# The Principle of Stationary Action

Varying the action

$\displaystyle{S[q](t_1, t_2) = \int_{t_1}^{t_2} L \circ \Gamma[q]}$

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The Principle of Stationary Action

$\displaystyle{\delta_\eta S[q] (t_1, t_2) = 0}$

$\delta_\eta S[q] (t_1, t_2) = \int_{t_1}^{t_2} \delta_\eta L \circ \Gamma[q]$

— Structure and Interpretation of Classical Mechanics

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2019.05.13 Monday ACHK

# Multiverse

A physics statement is meaningful only if it is with respect to an observer. So the many-world theory is meaningless.

— Me@2018-08-31 12:55:54 PM

— Me@2019-05-11 09:41:55 PM

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Answer me the following yes/no question:

In your multi-universe theory, is it possible, at least in principle, for an observer in one universe to interact with any of the other universes?

If no, then it is equivalent to say that those other universes do not exist.

If yes, then those other universes are not “other” universes at all, but actually just other parts of the same universe.

— Me@2019-05-11 09:43:40 PM

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# In Search of Lost Time, 4

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You can’t change the beginning, but you can change the ending.

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You can’t go back and change the beginning, but you can start where you are and change the ending.

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2019.05.11 Saturday ACHK

# 追憶逝水年華, 3

In Search of Lost Time, 3 | （反對）開夜車 3.1 | 止蝕 4

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1. 只要每晚睡少四小時，就每晚可以多四小時溫習。

2. 只要每晚可以多四小時溫習，就可以追回之前，落後了的進度。

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— Me@2019-05-09 10:04:55 PM

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# Physical laws are low-energy approximations to reality, 1.3.2

QCD, Maxwell, Dirac equation, spin wave excitation, superconductivity, …

~ low energy physics

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symmetry breaking

$\displaystyle{\downarrow}$

local minimum

$\displaystyle{\downarrow}$

simple physics

— Me@2019-05-06 11:12:02 PM

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# Ex 1.8 Implementation of $\delta$

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

The variation may be represented in terms of a derivative.

— Structure and Interpretation of Classical Mechanics

\displaystyle{ \begin{aligned} g( \epsilon ) &= f[q + \epsilon \eta] \\ \delta_\eta f[q] &= \lim_{\epsilon \to 0} \left( \frac{g(\epsilon) - g(0)}{\epsilon} \right) \\ &= D g(0) \\ \end{aligned}}

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A lambda expression evaluates to a procedure. The environment in effect when the lambda expression is evaluated is remembered as part of the procedure; it is called the closing environment.

— Structure and Interpretation of Classical Mechanics

(define (((delta eta) f) q)
(let ((g (lambda (epsilon) (f (+ q (* epsilon eta))))))
((D g) 0)))


— Me@2019-05-05 10:47:46 PM

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# Classical probability, 7

Classical probability is macroscopic superposition.

— Me@2012.04.23

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That is not correct, except in some special senses.

— Me@2019-05-02

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That is not correct, if the “superposition” means quantum superposition.

— Me@2019-05-03 08:44:11 PM

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The difference of the classical probability and quantum probability is the difference of a mixed state and a pure superposition state.

In classical probability, the relationship between mutually exclusive possible measurement results, before measurement, is OR.

In quantum probability, if the quantum system is in quantum superposition, the relationship between mutually exclusive possible measurement results, before measurement, is neither OR nor AND.

— Me@2019-05-03 06:04:27 PM

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# Forget oneself

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~ the state of releasing yourself

~ to let god take control of you

— Me@2009.07.25

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# PhD, 3.6

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— Me@2019-04-30 11:22:05 PM

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# Varying a path

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

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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

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2019.04.27 Saturday ACHK

# Mixed states, 4

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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

— answered Oct 12 ’13 at 1:42

— Andrew

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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

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— How is quantum superposition different from mixed state?

— Physics StackExchange

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2019.04.23 Tuesday ACHK

# The language of Change, 2

time ~ change (noun)

action ~ change (verb) or counter-change

— Me@2018-02-19 10:24 AM

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# （反對）開夜車 2.5

（問：「只要飛蚊不惡化」？你怎能保證？）

「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？）

— Me@2019-04-13 03:34:33 PM

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# Physical laws are low-energy approximations to reality, 1.3.1

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.

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

— Professor Renbao Liu

— Me@2019-04-08 10:46:32 PM

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# scmutils

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.

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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

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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

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# Confirmation principle

Verification principle, 2.2 | The problem of induction 4

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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

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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

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

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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.

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Accepting confirmation principle is equivalent to accepting induction.

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

— Me@2012.04.17

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# Authenticity

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

— Jean Paul Sartre

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2019.04.06 Saturday ACHK

# PhD, 3.5

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（問：實際上呢？）

（問：三重身份，哪有那麼多的時間？）

（問：你上司？）

（問：為什麼呢？）

（問：你的意思是，「誰是主角」和「誰是助手」？）

— Me@2019-04-05 12:00:42 PM

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