# 3.1 Lorentz covariance for motion in electromagnetic fields, 1

A First Course in String Theory

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The Lorentz force equation (3.5) can be written relativistically as

$\displaystyle{\frac{d p_\mu}{ds} = \frac{q}{c} F_{\mu \nu} \frac{d x^\nu}{ds}}$,

where $\displaystyle{p_{\mu}}$ is the four-momentum.

(a) Check explicitly that this equation reproduces (3.5) when $\displaystyle{\mu}$ is a spatial index.

(b) What does (1) gives when $\displaystyle{\mu = 0}$? Does it make sense?

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Eq. (3.5):

$\displaystyle{\frac{d \vec p}{dt} = q \left( \vec E + \frac{\vec v}{c} \times \vec B \right)}$

Eq. (2.20):

$\displaystyle{ds \equiv \sqrt{ds^2}}$    if    $\displaystyle{ds^2 > 0}$

Eq. (2.21):

$\displaystyle{-ds^2 = \eta_{\mu \nu} dx^\mu dx^\nu}$

The spacetime interval $\displaystyle{ds^2}$ is Lorentz invariant. If $\displaystyle{ds^2 > 0}$, we have Eq. (2.27) and (2.28):

\displaystyle{\begin{aligned} ds &= c dt_p \\ ds &= c dt \sqrt{1 - \beta^2} \end{aligned}}

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$\displaystyle{\frac{d p_\mu}{ds} \left( \frac{ds}{dt} \right) = \frac{q}{c} F_{\mu \nu} \frac{d x^\nu}{ds}} \left( \frac{ds}{dt} \right)$

\displaystyle{ \begin{aligned} \frac{d p_1}{dt} &= \frac{q}{c} F_{1 \nu} \frac{d x^\nu}{dt} \\ &= \frac{q}{c} \left( F_{1 0} \frac{d x^0}{dt} + F_{1 1} \frac{d x^1}{dt} + F_{1 2} \frac{d x^2}{dt} + F_{1 3} \frac{d x^3}{dt} \right) \\ \frac{d p_x}{dt} &= \frac{q}{c} \left( E_x c \frac{d t}{dt} + (0) \frac{d x^1}{dt} + B_z \frac{d x^2}{dt} - B_y \frac{d x^3}{dt} \right) \\ &= q \left( E_x + \frac{1}{c} \left( \vec v \times \vec B \right)_x \right) \\ \end{aligned}}

\displaystyle{ \begin{aligned} \frac{d p_0}{dt} &= \frac{q}{c} \left( F_{0 0} \frac{d x^0}{dt} + F_{0 1} \frac{d x^1}{dt} + F_{0 2} \frac{d x^2}{dt} + F_{0 3} \frac{d x^3}{dt} \right) \\ &= \frac{q}{c} \left( 0 \frac{d x^0}{dt} - E_x \frac{d x^1}{dt} - E_y \frac{d x^2}{dt} - E_z \frac{d x^3}{dt} \right) \\ \frac{d }{dt} \left( \frac{-E}{c} \right)&= - \frac{q}{c} \left( \vec v \cdot \vec E \right) \\ \frac{d E}{dt} &= \vec v \cdot \vec F_E \\ \end{aligned}}

— Me@2022-08-04 04:17:59 PM

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Anyone who expects to create, be it as scientist or artist, scholar or writer, needs self-confidence, even bravado. How else can one dare to imagine understanding what no one else has understood, discovering what no one else has discovered? Where does this confidence come from? Fortunately, every young person is blessed with some of it. It is part of human character. What of the girl or boy who reads about Newton and Maxwell and Bohr and Einstein and says, “I want to build on what they have built; I want to add to the sum of knowledge about the most basic laws of nature”?

– Geons, Black Holes & Quantum Foam, p. 84

– 2000
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# CSCI3420


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Design:
1: make car moving
2: make car stop itself
4: change direction
5: tuning

~~~

CSCI3420 Project Phase 2

~~~



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# 排列組合 1.1

nCr, 0

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$\displaystyle{n!}$

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1.1  意思：

$\displaystyle{n}$ 個人 $\displaystyle{n}$ 個座位的話，有多少種坐法？

1.2.1  算式：

$\displaystyle{n! = (n)(n-1)(n-2) \cdots (3)(2)(1)}$

1.2.2  由來：

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1.3

$\displaystyle{n! = (n)(n-1)(n-2) \cdots (3)(2)(1)}$

\displaystyle{\begin{aligned} 5! &= (5)(4)(3)(2)(1) \\ \\ \end{aligned}}

$\displaystyle{3!}$，就有 3 項；等等。

\displaystyle{\begin{aligned} 3! &= (3)(2)(1) \\ \end{aligned}}

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1.4.0  零的階乘，$\displaystyle{0!}$，還未有定義，因為，算式 $\displaystyle{n! = (n)(n-1) \cdots (2)(1)}$ 中的 $\displaystyle{n}$，只可以是正整體，不可以零。

1.4.1  既然 $\displaystyle{n!}$意思是「$\displaystyle{n}$ 個人 $\displaystyle{n}$ 個座位，有多少種坐法」，那樣，你就可以視，$\displaystyle{0!}$ 的意思是「$\displaystyle{0}$ 個人 $\displaystyle{0}$ 個座位，有多少種坐法」；那明顯是一，因為，那個情況之下，只有一個「坐法」，就是「沒有人又沒有位」這個唯一的可能性。

$\displaystyle{0! = 1}$

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1.4.2  另外一種設計定義的想法是，由 $\displaystyle{n!}$算式取靈感。

$\displaystyle{0! = a^0}$

「零項相乘」即是「乘了等如沒有乘」，所以是一，因為任何數乘了一，效果都等於沒有乘。

$\displaystyle{a^0 = 1}$

（「零項相乘」的正式學名是，「空積」或「零項積」。）

$\displaystyle{0! = 1}$

— Me@2022-08-02 02:41:43 PM

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# Mega Man Zero 3

Euler problem 1

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(proclaim '(optimize speed))

(reduce #'+ '(1 2 3 4))

; 10

(loop :for n :below 10 :collect n)

; (0 1 2 3 4 5 6 7 8 9)

(describe :below)

(defun range (max &key (min 0) (step 1))
(loop :for n :from min :below max :by step
collect n))

(- (+ (* 3 (reduce #'+ (range 334 :min 1 :step 1)))
(* 5 (reduce #'+ (range 200 :min 1 :step 1))))
(* 15 (reduce #'+ (range 67 :min 1 :step 1))))

; 233168

(defun sum-1-n (n)
(/ (* n (+ n 1)) 2))

(- (+ (* 3 (sum-1-n 333))
(* 5 (sum-1-n 199)))
(* 15 (sum-1-n 66)))

; 233168

— Me@2022-08-01 03:29:01 PM

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# Jupyter Notebook

SICMUtils, 3

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The goal of this post to setup Jupyter Notebook.

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1. Read and follow the exact steps of my post titled “SICMUtils“.

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2. To install the Jupyter Notebook software in Ubuntu, use this command:

sudo apt-get install sagemath-jupyter


3. Try to open the SageMath program.

4. It will open a Jupyter notebook page.

5. Click the “New” button at the top right corner and then select “SageMath“.

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6. Type

1 + 1


onto the input line.

7. Hit the keys shift-enter to get the output

2


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8. Input

Integrate(x^3, x)


9. Hit shift-enter:

NameError: name 'Integrate' is not defined


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10. Input

from sage.symbolic.integration.integral import *

indefinite_integral(x^3, x)


11. Hit shift-enter:

1/4*x^4


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12. Input

%display latex


13. Hit shift-enter.

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14. Input

indefinite_integral(x^3, x)


15. Hit shift-enter:

$\displaystyle{\frac{1}{4} \, x^{4}}$

— Me@2022-07-30 12:18:50 PM

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# Quantum as potential, 2

Only measurement results (aka physical phenomena) form the physical reality.

Quantum Mechanics is a theory of measurement results.

Quantum Mechanics is a theory of reality.

Quantum Mechanics is not a theory of unobservables (undefined-observables).

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Quantum mechanics is a story of reality, not a story of story.

— Me@2022-07-27 10:38:32 AM

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# Bee

Even if the Bee could explain to the fly why pollen is better than shit, the fly would not understand.

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2022.07.29 Friday ACHK

# 女敵人 2

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— Me@2022-07-29 02:37:02 PM

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# Org-babel-clojure

SICMUtils, 2

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The goal of this post to setup the Emacs editor for Clojure programming.

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2. Open the .emacs file. Go to the end of the file. Add the following code:

(require 'org)
(require 'ob-clojure)

(setq org-babel-clojure-backend 'cider)
(require 'cider)

(set-register ?c '(file . "~/my-stuff/my-stuff.org"))

(setq org-confirm-babel-evaluate nil)

(setq org-src-tab-acts-natively t)


3. Close Emacs.

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4. Go to the directory “~/my-stuff/” and then create a file named “my-stuff.org“.

5. Use Emacs to open the file.

6. Within the file, add the following code:

#+BEGIN_SRC emacs-lisp

(+ 1 1)

#+END_SRC


7. Place the text cursor in the code block (between the line #+BEGIN_SRC and the line #+END_SRC).

8. Hit the Emacs command

C-c C-c


9. You will get the evaluation result:

#+RESULTS:
: 2


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10. Hit the Emacs command:

M-x cider-jack-in


11. Within the file “my-stuff.org“, add the code:

#+BEGIN_SRC clojure :results value

(require '[sicmutils.env :as env])

#+END_SRC


12. Place the text cursor in the code block.

13. Hit the Emacs command

C-c C-c


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#+BEGIN_SRC clojure :results value

(env/bootstrap-repl!)

#+END_SRC


15. Place the text cursor in the code block and then hit the Emacs command

C-c C-c


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#+BEGIN_SRC clojure :results replace drawer

(->TeX (simplify ((D cube) 'x)))

#+END_SRC


17. Place the text cursor and then hit

C-c C-c


It will give you the $\LaTeX$ code

#+RESULTS:
:RESULTS:
"3\\,{x}^{2}"
:END:


— Me@2022-07-27 11:34:28 PM

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# SICMUtils

A Clojure(script) implementation of the scmutils system for math and physics investigations in the Clojure and Clojurescript languages.

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1. To install Clojure in Ubuntu, just this command is enough:

sudo apt-get install elpa-cider


Although the Clojure version you get is probably not the most updated one, that is not important, because you can specify which version you want in the config file of each project.

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2. Then use this command to generate a new project named my-stuff:

lein new app my-stuff


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3. Use Emacs to open the file:

~/my-stuff/project.clj


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4. Replace the existing :dependencies line with this one

  :dependencies [[org.clojure/clojure "1.11.1"]
[sicmutils "0.22.0"]]


And make sure that both clojure and sicmutils have the most updated version numbers.

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5. In Emacs, type the command

M-x cider-jack-in


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6. In the clojure window (cider-repl), type

(clojure-version)


with enter at the end.

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7. Type

(require '[sicmutils.env :as env])


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8. Type

(env/bootstrap-repl!)


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9. Code

((D cube) 'x)


will result

(+ (* x x) (* x (+ x x)))


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10. Type the Emacs command

M-p


to access the last input. Then modify it into

(simplify ((D cube) 'x))


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It will result

(* 3 (expt x 2))


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11. Code

(->TeX (simplify ((D cube) 'x)))


will give the $LaTeX$ code

3\\,{x}^{2}


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12. You can exit by the Emacs command

<C-c C-q>


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For the time being, SICMUtils is not suitable for the book SICM (Structure and Interpretation of Classical Mechanics). In other words, SICMUtils cannot replace the scmutils library yet, because:

a. You would have to do the translation manually, from the scmutils code in the book to SICMUtils.

b. Although it can generate $LaTeX$ source code, it does NOT do the $LaTeX$ rendering.

c. It cannot plot graphs.

However, SICMUtils has one advantage over scmutils. It can generate $LaTeX$ source of an expression, but scmutils cannot. So I am planning to use both scmutils and SICMUtils.

Also, I will learn how to use SICMUtils with other Clojure libraries and the Jupyter Notebook. That would get $LaTeX$ rendering and graph plotting running.

— Me@2022-07-26 11:03:51 AM

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# Quantum as potential

Realist view is wrong.

Before measurement, there are quantum potentials only.

quantum ~ potential

Note that it is NOT the “quantum potential” in the Bohm interpretation.

— Me@2016-08-21 06:13:49 PM

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A wave function encodes the probabilities of different potential measurement results of a physical experiment. It is not a physical wave.

Quantum superposition is NOT a superposition of realities.

Physics should consider only measurement results and their probabilities. Only measurement results are realities.

No measurement result, aka physical phenomenon, is in a superposition.

For example, in the double-slit experiment, the measurement results are (the locations of) the dots on the final screen. Every dot location is not in a superposition.

— Me@2022-07-25 06:43:05 PM

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# Inception 18

~ 潛移默化

— Me@2016-04-02 08:40:30 PM

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# Presentation 基本原理 1.2.2

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（安：雖然我不是從事教學工作，但是，在公司解釋東西給上司時，其實很多時也需要使用到，所謂的「教學技巧」。

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Keep the Sheep Moving in the Same Direction – a lecture should have a clear and simple plot. Avoid anything that distracts from this. Don’t make too many points. Don’t be afraid to repeat yourself.

— How to Teach Stuff

Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away.

— Antoine de Saint-Exupéry

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（假設每一節課，都是一小時以內。）

Every lecture should make only one main point.

The German philosopher G. W. F. Hegel wrote that any philosopher who uses the word “and” too often cannot be a good philosopher. I think he was right, at least insofar as lecturing goes. Every lecture should state one main point and repeat it over and over, like a theme with variations.

— Advice for the Young Scientist

— John Baez

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1. 你將如何為公司賺錢？

2. 為何要選你，而不是其他應徵者？

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（安：那是兩個重點，而不是一個。）

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— Me@2022-07-24 04:41:17 PM

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; sudo apt-get install sbcl

; sudo apt-get install slime

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(setq inferior-lisp-program "sbcl")

(save-excursion (slime))

(delete-other-windows)
)

(defun prelude-start-slime ()
(unless (slime-connected-p)

(set-register ?f '(file . "/path_to/lisp_file.lisp"))

— Me@2022-07-23 05:20:32 PM

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# Cyclic coordinate

A generalized coordinate component that does not appear explicitly in the Lagrangian is called a cyclic coordinate. The generalized momentum component conjugate to any cyclic coordinate is a constant of the motion.

— 1.8 Conserved Quantities

— Structure and Interpretation of Classical Mechanics

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This is a special case of Noether’s theorem. Such coordinates are called “cyclic” or “ignorable”.

— Wikipedia on Lagrangian mechanics

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If only the cyclic coordinate $\displaystyle{q(t)}$ varies with time (if it doesn’t, $\displaystyle{q}$ is superfluous), the Lagrangian, or the essential physical situation, doesn’t vary. Hence the initial value of $\displaystyle{q}$ doesn’t determine the path, which is only possible if the path is closed.

— edited Jul 28, 2014 at 15:55

— ACuriousMind

— answered Jul 28, 2014 at 15:50

— Pieter Kockx

— Why are they called “cyclic” coordinates?

— Physics Stack Exchange

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2022.07.22 Friday ACHK

# Lectures On Computation

Feynman’s philosophy of learning and discovery comes through strongly in these lectures. He constantly points out the benefits of play around with concepts and working out solutions to problems on your own before looking at the back for the answers. As Feynman says in the lectures: “If you keep proving stuff that others have done, getting confidence, increasing the complexities of your solutions — for fun of it — then one day you’ll turn around and discovered that nobody actually did that one! And that’s the way, to become a computer scientist.” Imagine that you are explaining your ideas to your former smart but ignorant, self, at the beginning of your studies!

— Feynman[ Lectures on ]Computation

— 30[.]06[.]2003

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2022.07.21 Thursday ACHK

# ENGG 2011

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ENGG 2011 - Advanced Engineering Maths - Assignment 1

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C++: function(...)
Many argument[s]

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C++: mid-term test (31/10/2011)

~~~


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# 機會再生論 1.2

「自力更生」的好處是，你的才能會越來越強。「他力更生」的壞處是，不一定有；即使有，你的財能會遇弱越弱。

「求之於己」的好處是，自己會越來越強，自己成自己的主人。「依賴他人」的壞處是，他人會越來越強，自己成了他人的奴隸。

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— Me@2022-07-14 03:27:39 PM

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