Causality 3

In quantum gravity, the metric tensor is a quantum observable. Also, the metric tensor determines the structure of the light cones and the rules for causality, and therefore the causal structure becomes uncertain and confusing. At any rate, string theory is smarter than we are and it is able to avoid these conceptual problems.

— Causality and entanglement

— Lubos Motl

2012.04.30 Monday ACHK

藉口 2

「理由」是一個「決定」。

「原因」並不是一個「決定」。

「理由」是一個「決定」。「理由」是權衡輕重時,支持一個「決定」的一些考慮元素。由於是內在的主觀判斷,「理由」有所謂「充不充分」。一個「決定」沒有充分的「理由」,就為之「不合理」。

「原因」不是一個「決定」。「原因」和「結果」,只是客觀描述事件發生的時間先後次序。由於是外在的客觀事實,「原因」沒有所謂「合不合理」。

— Me@2012-04-26 10:42:10 AM

2012.04.30 Monday (c) All rights reserved by ACHK

微積分驗算 1.4

這段改編自 2010 年 6 月 2 日的對話。

(CYW: 用兩種方法運算同一題,而答案相同的話,錯的機會就很微。但是,考試時,哪會有那麼多的時間?)

那就要靠你平日的訓練。你要在考試前,訓練到自己,每當做一題價值(例如)三分鐘時間的題目時,都可以在兩分鐘內完成。而餘下的一分鐘,你就可以用來驗算。

— Me@2012.04.30

2012.04.30 Monday (c) All rights reserved by ACHK

Naturalness

Naturalness means that the dimensionless parameters in physics are likely to be comparable to one – and very unlikely to be much greater or much smaller than one – unless an explanation why they’re very different from one exists.

— Lubos Motl

2012.04.29 Sunday ACHK

同一部電腦 1.2

Windows, 3.2 | Copy Me, 4.2

這段改編自 2010 年 3 月 20 日的對話。

這就是重點是:那沒有一個一定的標籤方法。那要視乎上文下理。相對於一個情境之下,哪一個標籤比較方便,就用那一個。

自我身份問題,有同樣的特性。如果我問「怎樣為之『同一個』自我」,雖然有一個相對客觀的標籤方法,但都沒有一個百份之一百,絕對客觀的標準答案。

例如,「十年前的我」和「今天的我」,外貌稍有不同,性格不盡相似,年齡天壤之別。那樣,他們還算不算是「同一個」自我呢?

除了「取最方便有用」的標籤方法以外,另一個可以使用的標準是 DNA(遺傳基因)。「十年前的我」和「今天的我」無論有多大不同,至起碼,「他們」的遺傳基因會百份百相同。這就是我所指「相對客觀的標籤方法」。這亦大概可以說是法律上的定義。

但是,孖生兄弟都可以「遺傳基因百份百相同」。但你總不可以把他們定義為「同一個」人,因為他們根本是兩個人。或者說,他們可以同一刻時間,在兩個不同的地方出現。所以,即使用了遺傳基因的異同,來辨別「是否『同一個』人」,也未能給你「一個百份之一百,絕對客觀的標準答案」。

— Me@2012.04.29 

2012.04.29 Sunday (c) All rights reserved by ACHK

Harmonic oscillator 2

At that time, Feynman already realized that the electromagnetic field is an infinite-dimensional harmonic oscillator. Well, the Dirac field is simply its Grassmann-valued counterpart and every other field is a sort of an infinite-dimensional oscillator, too.

— Feynman’s thesis: arrival of path integrals

— Lubos Motl

2012.04.28 Saturday ACHK

微積分驗算 1.3

這段改編自 2010 年 6 月 2 日的對話。

又再例如,求 d/dx (1/sqrt{x}) 時,你直接計算了以後,可以同時用「消滅分母法」和「消滅開方法」去驗算:

y = 1/sqrt{x}

y^2 = 1/x

x y^2 = 1

左右兩邊同時對 x 求導:

(Differentiate both sides with respect to x:)

(dx/dx) y^2 + x d/dx (y^2) = d(1)/dx

y^2 + x 2 y dy/dx = 0

2 x y dy/dx = – y^2

dy/dx = – y/(2x)

dy/dx = – (1/sqrt{x})/(2x)

dy/dx = – 1/(2 x sqrt{x})

— Me@2012.04.28

2012.04.28 Saturday (c) All rights reserved by ACHK

Residual self-image

Residual self-image is the concept that individuals tend to think of themselves as projecting a certain physical appearance, or certain position of social entitlement, or lack thereof. The term was used at least as early as 1968, but was popularized in fiction by the Matrix series, where persons who existed in a digitally created world would subconsciously maintain the physical appearance that they had become accustomed to projecting.

— Wikipedia on Self-image

2012.04.26 Thursday ACHK

Until it’s obvious

Feynman’s Blackboard, 3

You don’t truly understand it until you think it’s obvious.

— Chris Oliver

This is akin to how a society comes to understand something and why genius ideas sometimes take so long to become accepted. I believe “context” is the underlying principle here.

Arthur Schopenhauer said, “All truth passes through three stages: First, it is ridiculed; Second, it is violently opposed; Third, it is accepted as self-evident.”

If you present a truth to someone whom doesn’t have sufficient context for what you are saying, it may seem outrageous and ridiculous to them because the gap between their understanding and the insight you presenting is too great.

They would have to build up their understanding of the context around it until it expands to a point where they find a connection to what they already know. Then they can start to relate to it and eventually they may see it as self evident.   

— espeed 254 days ago

— Hacker News

2012.04.26 Thursday ACHK

同一部電腦

Windows, 3 | Copy Me, 4

這段改編自 2010 年 3 月 20 日的對話。

怎樣為之「同一部」電腦呢?

假設你的電腦換了幾個零件,那就牽涉到 identity(身份)的問題。你的電腦應該視為「新的電腦」,還是「升級了的舊電腦」?換句話說,改裝以後,你的電腦應該視作「另一部電腦」,還是「原本的電腦」呢?

(安:那要視乎 換了多少東西 和 換了什麼東西。例如,如果你的電腦只是換了 keyboard(鍵盤),那就應該算是「同一部」電腦。如果你的電腦連 CPU(central processing unit 中央處理器)都換掉,那就應該算是「另一部」電腦。)

那樣,如果我的電腦除了 CPU 以外,其他全部東西都換掉呢?你還叫它做「同一部」電腦嗎?

(安:那是灰色地帶,沒有一個絕對的標準答案。)

這就是重點是:那沒有一個一定的標籤方法。那要視乎上文下理。相對於一個情境之下,哪一個標籤比較方便,就用那一個。

自我身份問題,有同樣的特性。如果我問「怎樣為之『同一個』自我」,雖然有一個相對客觀的標籤方法,但都沒有一個百份之一百,絕對客觀的標準答案。

— Me@2012.04.26 

2012.04.26 Thursday (c) All rights reserved by ACHK

Black hole information paradox, 2

It shouldn’t be so surprising that unitarity survives completely while causality doesn’t. After all, the basic postulates of quantum mechanics, including unitarity, the probabilistic interpretation of the amplitudes, and the linearity of the operators representing observables, seem to be universally necessary to describe physics of any system that agrees with the basic insights of the quantum revolution.

On the other hand, geometry has been downgraded into an effective, approximate, emergent aspect of reality. The metric tensor is just one among many fields in our effective field theories including gravity.

— Black hole information puzzle

— Lubos Motl

2012.04.25 Wednesday ACHK

微積分驗算 1.2

這段改編自 2010 年 6 月 2 日的對話。

又例如,求 d/dx (1/x) 時,你既可以直接計算,又可以用「消滅分母法」:

y = 1/x

x y = 1

左右兩邊同時對 x 求導:

(Differentiate both sides with respect to x:)

(dx/dx) y + x dy/dx = d(1)/dx

y + x dy/dx = 0

dy/dx = -y/x

dy/dx = (-1/x)/x

dy/dx = -1/x^2

凡是有分母的 function(函數)做 differentiation(求導),你都可以用這個「消滅分母法」去驗算。

再例如,求 d/dx (sqrt{x}) 時,你既可以直接計算,又可以用「消滅開方法」:

y = sqrt{x}

y^2 = x

左右兩邊同時對 x 求導:

(Differentiate both sides with respect to x:)

d/dx (y^2) = dx/dx

2y dy/dx = 1

dy/dx = 1/2y

dy/dx = 1/(2 sqrt{x})

凡是有開方的 function(函數)做 differentiation(求導),你都可以用這個「消滅開方法」去驗算。

— Me@2012.04.25

2012.04.25 Wednesday (c) All rights reserved by ACHK

The Standard Model

The only special thing about the Standard Model is that it’s the “minimal” theory (when it comes to counting of the fields etc.) that is compatible with data we had known before the LHC.

— Theory vs phenomenology in the days of experimental reckoning

— Lubos Motl

2012.04.24 Tuesday ACHK

Teacher’s wisdom

Passive acceptance of the teacher’s wisdom is easy to most boys and girls. It involves no effort of independent thought, and seems rational because the teacher knows more than his pupils; it is moreover the way to win the favor of the teacher unless he is a very exceptional man. Yet the habit of passive acceptance is a disastrous one in later life. It causes man to seek and to accept a leader, and to accept as a leader whoever is established in that position.

— Bertrand Russell

2012.04.24 Tuesday ACHK

Firmware 3

這段改編自 2010 年 3 月 20 日的對話。

「韌體」本身是「軟件」,因為它是由一堆程式指令所組成。但是,你亦可以把「韌體」看成,介乎「硬件」和「軟件」之間一個概念,原因是:

第一,「韌體」是直接寫入電腦的電子零件之中,而不是儲存於硬碟(hard disk drive)之內。

第二,為一個硬件設計和編寫「韌體」時,會直接受制於,該個硬件自身的設定和侷限。

第三,一個硬件出廠前,會安裝好「韌體」。自此以後,就很少會修改更換,因為那相對複雜困難,而且通常也不會帶來明顯的好處。

— Me@2012.04.24 

2012.04.24 Tuesday (c) All rights reserved by ACHK

Black hole information paradox

The black hole information paradox results from the combination of quantum mechanics and general relativity. It suggests that physical information could permanently disappear in a black hole, allowing many physical states to evolve into the same state. This is controversial because it violates a commonly assumed tenet of science — that in principle complete information about a physical system at one point in time should determine its state at any other time. A fundamental postulate of quantum mechanics is that complete information about a system is encoded in its wave function. The evolution of the wave function is determined by a unitary operator, and unitarity implies that information is conserved in the quantum sense.

— Wikipedia on Black hole information paradox

2012.04.23 Monday ACHK

微積分驗算 1.1

這段改編自 2010 年 6 月 2 日的對話。

考試時,你怕做錯 differentiation 的話,就應該做驗算。驗算的方法有兩種。你選擇其中一種方法去用就可以。

第一種方法是,做了 differentiation 後,用計數機核對。現在,有一些計數機,有 differentiation 的功能。

第二種方法是,你用超過一種途徑,去運算同一題 differentiation,看看可不可以得到同一個答案。例如,如果要運算 d/dx ( sin x / x ),你既可以用 product rule,又可以用 quotient rule。

用 product rule 的話,你就要把「sin x 除以 x」看成「sin x 乘以 1/x」。

— Me@2012.04.23

2012.04.23 Monday (c) All rights reserved by ACHK