< 1984

Posted on April 30, 2019 by rpflee

< 1984

Varying a path

Posted on April 28, 2019 by rpflee

Suppose that we have a function $\displaystyle{f[q]}$ that depends on a path $\displaystyle{q}$ . How does the function vary as the path is varied? Let $\displaystyle{q}$ be a coordinate path and $\displaystyle{q + \epsilon \eta}$ be a varied path, where the function $\displaystyle{\eta}$ is a path-like function that can be added to the path $\displaystyle{q}$ , and the factor $\displaystyle{\epsilon}$ is a scale factor. We define the variation $\displaystyle{ \delta_\eta f[q]}$ of the function $\displaystyle{f}$ on the path $\displaystyle{q}$ by

$\displaystyle{\delta_\eta f [q] = \lim_{\epsilon \to 0} \left( \frac{f[q + \epsilon \eta] - f[q]}{\epsilon} \right)}$

The variation of $\displaystyle{f}$ is a linear approximation to the change in the function $\displaystyle{f}$ for small variations in the path. The variation of $\displaystyle{f}$ depends on $\displaystyle{\eta}$ .

— 1.5.1 Varying a path

— Structure and Interpretation of Classical Mechanics

Exercise 1.7. Properties of $\displaystyle{\delta}$

The meaning of $\displaystyle{\delta_\eta (fg)[q]}$ is

$\displaystyle{\delta_\eta (f[q]g[q])}$

— Me@2019-04-27 07:02:38 PM

2019.04.27 Saturday ACHK

Mixed states, 4

Posted on April 23, 2019 by rpflee

How is quantum superposition different from mixed state?

The state

$\displaystyle{|\Psi \rangle = \frac{1}{\sqrt{2}}\left(|\psi_1\rangle +|\psi_2\rangle \right)}$

is a pure state. Meaning, there’s not a 50% chance the system is in the state $\displaystyle{|\psi_1 \rangle }$ and a 50% it is in the state $\displaystyle{|\psi_2 \rangle}$ . There is a 0% chance that the system is in either of those states, and a 100% chance the system is in the state $\displaystyle{|\Psi \rangle}$ .

The point is that these statements are all made before I make any measurements.

— edited Jan 20 ’15 at 9:54

— Mehrdad

— answered Oct 12 ’13 at 1:42

— Andrew

Given a state, mixed or pure, you can compute the probability distribution $\displaystyle{P(\lambda_n)}$ for measuring eigenvalues $\displaystyle{\lambda_n}$ , for any observable you want. The difference is the way you combine probabilities, in a quantum superposition you have complex numbers that can interfere. In a classical probability distribution things only add positively.

— Andrew Oct 12 ’13 at 14:41

— How is quantum superposition different from mixed state?

— Physics StackExchange

2019.04.23 Tuesday ACHK

The language of Change, 2

Posted on April 18, 2019 by rpflee

time ~ change (noun)

action ~ change (verb) or counter-change

— Me@2018-02-19 10:24 AM

（反對）開夜車 2.5

Posted on April 16, 2019 by rpflee

本文章並(!)不(!)可作為醫學建議。如需醫學意見，請諮詢專業人士。

…

（問：「只要飛蚊不惡化」？你怎能保證？）

不能。那正正就是，我更大的苦惱。

一日不能知道，我當年開始患飛蚊症的真正原因，我也會不安，擔心症狀加劇。

「飛蚊症」只是某個或某些疾病的一個「症」，而不是「疾病」本身。一日不能知道，我飛蚊症的病因，我也不能有力預防，症狀的加劇。

（問：你不是說，長期夜睡少睡，導致你的飛蚊症嗎？）

那只是估計，不是肯定。

那一段時間，「出事」前的一兩個星期，我剛好時常睡不著，導致睡了很少。所以，長期夜睡少睡，很可能是主要的原因。

當然，如果平日的睡眠充足，並不會因為單一事件，某一晚的夜睡少睡，就立刻有飛蚊。如果人體是那麼沒有彈性，人類這種生物，可能一早就已經絕種了。

但是，如果是長期夜睡少睡，身體自然會越來越虛弱。到達某個臨界點時，意外事件就可以隨時發生。從相反的角度來講，如果平日睡眠適量，就等於刪除了，飛蚊症的其中一個主要誘因，從而大大減低了，其發生的機會率。

本文章並(!)不(!)可作為醫學建議。如需醫學意見，請諮詢專業人士。

— Me@2019-04-13 03:34:33 PM

Physical laws are low-energy approximations to reality, 1.3.1

Posted on April 10, 2019 by rpflee

d_2019_04_07__22_39_01_PM_

Symmetry breaking is important.

When there is symmetry-breaking, the system goes to a low-energy state.

Each possible low-energy state can be regarded as a new “physical world”.

One “physical world” cannot jump to another, unless through quantum tunnelling. But the probability of quantum tunnelling happening is low.

Low-energy physics theories, such as harmonic oscillator, are often simple and beautiful.

— Professor Renbao Liu

— Me@2019-04-08 10:46:32 PM

scmutils

Posted on April 7, 2019 by rpflee

In order to run the SICM code, you need to install the scmutils library. Just go to the official page to download the library and follow the official instructions to install it in a Linux operating system.

When you try to run it, your system may give the following error message:

/usr/local/bin/mechanics: line 16: exec: xterm: not found

If so, you should install the program xterm first.

Also, in case you like to use Emacs as editor, you can:

Just include the following in your .emacs file:

(defun mechanics ()
  (interactive)
  (run-scheme
    "ROOT/mit-scheme/bin/scheme --library ROOT/mit-scheme/lib"
  ))

Replace ROOT with the directory in which you installed the scmutils software. (Remember to replace it in both places. If it is installed differently on your system, just make sure the string has the form “/path/to/mit-scheme --library /path/to/scmutils-library“.) Restart emacs (or use C-x C-e to evaluate the mechanics defun), and launch the environment with the command M-x mechanics.

— Using GNU Emacs With SCMUtils

— Aaron Maxwell

In my Ubuntu 18.04, the paths are:

(defun mechanics()
  (interactive)
  (run-scheme
   "/usr/local/scmutils/mit-scheme/bin/scheme --library 
/usr/local/scmutils/mit-scheme/lib"
  ))

— Me@2019-04-07 02:52:50 PM

Confirmation principle

Posted on April 6, 2019 by rpflee

Verification principle, 2.2 | The problem of induction 4

The statements “statements are meaningless unless they can be empirically verified” and “statements are meaningless unless they can be empirically falsified” are both claimed to be self-refuting on the basis that they can neither be empirically verified nor falsified.

— Wikipedia on Self-refuting idea

In 1936, Carnap sought a switch from verification to confirmation. Carnap’s confirmability criterion (confirmationism) would not require conclusive verification (thus accommodating for universal generalizations) but allow for partial testability to establish “degrees of confirmation” on a probabilistic basis.

— Wikipedia on Verificationism

Confirmation principle should not be applied to itself because it is an analytic statement which defines synthetic statements.

Even if it does, it is not self-defeating, because confirmation principle, unlike verification principle, does not requires a statement to be proven with 100% certainty.

So in a sense, replacing verification principle by confirmation principle can avoid infinite regress.

Accepting confirmation principle is equivalent to accepting induction.

“This is everything to win but nothing to lose.”

— Me@2012.04.17

Authenticity

Posted on April 6, 2019 by rpflee

If you seek authenticity for authenticity’s sake, you are no longer authentic.

— Jean Paul Sartre

2019.04.06 Saturday ACHK

PhD, 3.5

Posted on April 5, 2019 by rpflee

碩士 4.5 | On Keeping Your Soul, 2.2.5

這段改編自 2010 年 4 月 18 日的對話。

…

要完成一個「研究式碩士」課程，上課考試雖然必須，但只是次要的劇情。你「正職」要做的是，做研究。你雖然需要交學費，但大學會有資助給你。一般而言，大學給你的資助，會大於你給大學的學費。

理論上，你可以視那個差額，為你的「薪金」，或者「生活費」。有了這個「薪金」，你就可全職做研究。

（問：實際上呢？）

實際上，就當然沒有那麼理想。

讀研究式碩士或博士課程，因為有資助，你需要做本科課程的助教；職責包括，批改大學本科生的功課、開導修課等。所以，作為一位研究生，你做研究以外，既要上課考試，亦要做助教。

（問：三重身份，哪有那麼多的時間？）

無錯。你真正可以做研究的時間，不多於半職。

即使是研究部分，大部分情況下，你也只可以研究，你上司有興趣的課題。而那課題，往往也未必是，你自己最想研究的東西。

（問：你上司？）

即是你碩士或博士的論文導師。那教授有雙重角色。他既是指導你的老師，亦是指示你的上司。

那兩個角色，本來就不應由，同一個人飾演。

（問：為什麼呢？）

如果甲是你的老師，他做決定時，主要會由誰的利益出發？

如是甲是你的上司，他做決定時，又主要會由誰的利益出發？

（問：你的意思是，「誰是主角」和「誰是助手」？）

如果甲是你的老師，甲你二人，誰是僱主？誰是僱員？

如果甲是你的上司，甲你二人，那誰是僱主？誰是僱員？

— Me@2019-04-05 12:00:42 PM

Physics Town

continues

Monthly Archives: April 2019

< 1984

Varying a path

Mixed states, 4

The language of Change, 2

（反對）開夜車 2.5

Physical laws are low-energy approximations to reality, 1.3.1

scmutils

Confirmation principle

Authenticity

PhD, 3.5