時間定義 7.1

為什麼要有「時間」這個概念呢?

那是因為我們要把不同的東西,用同一個標籤來指示。

例如,「十年前的你」和「現在的你」原本可以被定義為不同的人。「十年前的你」和「現在的你」無論在高矮肥瘦,或者思考想法都完全不同。把兩者定義為「不同的人」—— 前者叫做「甲」;後者叫做「乙」—— 並沒有大錯。那樣的話,「甲」和「乙」並沒有所謂「時間」的關係。

但是,如果你堅持「甲」和「乙」是同一個人,都是叫做「阿安」的話,你怎樣解釋「甲」和「乙」那些互不相容的性質呢?恰當的解釋是,因為「阿安」有「變化」:「阿安」由「2000 安」逐漸「變化成」「2010 安」。因為有「變化」,所以「甲」和「乙」的很多性質,例如身高,並不相同。

引入「變化」這個概念的話,「時間」概念就隨之而產生。例如,我們可以問,「甲」和「乙」有什麼關係呢?

「甲」其實是「乙」的「過去」;「乙」其實是「甲」的「將來」。「乙」是由「甲」變化而成的。他們都同樣叫做「阿安」。「他們」並不是「他們」,而是「他」。

— Me@2011.01.27

2011.01.27 Thursday (c) All rights reserved by ACHK  

String theory 6

Contact with experiment

The mathematics of string theory may lead to new insights on quantum chromodynamics, a gauge theory which is the fundamental theory of the strong nuclear force. To this end, it is hoped that a gravitational theory dual to quantum chromodynamics will be found.

This means that the discovery of a new gauge group with a small quantum of charge and only heavy charged particles would falsify string theory. Since this argument is very general — relying only on black-hole evaporation and the holographic principle, it has been suggested that this prediction would be true of any consistent holographic theory of quantum gravity, although the phrase “consistent holographic theory of quantum gravity” might very well be synonymous with “String Theory”.

It is notable that all the gross features of the Standard model can be embedded within String theory, so that the standard model is not in the swampland. This includes features such as non-abelian gauge groups and chiral fermions which are hard to incorporate in non-string theories of quantum gravity.

— Wikipedia on String theory

2011.01.26 Wednesday ACHK

CKY 1

這段改篇自 2010 年 4 月 30 日的對話。

AMaths(附加數學)之後,相隔多少日才考英文?

(CKY:下星期二考 AMaths,然後星期五考英文。)

再下一個星期就考生物?

(CKY:還有會計。)

你 AMaths 有沒有做 past papers(歷屆試題)?

(CKY:沒有。)

那樣不行。因為下星期就考 AMaths,所以你現在主要需要做的,不是溫習課文,而是做 past papers。

還有,不同的 grade(成績等級)有不同的溫習策略。你想奪取哪一個 grade?

(CKY:最好是有 C 或以上。)

如果目標是 C 的話,你應狂轟 section A (甲部),因為 section A 比 section B 淺很多,最符合成本效益。狂轟 section A 時,記緊提高運算的準確度。

還有,你溫習時要取捨。例如,如果 Equations of Circles(圓形方程)從來只會在 section B,而不會在 section A 出現的話,那你就可以暫時不理 Equations of Circles。明不明白我的意思?

(CKY:我明。)

你現在先檢查一下,section A 有沒有 Circles 的題目。

你看。完全沒有。所以你就可以暫時不理它。

現在,對你來說,溫習的「絕招」,是狂轟所有 past papers 的 section A。不屬於 section A 題目的個別課題,你就可以暫時不理它們。其實,只要你在 section A 的作答完全正確,你奪取到 C 級成績的機會就會很大。或者說,即使你在 section B 一題也不做,一分也得不到,只要你在 section A 運算準確,準確到連一個標點符號都沒有錯的話,你奪取到 C 級成績的機會就會很大,因為 section A 在全卷 110 分之中,佔了 62 分。

(CKY:那會很難做到。)

— Me@2011.01.26

2011.01.26 Wednesday (c) All rights reserved by ACHK

Physics Today

Physics Today, created in 1948, is the membership journal of the American Institute of Physics. It is provided to 130,000 members of twelve physics societies, including the American Physical Society. Over the last 60 years many famous physicists have written for the magazine, including Albert Einstein, Niels Bohr, and Richard Feynman.

Although its content is scientifically rigorous and up to date, it is not a true scholarly journal in the sense of being a primary vehicle for communicating new results. Rather, it is more of a hybrid magazine that informs readers about important developments in the form of overview articles written by experts, shorter review articles written internally by staff, and also discusses the latest issues and events of importance to the science community such as science politics.

The physics community’s main vessel for new results is the Physical Review suite of scientific journals published by the American Physical Society and Applied Physics Letters published by the American Institute of Physics.

— Wikipedia on Physics Today

2011.01.25 Tuesday ACHK

奇蹟一二

第一個奇蹟是,我竟了上了天堂。

第二個奇蹟是,天堂和地獄竟然沒有分別。

— Me@2011.01.22

以上內容純粹講笑,請勿當真。

— Me@2011.01.25

2011.01.25 Tuesday (c) All rights reserved by ACHK  

String theory 5

Gauge-gravity duality

Gauge-gravity duality is a conjectured duality between a quantum theory of gravity in certain cases and gauge theory in a lower number of dimensions. This means that each predicted phenomenon and quantity in one theory has an analogue in the other theory, with a “dictionary” translating from one theory to the other.

Description of the duality

In certain cases the gauge theory on the D-branes is decoupled from the gravity living in the bulk; thus open strings attached to the D-branes are not interacting with closed strings. Such a situation is termed a decoupling limit. In those cases, the D-branes have two independent alternative descriptions.

As discussed above, from the point of view of closed strings, the D-branes are gravitational sources, and thus we have a gravitational theory on spacetime with some background fields.

From the point of view of open strings, the physics of the D-branes is described by the appropriate gauge theory.

Therefore in such cases it is often conjectured that the gravitational theory on spacetime with the appropriate background fields is dual (i.e. physically equivalent) to the gauge theory on the boundary of this spacetime (since the subspace filled by the D-branes is the boundary of this spacetime).

So far, this duality has not been proven in any cases, so there is also disagreement among string theorists regarding how strong the duality applies to various models.

— Wikipedia on String theory

2011.01.24 Monday ACHK

Grown-ups

.

Grown-ups never understand anything by themselves, and it is tiresome for children to be always and forever explaining things to them.

— Antoine de Saint Exupery

.

.

.

2011.01.24 Monday ACHK

魔間傳奇 2.6

千萬不要原諒壞人,除非對方已經真心悔改,願意盡力彌補自己的過錯。

我第一步會對人好。如果對方都對我好的話,我會對他更好。如果對方對我不好的話,我不會再對他好。但是,我亦不會對他不好,因為,我會直情不再跟他相處。

人生苦短,不應花任何一秒在壞人身上。

— Me@2011.01.24

機器人第一法則

    機械人不得傷害人類,或袖手旁觀坐視人類受到傷害;

— 以撒·艾西莫夫

2011.01.24 Monday (c) All rights reserved by ACHK

String theory 4

But the theory also describes universes like ours, with four observable spacetime dimensions, as well as universes with up to 10 flat space dimensions, and also cases where the position in some of the dimensions is not described by a real number, but by a completely different type of mathematical quantity. So the notion of spacetime dimension is not fixed in string theory: it is best thought of as different in different circumstances.

This can be better understood by noting that a photon included in a consistent theory (technically, a particle carrying a force related to an unbroken gauge symmetry) must be massless.

— Wikipedia on String theory

2011.01.23 Sunday ACHK

Twelve Monkeys 2

Themes

Memory, time, and technology

“Cole has been thrust from another world into ours and he’s confronted by the confusion we live in, which most people somehow accept as normal. So he appears abnormal, and what’s happening around him seems random and weird. Is he mad or are we?”

— Director Terry Gilliam

— Wikipedia on 12 Monkeys

2011.01.23 Sunday ACHK

Twelve Monkeys

Themes

.

Memory, time, and technology

“Cole has been thrust from another world into ours and he’s confronted by the confusion we live in, which most people somehow accept as normal. So he appears abnormal, and what’s happening around him seems random and weird. Is he mad or are we?”

— Director Terry Gilliam

.

.

12 Monkeys studies the subjective nature of memories and their effect upon perceptions of reality. Examples of false memories include:

* Cole’s recollection of the airport shooting which is altered each time he has a dream.
* A “mentally divergent” man at the asylum who has false memories.
* Railly telling Cole “I remember you like this” when a barely recognizable Cole and Railly are seen in disguise for the first time.

References to time, time travel, and monkeys are scattered throughout the film, including the Woody Woodpecker “Time Tunnel” cartoon playing on the TV in a hotel room, The Marx Brothers movie Monkey Business (1931) on TV in the asylum and the subplots of monkeys (drug testing, news stories and animal rights). The film is also a study of modern civilization’s declining efforts to communicate with each other due to the interference of technology.

— Wikipedia on 12 Monkeys

.

.

.

2011.01.23 Sunday ACHK

地圖原理 1.2

「地圖原理」和「間書原理」,是指同一樣東西。但是,我覺得「間書原理」好一點,因為它在表達上比較省時。

(安:你在很多年前就開始講「間書原理」。那時應該是大學時代?)

不是。那時已經是我的碩士時代。我讀碩士時,我們才開始這樣對話。

(安:這麼多年來,我也找不到一個比喻,及得上「間書原理」那麼精簡易明。)

「地圖原理」呢?

(安:「地圖原理」和「間書原理」應該不是指同一樣東西。「間書原理」的意思是,例如,如果所有東西都「緊急」,就即是沒有東西緊急;如果所有東西都「特別」,就即是沒有東西特別。)

「地圖原理」都差不多,可以完全套用這個講法。「地圖」的作用是紀錄實地。如果實地的所有東西都紀錄的話,效果就等如所有東西都沒有紀錄,因為那張所謂的「地圖」已經沒有任何作用。

不過,我同意,雖然「地圖原理」和「間書原理」是指同一樣東西,但是,它們的著眼點不同。

— Me@2011.01.22

2011.01.23 Sunday (c) All rights reserved by ACHK  

String theory 3

Investigating how a string theory may include fermions in its spectrum led to the invention of supersymmetry, a mathematical relation between bosons and fermions.

T-duality relates the large and small distance scales between string theories, whereas S-duality relates strong and weak coupling strengths between string theories. U-duality links T-duality and S-duality.

— Wikipedia on String theory

2011.01.22 Saturday ACHK

Succeeding

by John T. Reed

.

The book is available only through the author’s own website.

— Me@2011.01.22

— Me@2022.10.04

.

.

2011.01.22 Saturday ACHK

Intolerance for ugliness

.

Intolerance for ugliness is not in itself enough. You have to understand a field well before you develop a good nose for what needs fixing. You have to do your homework. But as you become expert in a field, you’ll start to hear little voices saying, What a hack! There must be a better way. Don’t ignore those voices. Cultivate them. The recipe for great work is: very exacting taste, plus the ability to gratify it.

— Paul Graham

.

.

.

2011.01.21 Friday ACHK