果,宇宙的次元數目,的確是「三加一」,即是「『三次元空間』加『一次元時間』」;但是,該段短片的主題是,理論上,「更高次元」的「樣子」是怎麼樣。所以,它完全沒有提及,「第四個次元」是「空間次元」的那個情況,並不是因為作者刻意的剪接。

— Me@2013.01.05

2013.01.06 Sunday (c) All rights reserved by ACHK

Coherent quantum superpositions 1.2

remain secret = is not lost to the environment yet

— Me@2013-01-03 11:07:30 AM

The no-cloning theorem is a result of quantum mechanics that forbids the creation of identical copies of an arbitrary unknown quantum state.

— Wikipedia on No-cloning theorem

[guess]

conservation of information

= you can only move, but not copy, a piece of information

Classical information can be copied because “identical” classical systems are not really identical if we consider their microscopic details. One macrostate can be corresponding to a lot of microstates, e.g.

4 = 1 + 1 + 2

4 = 1 + 3 + 0

copy one macrostate = find another microstate which is corresponding to the same macrostate

Whether two states are “identical” depends on the resolution of the observer.

[guess]

— Me@2013-01-03 11:07:30 AM

2013.01.04 Friday (c) All rights reserved by ACHK

The Dark Knight Makes Sense

Magic | Science, 2  

Nolan’s Batman movies’ are created by making sense out of the nonsense, turning fictional elements into their corresponding reality-based versions. 

As long as you keep removing unreasonable elements, replacing them with reasonable ones, you can get a good story.

只要你把不合理的情節刪除,換上合理的版本,故事自然圓滿,人生方能完善。

— Me@2013.01.03

2013.01.04 Friday (c) All rights reserved by ACHK

Past papers 26.6

這段改編自 2010 年 6 月 15 日的對話。

(LMC:做 past paper(歷屆試題)時,有何要那麼整齊?)

我不是叫你要「整齊」。那不是重點。重點是,考試時,你要做什麼,現在就照樣做,力求逼真。例如,考試時,不會要求你字體「優美」,但是會要求你字體「清楚」。那你就要在平日,習慣字體清楚。

考試時,一方面,你的字體不要太醜陋,因為那會令到評卷員看不清楚,情緒不安;另一方面,你的字體亦不要太優美,因為那會浪費你很多時間,可能導致你,來不及完成全部試題。理想的考試字體是,不美不醜,清晰自然。

— Me@2013.01.04

2013.01.04 Friday (c) All rights reserved by ACHK

Coherent quantum superpositions

Decoherence was worked out in great detail by Los Alamos scientist Wojciech Zurek, Zeh and others over the following decades. They found that coherent quantum superpositions persist only as long as they remain secret from the rest of the world.

— from Max Tegmark; John Archibald Wheeler (2001). “100 Years of the Quantum”. Scientific American 284 (2003): 68–75

— Wikipedia on Quantum entanglement

That means the superposition information is not lost to the environment yet.

— Me@2012.12.31

2013.01.03 Thursday (c) All rights reserved by ACHK

教學無用 2.3

這段改編自 2010 年 4 月 3 日的對話。

你覺得這個定義,還有沒有漏洞?

(安:暫時未發現到有。你的意思是,如果是物理科,就應該給有興趣讀物理的人,來評價他們物理教員的教學質素。)

無錯。又或者,在一個學期完結時,看看那些「愛智人士」,成績進步的多寡。甚至乎,用所謂的「快樂指數」都可以,因為聽課時,要「明白」才會「快樂」。「明白」會帶來舒服的感覺,而「不明白」則會帶來不安的情緒。

當然,「明白的感覺」不等於「明白」。有時,「明白的感覺」是來自「誤解」。但是,如果有「明白感覺」的,不只是一個人,而是一大班有心聽課讀書的人,那「感覺」就有一定的客觀性,不可能完全是「幻覺」。那「感覺」在很大程度上,是來自真正的「理解」。那樣,「教學質素」就可算是合格。

— Me@2013.01.02

2013.01.03 Thursday (c) All rights reserved by ACHK

Light cone

Light-like is between space-like and time-like.

Light is the boundary between space and time.

[guess]

Nothing can be faster than light” may be a tautology due to the definitions of the words “mass“, “speed of light“, “space” and “time“.

— Me@2013.01.01

2013.01.02 Wednesday (c) All rights reserved by ACHK

The World as Will and Representation

… Schopenhauer notes importantly that our body — which is just one among the many objects in the world — is given to us in two different ways: we perceive our body as a physical object among other physical objects, subject to the natural laws that govern the movements of all physical objects, and we are aware of our body through our immediate awareness, as we each consciously inhabit our body, intentionally move it, and feel directly our pleasures, pains, and emotional states. We can objectively perceive our hand as an external object, as a surgeon might perceive it during a medical operation, and we can also be subjectively aware of our hand as something we inhabit, as something we willfully move, and of which we can feel its inner muscular workings.

From this observation, Schopenhauer asserts that among all the objects in the universe, there is only one object, relative to each of us — namely, our physical body — that is given in two entirely different ways. It is given as representation (i.e., objectively; externally) and as Will (i.e., subjectively; internally).

— Wicks, Robert, “Arthur Schopenhauer”

— The Stanford Encyclopedia of Philosophy (Winter 2011 Edition), Edward N. Zalta (ed.)

2013.01.01 Tuesday ACHK

Past papers 26.5

這段改編自 2010 年 6 月 15 日的對話。

製作「魔法筆記」時,記住用一本完整的筆記簿。練習 past paper(歷屆試題)時,亦都要那樣。唯一的分別是,past paper 的練習簿,每科也要用很多本。

千萬不要用草稿紙來做 past paper,因為那樣的話,就會有神奇的事情發生。我的經驗是,只要我把練習做在個別的紙張上,第二日就會立刻找不到。

— Me@2013.01.01

2013.01.01 Tuesday (c) All rights reserved by ACHK

EPR paradox, 9

In an EPR experiment, once you have measured one particle’s spin, you know the spin of the opposite particle instantaneously.

Your ability of getting the total information at once is due to the fact that you know partial information in advance. Since the time of the separation of the two particles, you have already known that “the opposite particle must have an opposite spin”. 

Let

A = the spin of your particle

B = the fact that the opposite particle must have an opposite spin

C = the spin of the opposite particle

knowing A + knowing B = knowing C

There are no superluminal (faster-than-light) communications between the two particles. So the whole EPR experiment is compatible with classical locality, aka special relativity.

The strange thing is the quantum non-locality part.

— Me@2012-04-04 5:21:25 PM  

2013.01.01 Tuesday (c) All rights reserved by ACHK