1990s, 8

Posted on April 30, 2021 by rpflee

— Me@2021-04-30 04:11:55 PM

Ex 1.21 The dumbbell, 2.2.1

Posted on April 28, 2021 by rpflee

Structure and Interpretation of Classical Mechanics

b. Write the formal Lagrangian

$\displaystyle{L(t;x_0, y_0, x_1, y_1, F; \dot x_0, \dot y_0, \dot x_1, \dot y_1, \dot F)}$

such that Lagrange’s equations will yield the Newton’s equations you derived in part a.

~~~

[guess]


(define (U-constraint q0 q1 F l)
  (* (/ F (* 2 l))
     (- (square (- q1 q0))
        (square l))))

(define ((extract-particle pieces) local i)
  (let* ((indices (apply up (iota pieces (* i pieces))))
         (extract (lambda (tuple)
                    (vector-map (lambda (i)
                                  (ref tuple i))
                                indices))))
    (up (time local)
        (extract (coordinate local))
        (extract (velocity local)))))

(define q-rect
  (up (literal-function 'x_0)
      (literal-function 'y_0)
      (literal-function 'x_1)
      (literal-function 'y_1)
      (literal-function 'F)))

(show-expression q-rect)


(show-expression (q-rect 't))


(show-expression (Gamma q-rect))


(show-expression ((Gamma q-rect) 'w))


(show-expression ((Gamma q-rect) 't))


(show-expression (time ((Gamma q-rect) 't)))


(show-expression (coordinate ((Gamma q-rect) 't)))

[guess]

— based on /sicmutils/sicm-exercises

— Me@2021-04-27 05:03:59 PM

Alfred Tarski 4

Posted on April 27, 2021 by rpflee

Godel 20

[guess]

A system can be both complete and consistent because in that system, a metatheorem cannot be translated into a theorem, so a paradox cannot be made.

[guess]

— Me@2017-04-10 10:40:38 AM

深淵 3

Posted on April 26, 2021 by rpflee

愚善 3.2 | Good intentions 2 | 地獄之路 2.2

魔鬼，也是由天使變成的。

不企圖做天使，就不會變成魔鬼。

— Me@2016-08-06 03:02:36 PM

— Me@2021-04-26 06:26:35 PM

一萬個小時 3.3

Posted on April 26, 2021 by rpflee

這段改編自 2010 年 4 月 24 日的對話。

我現在的狀態是，在某些範疇中，有能力教人之餘，還有能力教人如何教。亦即是話，如果教員甲的教學質素，好過教員乙的話，我可以解釋到，甲比乙好在哪裡。

（安：這一點對我好有用。）

但那不能成為課程，因為，它只需一個下午，就可以大概完整地，講給你聽。

（安：你的講法是，有些知識，你只需要幾個小時，就可以傳授給我，不成課程，因為時間所需太短；而另一些知識，我就需要花「幾年加幾年」，才可以領會得到，不成課程，因為時間所需太長。）

現在，有三個概念混淆在一起。我們先釐清一下。

1. 幾乎

任何學問，或者才藝，如果要訓練自己，純熟到足以用來維生賺錢，或者娛樂滿足，需要的時間幅度是，一日幾小時，持續一兩年，才會開竅；然後，再持續一兩年，才會知道自己，在該門學問才藝，為何會開竅，開了什麼竅；又再過一兩年，才會有能力教人，如何在該門學問才藝開竅。

2. 過程中的一個重要環節是，會領悟到一些洞見。

3. 雖然要「自己領悟」第二點中的洞見，來自第一點中的「幾年加幾年」過程，但是，如果只是「吸收別人已知的」知識本身，絶不需要花「幾年加幾年」。有時，甚至只是，花數個小時就可以。

4. 1. 但是，「知道」本身，並不代表自己有足夠功力去「運用」，而「運用」則是，第一點的水平。不過，如果中途有第三點，即是別人情報資料上的提點，你就可以走少很多冤往路。那樣，原本是（例如）十年的過程，可以壓縮到（例如）三年。　

— Me@2021-04-25 09:29:14 PM

1990s, 7

Posted on April 25, 2021 by rpflee

— Me@2021-04-25 03:44:52 PM

2.9 Lightlike compactification, d, 2

Posted on April 24, 2021 by rpflee

A First Course in String Theory

Represent your answer to part (c) in a spacetime diagram. Show two points related by the identification (2) and the space and time axes for the Lorentz frame S’ in which the compactification is standard.

~~~

[guess]

In case you would like to have a fundamental domain:

[guess]

— Me@2021-04-21 10:35:13 PM

Modification of the cumulative concept of time

Posted on April 21, 2021 by rpflee

The past is part of the present, in the sense that part of the present is the same as the past, or is based on something of the past. For example, “I was 10 years old in the past” is the necessary condition for “I am 20 years old in the present”.

However, not all of the past is still part of the present, because some of the past is already lost. In other words, some of the past is not stored in the present.

You need physical macroscopic law (induction) in order to get the cumulative property of time.

Microscopically, due to the unitarity of the Schrödinger equation, any past quantum state has a one-one correspondence to a quantum state at any particular future moment. So any future quantum state already has all the information needed to deduce its past state. In this sense, there is no time microscopically.

Time is not cumulative microscopically, because the past is not part of the future.

We can also say that time is 100% cumulative microscopically, because the past is all of the future; instead of being part of any future quantum state, the past quantum state already has all the (equivalent) information of a quantum state at any particular future moment.

— Me@2013-08-10 07:45 PM

— Me@2021-04-21 04:24 PM

Publish! 12

Posted on April 21, 2021 by rpflee

Whatever I have published, I can remember. In this sense, the outside world is my mind.

— Me@2011.08.27

相聚一刻

Posted on April 20, 2021 by rpflee

光速飛行 1.2.3 | 尋覓 2.2.3.3 | Passion Test 2

我是一個奇怪的人。我比一般人益智和勵志。我不會因為愛情問題，而無心向學，放慢工作。我既不會因為單身一人，而茶飯不思，亦不會因為有心上人，而心神恍惚。

（我只會因自身的問題，而頹廢怠慢，無所事事。）

如果你的所謂「愛情」，會打擊你的學業或者事業的話，你的「愛情」，大概是假的，因其不會長久，更遑論永久。

如果你覺得的女朋友，會阻礙你的工作進度，或者是你的時間負擔的話，你倆大概由始至終，就不應在一起；你倆根本不是，對方的另一半。

第一，如果你喜歡一個人，她真的是你的另一半的話，你會願意花無限的時間，在她身上。

你不會覺得她是，你時間上的負擔。相反，你其他時間的所有努力，尤其是工作上的辛勞，都只為賺取，與她相處的一分一秒。

穿越人海只為與你相擁

— 尹初七

— Me@2021-04-11 07:10:08 AM

2007, 3

Posted on April 19, 2021 by rpflee

— Me@2021-04-19 08:39:47 PM

Ex 1.21 The dumbbell, 3

Posted on April 18, 2021 by rpflee

Structure and Interpretation of Classical Mechanics

c. Make a change of coordinates to a coordinate system with center of mass coordinates $x_{cm}$ , $y_{cm}$ , angle $\theta$ , distance between the particles $c$ , and tension force $F$ . Write the Lagrangian in these coordinates, and write the Lagrange equations.

~~~

[guess]

$\displaystyle{ \begin{aligned} y_{cm} &= \frac{m_0 y_0 + m_1 y_1}{m_0 + m_1} \\ x_{cm} &= \frac{m_0 x_0 + m_1 x_1}{m_0 + m_1} \\ \end{aligned}}$

$\displaystyle{ \begin{aligned} y_{cm} &= \frac{m_0 y_0 + m_1 (y_0 + c(t) \sin \theta)}{m_0 + m_1} \\ x_{cm} &= \frac{m_0 x_0 + m_1 (x_0 + c(t) \cos \theta)}{m_0 + m_1} \\ \end{aligned}}$

Let $\displaystyle{M = m_0 + m_1}$ .

$\displaystyle{ \begin{aligned} y_{cm} &= \frac{M y_0 + m_1 c(t) \sin \theta}{M} \\ x_{cm} &= \frac{M x_0 + m_1 c(t) \cos \theta}{M} \\ \end{aligned}}$

$\displaystyle{ \begin{aligned} y_0 &= y_{cm} - \frac{m_1}{M} c(t) \sin \theta \\ x_0 &= x_{cm} - \frac{m_1}{M} c(t) \cos \theta \\ \end{aligned}}$

$\displaystyle{ \begin{aligned} y_1 &= y_{cm} + \frac{m_0}{M} c(t) \sin \theta \\ x_1 &= x_{cm} + \frac{m_0}{M} c(t) \cos \theta \\ \end{aligned}}$

The Lagrangian

$\displaystyle{ \begin{aligned} L &= \frac{1}{2} m_0 (\dot x_0^2 + \dot y_0^2) + \frac{1}{2} m_1 (\dot x_1^2 + \dot y_1^2) + \lambda \left[ (x_1(t) - x_0(t))^2 + (y_1(t) - y_0(t))^2 - l^2 \right] \\ &= \frac{1}{2} m_0 (\dot x_0^2 + \dot y_0^2) + \frac{1}{2} m_1 (\dot x_1^2 + \dot y_1^2) - \frac{F}{2l} \left[ (c(t))^2 - l^2 \right] \\ \end{aligned}}$

$\displaystyle{ \begin{aligned} \dot y_0 &= \dot y_{cm} - \frac{m_1}{M} \dot c(t) \sin \theta - \frac{m_1}{M} c(t) \dot \theta \cos \theta\\ \dot x_0 &= \dot x_{cm} - \frac{m_1}{M} \dot c(t) \cos \theta - \frac{m_1}{M} c(t) \dot \theta \sin \theta \\ \end{aligned}}$

…

[guess]

— Me@2021-04-17 05:40:46 PM

Causal diamonds in time travel

Posted on April 17, 2021 by rpflee

Quantum mechanics is a set of rules that allows an observer to predict, explain, and/or verify observations (and especially their mutual relationships) that he has access to.

…

No observer can detect inconsistencies within the causal diamonds. However, inconsistencies between “stories” as told by different observers with different causal diamonds are allowed (and mildly encouraged) in general (as long as there is no observer who could incorporate all the data needed to see an inconsistency).

— Raphael Bousso is right about firewalls

— Lubos Motl

There is no “god’s eye view” in physics.

— Me@2021-04-17 03:12:58 PM

Macroscopic time is with respect to an observer. Actually, physics is with respect to an observer.

In the real universe, any observer’s observations must be consistent. When two observers compare their observations, their results must be consistent, because the comparison itself is an observation of an observer.

Time travel in the absolute sense is logically impossible. Let’s assume that it is logically possible.

If a time travel story follows the principle of “an observer’s observations must be consistent”, each character in that story must see a consistent timeline, even if different characters’ timelines may be inconsistent. That is fine as long as such inconsistent observers never meet to compare their results.

If two of such observers choose to meet to compare their results, the action to “meet to compare” itself will render the results consistent. It is similar to the resolution of the twin paradox in special relativity.

There is no “god’s eye view” in physics. Every physical event must be described with respect to an observer. Every physical event, even if the event is “to compare observation results”, must be described with respect to an observer.

— Me@2017-05-10 07:45:36 AM

黎明 3

Posted on April 17, 2021 by rpflee

講到做唔到，唔好講。

好辛苦做咗啲嘢無人知，唔好做。

— 黎明

— Me@2016-05-16 05:58:16 PM

2021.04.17 Saturday ACHK

To realize is to realize, 1.2

Posted on April 16, 2021 by rpflee

For example, when you ask “how to be a polite person”, you become a polite person.

In other words, when you realize that you should be a polite person, that polite person is realized at that moment.

The ultimate self-fulfilling prophecies:

1. free will or not

2. god or no god

3. afterlife or not

4. future spouse exists or not

Why self-fulfilling?

1. free will or not

If we knew the exact physical laws and all the data of the present state of the universe, we would be able to predict, with 100% accuracy, the state of the universe at any future moment.

In theory, the exact physical laws exist, whether we know them or not. Also, in theory, all the details of the present state of the universe exist, whether we know them or not.

So in theory, there is no free will, because the future is already fixed, by the physical laws.

However, even if we knew the exact physical laws, it would be still logically impossible to get all the data of the present state of the whole universe, because it is logically impossible for any observer to observe itself directly. For example, no camera can take a picture of itself directly.

So “in practice”, which is actually “in theory”, there is free will, because logically, no one can predict, with 100% accuracy, your future actions.

— Me@2021-04-16 04:45:47 PM

PC Home

Posted on April 14, 2021 by rpflee

— Me@2021-04-13 05:40:22 PM

2.9 Lightlike compactification, d

Posted on April 14, 2021 by rpflee

A First Course in String Theory

Represent your answer to part (c) in a spacetime diagram. Show two points related by the identification (2) and the space and time axes for the Lorentz frame $S'$ in which the compactification is standard.

~~~

Note 1:

The identifications $\displaystyle{ x \sim x + 0 }$ and $\displaystyle{ x \sim x + \infty }$ have the same meaning, which is that $x$ has no identification at all. In other words, there is NO non-zero real number $r$ such that

$\displaystyle{ x \sim x + r }$

Note 2:

$\displaystyle{ \begin{aligned} \begin{bmatrix} ct \\ x \\ \end{bmatrix} &\sim \begin{bmatrix} ct - 2 \pi R \\ x + 2 \pi \sqrt{R^2 + R_S^2} \\ \end{bmatrix} \end{aligned} }$

This identification must be done to both the space and time coordinates. In other words, it cannot be done to only one of $ct$ and $x$ .

— Me@2021-04-13 12:02:13 PM

Time travel, 3.2

Posted on April 13, 2021 by rpflee

時光機 3.2 | Time is other things, 4 | Cumulative concept of time, 9.2

If you keep deleting your blog posts one by one, your blog effectively keeps becoming its past. However, its environment is still cumulative. In other words, the environment is not becoming its past.

If the environment and the blog interchange labels, the blog’s environment is going to the past, while the blog is not.

— Me@2013-08-10 07:41 PM

— Me@2021-04-12 06:02 PM

龍珠 3

Posted on April 12, 2021 by rpflee

On knowledge independent vectors:

When you already have a complete set of vectors in $n$ dimensional space, you have to go up one extra dimension in order to find a new independent vector.

— Me@2011.08.27

相聚零刻

Posted on April 11, 2021 by rpflee

光速飛行 1.2.2 | 尋覓 2.2.3.2

我是一個奇怪的人。我比一般人益智和勵志。我不會因為愛情問題，而無心向學，放慢工作。我既不會因為單身一人，而茶飯不思，亦不會因為有心上人，而心神恍惚。

（我只會因自身的問題，而頹廢怠慢，無所事事。）

大一時，在某一活動中遇到她。之後，我該組還有一次後續的活動聚會。但是，她剛巧沒有參加。所以，之後就再沒有機會見到她。我和她僅有的相處，就只是於 ICQ（一款網絡即時通訊軟件）中的聊天，為數不多。

後來，一年半載後的後來，我就在和她不太熟絡（其實是不太認識）的情況下，向她表白。那十分突然，被拒絶是情理之中，意料之內。但是，我當時也沒有辦法，因為就快畢業，再不說就沒有機會說了。

我當時的主要目的是，以防一個情況是，原來她也暗戀我而又不敢說，而導致雙方錯失良緣。然後，又要輪迴多少世，才再相遇，十分可惜。

其實，以我現在的智力，是有辦法的。但是，我當時就只有，當時的智力。以當時的智力，我實在沒有辦法。

之後，我又不會時常想到她。但是，每當想起她時，仍然是會有快樂的情緒。

「拒絶」是她的權利，而且是正確的決定。只要是她的決定，就是正確的決定。所以其實，她是沒有做錯任何事。她在品德上沒有問題，所以，我仍然會是十分欣賞她的。我的人生之中，可以遇過如此仙子，已經是莫大的榮幸。

只不過，我不會再對她，有愛情上的喜歡；因為喜歡人的先決條件是，你感到對方也喜歡你，或有機會喜歡你。愛情是雙向的，單向的不是愛情。心上人已拒絶，那就證明，她不是我的未來人，我自然不會再花，太多的心神時間去想念她。

換句話說，我不會在「肯定對方對我沒有愛情感覺」的情況下，仍然對她，有愛情的感覺。在愛情上，我只會愛自己的（未來）太太。

— Me@2021-04-11 07:10:08 AM

Physics Town

continues

Monthly Archives: April 2021

1990s, 8

Ex 1.21 The dumbbell, 2.2.1

Alfred Tarski 4

深淵 3

一萬個小時 3.3

1990s, 7

2.9 Lightlike compactification, d, 2

Modification of the cumulative concept of time

Publish! 12

相聚一刻

2007, 3

Ex 1.21 The dumbbell, 3

Causal diamonds in time travel

黎明 3

To realize is to realize, 1.2

PC Home

2.9 Lightlike compactification, d

Time travel, 3.2

龍珠 3

相聚零刻