Logical arrow of time, 7

When we imagine that we know and keep track of all the exact information about the physical system – which, in practice, we can only do for small microscopic physical systems – the microscopic laws are time-reversal-symmetric (or at least CPT-symmetric) and we don’t see any arrow. There is a one-to-one unitary map between the states at times “t1” and “t2” and it doesn’t matter which of them is the past and which of them is the future.

A problem is that with this microscopic description where everything is exact, no thermodynamic concepts such as the entropy “emerge” at all. You might say that the entropy is zero if the pure state is exactly known all the time – at any rate, a definition of the entropy that would make it identically zero would be completely useless, too. By “entropy”, I never mean a quantity that is allowed to be zero for macroscopic systems at room temperature.

But whenever we deal with incomplete information, this one-to-one map inevitably disappears and the simple rules break down. Macroscopic laws of physics are irreversible. If friction brings your car to a halt and you wait for days, you won’t be able to say when the car stopped. The information disappears: it dissipates.

— The arrow of time: understood for 100 years

— Lubos Motl


If there is a god-view, there is no time arrow.

Time arrow only exists from a macroscopic point of view. Microscopically, there is no time arrow.

If there is a god-view that can observe all the pieces of the exact information, including the microscopic ones, there is no time arrow.

Also, if there is a god-view, there will be paradoxes, such as the black hole information paradox.

Black hole complementarity is a conjectured solution to the black hole information paradox, proposed by Leonard Susskind, Larus Thorlacius, and Gerard ‘t Hooft.

Leonard Susskind proposed a radical resolution to this problem by claiming that the information is both reflected at the event horizon and passes through the event horizon and cannot escape, with the catch being no observer can confirm both stories simultaneously.

— Wikipedia on Black hole complementarity

The spirit of black hole complementarity is that there is no god-view. Instead, physics is always about what an observer can observe.

— Me@2018-06-21 01:09:05 PM



2019.02.11 Monday (c) All rights reserved by ACHK


E: Can you just, you know, like, just tell me the answer?

J: Sorry?

E: You know, the answer. To everything.

What’s the point of love if it’s just disappear?

There has to be meaning to existence, otherwise the universe is made of pain and I don’t like the thought of that.

So, tell me the answer!

J: The more human I become, the less things make sense.

But that’s part of the fun. Right?

E: What do you mean?

J: If there were an answer I can give you to, how the universe works, it wouldn’t be special. It would be just a machinery fulfilling its cosmic design. It would be just a big, dumb food processor.

But, since nothing seems to make sense, when you find something or someone that does, it’s euphoria.


In all of this randomness, in this pandemonium, you and Chidi found each other and you had a life together.

Isn’t that remarkable?

E: Pandemonium is from Paradise Lost. Milton called the center of hell “pandemonium”, meaning “place of all demons”.

I guess all I can do is to embrace the Pandemonium.

Find happiness in the unique insanity of being here, now.

— The Good Place



2019.01.27 Sunday ACHK

(反對)開夜車 2.2

Ken Chan 時光機


The light that burns twice as bright burns half as long, …

— Blade Runner (1982)


我現在的記憶,暫時未能確定,他在課堂中,有沒有明示推介過,用這個方法。但是,我記得在他派發的筆記中,其中一頁,有一個正在深夜讀書的漫畫。而在漫畫下面,有一句「study to 3 a.m.」(讀書至深夜三點鐘)。





在 Ken Chan 的部分課堂,特別是假期的補課中,我就見到他時常咳嗽。可能,他在工作時代,仍然過著,極度忙碌的生活。


還記得在九月,在課程的第一課,他就已經遲到,遲了大概 15 至 30 分鐘之間。那課原定於早上八時半開始。上課中途,他有點咳嗽。他說,因為當天早上之前,吸入了太多的氮氣。他懷疑一位同事,作弄了他。

話說,他工作的地方,有一部儀器壞了。他的同事跟他說:「部機好似壞咗,漏緊啲 nitrogen 喎,你聞下係唔係?」(那儀器疑似壞了,正在洩漏氮氣。你聞一聞,看看是不是。)

Ken Chan 事後回心一想,才醒起:「Nitrogen 又點會有味咖?」(氮氣又何來會有味道呢?)




— Me@2019-02-03 07:02:42 AM



2019.02.03 Sunday (c) All rights reserved by ACHK



Structure and Interpretation of Classical Mechanics (SICM) is a classical mechanics textbook written by Gerald Jay Sussman and Jack Wisdom with Meinhard E. Mayer. The first edition was published by MIT Press in 2001, and [the] second edition was released in 2015. The book is used at the Massachusetts Institute of Technology to teach a class in advanced classical mechanics, starting with Lagrange’s equations and proceeding through canonical perturbation theory.

— Wikipedia on Structure and Interpretation of Classical Mechanics



2019.02.02 Saturday ACHK