# 無限循環

A time to fear, 4 | Recursion 8

— Me@2012.03.08

— Me@2012.12.31

# 教學無用 2.2

（安：暫時我也想不到。）

（安：暫時未發現到有。你的意思是，如果是物理科，就應該給有興趣讀物理的人，來評價他們物理教員的教學質素。）

（安：依你這樣說，教高中課程的補習社，都是理想的學校，因為在那裡，學生可以選擇，哪一位教員，教哪一科的課程。）

— Me@2012.12.30

# Universe 1.2

exists = is in = belongs to = can be found

Exists” is “存在” in Chinese. Literally,

exists = 存在 = is stored in

X is stored in” is not a complete sentence because it lacks an object. X is stored in where?

— Me@2012.10.16

— Me@2012.12.30

# 自動時間表 2

Past papers 26.4

（CPK：即是要花全日？）

 Monday Tuesday Wednesday Thursday Friday 3 hours Physics Applied Maths Pure Maths Physics Applied Maths 1 hour Chinese English Chinese English Chinese 1 hour 3 hours Pure Maths Physics Applied Maths Pure Maths Physics

 Monday Tuesday Wednesday Thursday Friday 3 hours Physics Applied Maths Pure Maths Physics Applied Maths 1 hour Chinese English Chinese English Chinese 1 hour 3 hours Pure Maths Physics Applied Maths Pure Maths Physics

 Monday Tuesday Wednesday Thursday Friday 3 hours Physics Applied Maths Pure Maths Physics Applied Maths 1 hour Chinese English Chinese English Chinese 1 hour 3 hours Pure Maths Physics Applied Maths Pure Maths Physics

Physics –> Pure Maths –> Applied Maths –> Physics –> …

 Monday Tuesday Wednesday Thursday Friday 3 hours Physics Applied Maths Pure Maths Physics Applied Maths 1 hour Chinese English Chinese English Chinese 1 hour 3 hours Pure Maths Physics Applied Maths Pure Maths Physics

— Me@2012.12.29

# Single-world interpretation, 7.2

Quantum Mechanics 3

Under the many-worlds interpretation, the Schrodinger equation, or relativistic analog, holds all the time everywhere. An observation or measurement of an object by an observer is modeled by applying the wave equation to the entire system comprising the observer and the object. One consequence is that every observation can be thought of as causing the combined observer-object’s wavefunction to change into a quantum superposition of two or more non-interacting branches, or split into many “worlds”. Since many observation-like events have happened, and are constantly happening, there are an enormous and growing number of simultaneously existing states.

If a system is composed of two or more subsystems, the system’s state will be a superposition of products of the subsystems’ states. Once the subsystems interact, their states are no longer independent. Each product of subsystem states in the overall superposition evolves over time independently of other products. The subsystems states have become correlated or entangled and it is no longer possible to consider them independent of one another. In Everett’s terminology each subsystem state was now correlated with its relative state, since each subsystem must now be considered relative to the other subsystems with which it has interacted.

— Wikipedia on Many-worlds interpretation

This is insightful, but incorrect. Please refer to my previous post “Single-world interpretation, 7” for details.

The main theme is that the macroscopic reality can never be an eigen-quantum-state. Instead, the macroscopic reality is the resultant effect of the superposition of eigen-quantum-states. For example, without quantum superposition, there would be no Principle of Least Action in classical mechanics.

— Me@2012-12-28 12:52:12 PM

In particular, Sidney explains that our world is a quantum world and any phenomena that look classical are approximate or derived. So it’s really nonsensical to ask for an “interpretation of quantum mechanics”. Instead, one should really discuss the “interpretation of classical physics” and its derivative appearance from the quantum framework.

Of course, Sidney was well aware of the fact – and made this fact explicit – that the people who have problems with these concepts have those problems simply because they believe that underneath quantum mechanics, there is still some classical physics operating.

— Sidney Coleman: Quantum mechanics in your face

— Lubos Motl

# Palace 2

Focus on yourself instead of the world, for this world is so corrupt. You have to create your own world anyway.

— Me@10:38 AM 12/30/2011

— John Donne

— Me@2012-10-03

# 教學無用 2.1

「客觀評價一個人的教學才能」這個講法，有自相矛盾之嫌，因為「教學才能」，並不能「客觀評價」。「教學才能」只可以在某些人工標準下，予以評定。例如，如果你在補習社教書，你的學生人數多少，就會疑似反映，你教學才能的高低。但是，那又不完全是，我們原初想考慮的東西，因為學生的人數多，又不一定代表教學才能高。

— Me@2012.12.27

# Universe 4

exists = can be found

Existence is a relation. In order words, the sentence “X exists” means:

X exists = X can be found by something else

If there is only one object, the word “existence” has no meaning, because there is no “something else”. For example, by the definition of the word “universe“, there is only one universe. So the sentence “universe exists” has no meaning.

uni- = one

universe = all the things = all as one

— Me@2012.10.16

# Past papers 26.3

（CPK：那如果我只要求有 B 級的成績，我需要做多少年的 past paper 呢？）

（CPK：奪 A 要 20 年，而奪 B 只要 10 年。為何會相差那麼多？）

— Me@2012.12.26

# Gravity as an entropic force, 2

The authors of the flawed preprint used at least two (but related) invalid arguments in their attempts to resuscitate Erik Verlinde’s theory. One of them was the claim that Verlinde’s theory produces the “right classical limit”. When this classical limit is quantized, one obtains the right quantum theory, including the neutron interference. However, this argument incorrectly assumes that quantum physics is uniquely determined by a classical limit. It’s not. If you take the classical limit C of a quantum theory Q and “quantize” C again, you don’t necessarily get Q.

In particular, when we talk about the distance-dependent entropy, it’s a feature of a physical theory that holds both in the quantum theory Q and in the classical limit C. And in the quantum theory, it automatically destroys the interference patterns because there exists no one-to-one way how to link microstates at different separations (because their numbers differ). So there can’t exist any quantum theory that preserves the interference but that still produces a classical limit with a distance-dependent entropy.

— Once more: gravity is not an entropic force

— Lubos Motl

2012.12.25 Tuesday ACHK

# SICM, 3.2

《SICM》（Structure and Interpretation of Classical Mechanics）中的編程語言，除了 Scheme 的本體外，還會用到作者特製的力學程式庫 Scmutils。而這個程式庫（library）卻只有 Linux 的版本，不能安裝在 Windows 之中。那導致我要特意在我的 Windows 中，先裝一個 virtual machine（虛擬機器），從而在那個虛擬機器之上，再安裝一個 Linux 作業系統。

— Me@2012.12.25

# For all, 1.2

Universe 2.2

Defining the word “universe” as “all the things” does not totally make sense, since the meaning of “all” is relative to a place. Without a context such as “all things in this house“, the word “all” is meaningless. To be meaningful, you have to specify what the word “all” is with respect to.

Instead of “all the things“, we can define “universe” as

universe = all the things observable by an observer, directly or indirectly, in practice or in principle, plus the observer itself

— Me@2012.10.16

— Me@2012.12.24

# Civilisation

All civilisation was just an effort to impress the opposite sex …

— I Dated a Robot

— Futurama

.

.

2012.12.24 Monday ACHK

# Past papers 26.2

（CPK：六個小時？）

（CPK：但是，高考的課程，還有大概有三分之一的課題，學校還未開始教。）

（CPK：不理會？）

— Me@2012.12.24

Nonlocality vs entanglement

In the media and popular science, quantum nonlocality is often portrayed as being equivalent to entanglement. While it is true that a bipartite quantum state must be entangled in order for it to produce nonlocal correlations, there exist entangled states which do not produce such correlations. A well-known example of this is the Werner state that is entangled for certain values of p_{sym}, but can always be described using local hidden variables. On the other hand, reasonably simple examples of Bell inequalities have been found for which the quantum state giving the largest violation is never a maximally entangled state, showing that entanglement is, in some sense, not even proportional to nonlocality.

In short, entanglement of a two-party state is necessary but not sufficient for that state to be nonlocal. It is important to recognise that entanglement is more commonly viewed as an algebraic concept, noted for being a precedent to nonlocality as well as quantum teleportation and superdense coding, whereas nonlocality is interpreted according to experimental statistics and is much more involved with the foundations and interpretations of quantum mechanics.

— Wikipedia on Quantum nonlocality

2012.12.23 Sunday ACHK

# 尋找時間的定義

SICM, 3 | SICP, 2

《SICP》跟《SICM》，同樣是超級名著。但是它不易理解。幸好，它官方網站提供了，一些 1986 年的講課錄影。當年（2006），尚未流行使用 YouTube，所以我要花很多時間，下載那些錄影。我還記得，每節課的錄影檔案，有 600MB 那麼大。

— Me@2012.12.23