Entropy at the Beginning of Time, 1.1

Posted on January 9, 2022 by rpflee

Logical arrow of time, 10.2.1

Two distinguishable macrostates can both evolve into one indistinguishable macrostate.

— Me@2013-08-11 11:08 AM

Note that, tautologically, any system can be at only one single macrostate at any particular time.

So the statement actually means that it is possible for two identical systems at different macrostates evolve into the same later macrostate.

— Me@2022-01-08 03:12 PM

But the opposite is not possible. Two indistinguishable macrostates is actually, by definition, one macrostate. It cannot evolve into two distinguishable macrostates.

One single macrostate is logically impossible to be corresponding to two different possible later macrostates.

— Me@2022-01-08 01:29 PM

If the beginning universe state had a high entropy, by definition, it was at a macroscopic state with many possible macroscopically-indistinguishable microstates.

However, if it is really the state of the universe at the beginning, it is, by definition, a single microstate, because “different microstates” is meaningful only if they were once distinguishable.

— Me@2013-08-11 01:42 PM

a macrostate = a set of macroscopically-indistinguishable microstates

— Me@2022-01-09 07:43 AM

The meaning of “entropy increases” is that state $\displaystyle{S_1}$ and state $\displaystyle{S_2}$ both evolve into state $\displaystyle{S_3}$ .

But for the beginning of the universe, there were no multiple possible macrostates that the beginning state could be evolved from.

— Me@2013-08-11 01:44 PM

魚目混珠 1.2

Posted on January 8, 2022 by rpflee

Pure evil does no harm, because if someone is purely evil, everyone will know that and avoid him.

It is the evilness of a good man that creates big harm.

The evilness of great man creates the biggest harm.

An organization cannot be purely evil.

Anything purely evil cannot be big, because being big requires consistency, which requires good.

— Me@2011.10.11

— Me@2022-01-08

To realize is to realize, 1.5

Posted on January 7, 2022 by rpflee

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?

4. you have another half or not

If you act as if your future wife exists, you have a much higher chance of finding her, because you have actually been providing the environment for her to exist.

If you act as if your future wife exists, compared with assuming not having one, you live completely differently. You will make yourself financially stable; you will earn and save money for your future wife and children. You will make yourself healthy so that you can live long enough to finally find her; and then stay with her for decades. You will make and meet genuine friends, for you know that one of them is either your future wife or the one who introduces her to you.

If you know that your future wife exists, you will not have any romantic relationship with anyone that is certainly not your future wife, no matter how beautiful she is. Actually, you will not start any romantic relationship with anyone at all, unless she is potentially your future wife.

You will keep writing letters, sending them to the future; to your future wife. Once your future wife realizes that those letters may be actually for her, she will find you to confirm.

— Me@2021-02-19 06:32:05 AM

— Me@2021-03-02 04:39:33 PM

— Me@2022-01-07 10:00:29 AM

If you act as if your future wife exists, you know that the goal is not to find the “best” lady, but to find your future wife.

Your wife is the key to the lock of your life. Your goal is not to find the “best” key in the world, but to find the key of your life.

It is not to find the “best” key, but to find your key.

— Me@2021-12-03 12:03 PM

— Me@2021-12-05 03:22 AM

— Me@2022-01-07 12:30 PM

Somewhere out there
beneath the pale moonlight
Someone’s thinking of me
and loving me tonight

— James Horner, Barry Mann, Cynthia Weil

1990s, 11

Posted on January 6, 2022 by rpflee

— Me@2022-01-06 12:14:03 PM

2.10 A spacetime orbifold in two dimensions, 6

Posted on January 5, 2022 by rpflee

A First Course in String Theory

(d) Consider the two curves $\displaystyle{x^+ x^- = a^2}$ for some fixed $\displaystyle{a}$ . The identification (2) makes each of these curves into a circle. Find the invariant circumference of this circle by integrating the appropriate root of $\displaystyle{ds^2}$ between two neighboring identified points. Give your answers in terms of $\displaystyle{a}$ and $\displaystyle{\lambda}$ . Answer: $\displaystyle{\sqrt{2} a \lambda}$ .

~~~

Identification (2):

$\displaystyle{(x^+, x^-) \sim \left( e^{-\lambda} x^+, e^{\lambda} x^- \right)}$ , where $\displaystyle{e^\lambda \equiv \sqrt{\frac{1+\beta}{1-\beta}}}$ .

$\displaystyle{ \begin{aligned} ds &= \sqrt{- ds^2} \\ \int_{(x^+, x^-)}^{(e^{-\lambda} x^+, e^{\lambda} x^-)} ds &= \int_{x^+}^{e^{-\lambda} x^+} \sqrt{2 \frac{a^2}{(x^+)^2} (dx^+)^2} \\ &= \sqrt{2} a \int_{x^+}^{e^{-\lambda} x^+} \sqrt{\frac{1}{(x^+)^2}} dx^+ \\ \end{aligned}}$

Choose a segment on which $\displaystyle{x^+ > 0}$ .

$\displaystyle{ \begin{aligned} \int_{(x^+, x^-)}^{(e^{-\lambda} x^+, e^{\lambda} x^-)} ds &= \sqrt{2} a \int_{x^+}^{e^{-\lambda} x^+} \frac{1}{x^+} dx^+ \\ &= \sqrt{2} a \ln \left|\frac{e^{-\lambda} x^+}{x^+} \right| \\ &= - \sqrt{2} a \lambda \\ \end{aligned}}$

The lower limit should be smaller than the upper limit.

$\displaystyle{ \begin{aligned} \left| \int_{(x^+, x^-)}^{(e^{-\lambda} x^+, e^{\lambda} x^-)} ds \right| &= \sqrt{2} a \int_{e^{-\lambda} x^+}^{x^+} \frac{1}{x^+} dx^+ \\ &= \sqrt{2} a \lambda \\ \end{aligned}}$

— Me@2022-01-05 02:40:45 PM

時光起源

Posted on January 5, 2022 by rpflee

The Origin of Time

這段改編自 2021 年 12 月 5 日的對話。

昨日的那段影片說，個別的粒子，其實都是質量零；以光速行走，感受不到時間。

但是，把一堆粒子圈成一件東西的話，那件東西整體而言，就會有質量；就會低於光速行走；就會感受到時間。

變相來說，時間的來源就是，你將一堆粒子組成一個物件、一個身份、一個自我時，那個自我就會，感受到時間。

— Me@2022-01-04 12:23:25 PM

To form an object (an observer), the component particles cannot all always move at light speed in the same direction, for that would prevent the object as a whole from feeling time.

Anything moving at the speed of light cannot feel the passage of time. If a set of particles all moves at light speed in the same direction all the time, they cannot feel time either as individuals or as a whole; so they cannot form an “object”.

To form an object (an observer), the component particles need to interact. So some component particles need to move in other directions sometimes.

An object requires an internal structure to exist and evolve. The component particles need to interact in order to evolve as a single identity. So different particles need to move in different directions sometimes. As a result, the component particles as a whole, aka “the object”, will move slower than light.

— Me@2021-12-08 08:09:17 AM