Category Archives: physics

Quantum observer 1.1

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In ordinary quantum mechanics, observers or measuring devices are macroscopic. So they are classical, in the sense that each of them is always in a macroscopic-eigenstate, aka “a macrostate“. A classical object would not be in a macroscopic superposition, in the sense that there would not be in a superposition of macroscopic-eigenstates. Macroscopic reality is always definite, unless you are talking about future events.

Then, would the macroscopic reality actually be a superposition of microscopic eigenstates?

Yes, it is. That is a logical implication from quantum mechanics. However, that makes no experimental difference, since those microstates of a lot of particles constitute a single macrostate.

In conclusion, a macrostate is not a superposition of macroscopic eigenstates. And although it is a superposition of microscopic eigenstates, it makes only conceptual difference but no experimental difference even if we ignore this fact. So for a classical observer, we do not have to consider whether it is in a superposition or not.

How about the observed particle? Would it be in a superposition?

It can and probably is.

However, superposition is a logical implication only. It cannot be observed directly using a macroscopic measuring device. Also, by using a macroscopic measuring device, aka “a classical observer“, to measure or observe a microscopic event, we will always collapse the wave function of the observed system (due to the decoherence effect), yielding a definite macroscopic result (which is corresponding to one of the eigenstate components in the original microscopic superposition). 

What if I have a microscopic measuring device as a “quantum observer”?

— Me@2013-01-16 10:53:06 AM

2013.01.16 Wednesday (c) All rights reserved by ACHK

Looper, 2

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二次元時間 2.3 | Dimension 1.3.3 | Two dimensional time 2.3 | 孖生宇宙 2.3

這段改編自 2010 年 4 月 3 日的對話。

所以，我剛才視「多重宇宙標籤」為「第二個時間」次元，是建基於「平行宇宙機」的假設。那個科幻故事的主角，發明了「平行宇宙機」，令到自己可以，由原本的宇宙（甲），走到另一個宇宙（乙）行事。那樣，「宇宙甲」的歷史，就可以透過主角，影響到「宇宙乙」的演化，反之亦然。

其中一個有「二次元時間」的科幻小說是，電影《時凶獵殺》（Looper）。故事中只有「時光機」，而沒有「平行宇宙機」，所以，不同「時間線」之間的演化，只能是單向。意思是，「宇宙一」（時間線一）會影響「宇宙二」；「宇宙二」會影響「宇宙三」；如此類推。但是，「宇宙二」不會影響「宇宙一」。

單向的「平行宇宙」演化，比較接近平時意思下的「時間次元」，因為「時間次元」，應該是單向的 —— 由「過去」到「將來」，而不會由「將來」到「過去」。在這個例子中，「宇宙一」就是「宇宙二」的「過去」。而「宇宙三」，就是「宇宙二」的「將來」。

「平行宇宙」中的每一個，內部都會有自己事件演化的「因果鏈」，簡稱「歷史」。所以，每一個宇宙，即為一條「時間線」。那就是「第一個時間次元」。而「平行宇宙」間的演化，即為「第二個時間次元」：

「宇宙一」 –> （影響）「宇宙二」–> （影響）「宇宙三」–> … …

— Me@2013.01.15

2013.01.15 Tuesday (c) All rights reserved by ACHK

Phe-nomenon

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Universal wave function, 19 | Reductionism 4

Impartial/All is the Noumenon, which is logically impossible for any single observer to observe directly, unless the observer is the whole of the universe. But “self-observation” is meaningless.

— Me@2012.04.07

Because “state” is expressed in RQM as the correlation between two systems, there can be no meaning to “self-measurement”.

— Wikipedia on Relational quantum mechanics

The Noumenon is a logical implication. It cannot be observed directly. It can be observed partially only, through senses, or phenomena. An observation is an interaction between the observer and the observed.

To really “observe” the Noumenon, all we can do is to observe as many phenomena as possible. In other words, we consider as many observer-observed pairs as possible.

— Me@2013.01.14

This is because this state would have to be ascribed to a correlation between the universe and some other physical observer, but this observer in turn would have to form part of the universe, and as was discussed above, it is impossible for an object to give a complete specification of itself. Following the idea of relational networks above, an RQM-oriented cosmology would have to account for the universe as a set of partial systems providing descriptions of one another. The exact nature of such a construction remains an open question.

— Wikipedia on Relational quantum mechanics

nomenon = all

phe- = part

noumenon = all aspects of the universe

phenomenon = part of the reality of the universe

— Me@2012.04.07

2013.01.14 Monday (c) All rights reserved by ACHK

二次元時間 2.2

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Dimension 1.3.2 | Two dimensional time 2.2 | 孖生宇宙 2.2

這段改編自 2010 年 4 月 3 日的對話。

你可以想像，隨著主角多次的「時間旅行」，改變歷史的次數越多，「平行宇宙」的數目亦會越大。假設，主角除了擁有「時光機」，可以「時間旅行」外，他在後來還發明了「平行宇宙機」，令到自己可以，穿梭遊走於各個「平行宇宙」之間。那樣，我們就可以說，「平行宇宙機」連繫了眾多「平行宇宙」。原本的「平行宇宙」，不再完全「平行」。

那樣，要指清一件事件時，除了要指出它發生的時間 —— 例如「2013 年 1 月 14 日 5 時 20 分」—— 外，還要講清楚，它發生在哪一個宇宙的「2013 年 1 月 14 日 5 時 20 分」。原本的時間標籤，是「第一個時間次元」。多重宇宙的標籤，則可以視為「第二個時間次元」。

（安：我覺得有點奇怪。我覺得「多重宇宙的標籤」，既不可以叫做「空間次元」，因為那個標籤或者數字，並不是用來描述「同一個宇宙」中的空間位置；亦不可以叫做「時間次元」，因為「時間」有「因果鏈」的意思。「多重宇宙」是「平行宇宙」，互不相干，沒有「因果關係」可言。）

所以，我剛才視「多重宇宙標籤」為「第二個時間」次元，是建基於「平行宇宙機」的假設。那個科幻故事的主角，發明了「平行宇宙機」，令到自己可以，由原本的宇宙（甲），走到另一個宇宙（乙）行事。那樣，「宇宙甲」的歷史，就可以透過主角，影響到「宇宙乙」的演化，反之亦然。

（安：依你這個講法，除了在科幻小說外，日常現實生活中 —— 如果用比喻 —— 都會有「二次元時間」的現象。）

什麼意思？

— Me@2013.01.14

2013.01.14 Monday (c) All rights reserved by ACHK

Everett’s relative-state formulation, 2

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The relative-state interpretation makes two assumptions.

The first is that the wavefunction is not simply a description of the object’s state, but that it actually is entirely equivalent to the object, a claim it has in common with some other interpretations.

The second is that observation or measurement has no special role, unlike in the Copenhagen interpretation which considers the wavefunction collapse as a special kind of event which occurs as a result of observation.

— Wikipedia on Many-worlds interpretation

2013.01.12 Saturday ACHK

二次元時間 2.1

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Dimension 1.3.1 | Two dimensional time 2.1 | 孖生宇宙 2.1

這段改編自 2010 年 4 月 3 日的對話。

（安：我有一點不明白。你說「dimension」（次元）有兩種，可以是「spatial dimension」（空間次元），或者「temporal dimension」（時間次元）。宇宙的次元數目是「三加一」，即是「『三次元空間』加『一次元時間』」。

假設有一個科幻故事，描述一個有「二次元時間」的虛構宇宙。那樣，「二次元時間」是什麼意思？）

其實，「四次元空間」同樣難想像。不過，我們容後再談。我們先討論，何謂「二次元時間」。

一個宇宙，有一個「時間次元」，即是有一條「時間線」。「時間線」又可以稱為「因果鏈」。

如果一個科幻故事，容許「時間旅行」，而又不想引起矛盾，就唯有容許多個「平行宇宙」的存在。例如，二十歲的主角，回到十年之前，殺害十歲時的自己。但是，十歲時的主角既然之死，二十歲的主角又怎會存在呢？

「解決」之道是，宣稱在「二十歲的主角」殺害「十歲自己」時，宇宙歷史的發展被改變了，形成一分為二的「歷史分支」。或者說，宇宙的「時間線」，由一條分裂成兩條。

而科幻故事的通常用語是，在「二十歲的主角」殺害「十歲自己」時，宇宙由「一個」，分支成「兩個平行宇宙」。在一個宇宙中，主角活到起碼二十歲；而在另一個宇宙中，主角在十歲已遭人殺害。「平行」的意思是，再互不相干。亦即是話，「二十歲的主角」進入了另一個平行宇宙，再不能回到自己原本的世界。

你可以想像，隨著主角多次的「時間旅行」，改變歷史的次數越多，「平行宇宙」的數目亦會越大。假設，主角除了擁有「時光機」，可以「時間旅行」外，他在後來還發明了「平行宇宙機」，令到自己可以，穿梭遊走於各個「平行宇宙」之間。那樣，我們就可以說，「平行宇宙機」連繫了眾多「平行宇宙」。原本的「平行宇宙」，不再完全「平行」。

— Me@2013.01.12

2013.01.12 Saturday (c) All rights reserved by ACHK

Professor 2

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lisper 4 days ago | link

I was never in academia, but I was a researcher (at NASA) so I played the publishing game. And if you look at my record, I was relatively good at it. Not only was my publications list fairly long, but my work was also pretty widely referenced. But since my career no longer depends on it, I am now free to say that I credit my success almost entirely to gaming the system. This is not to say that I didn’t do good work (I think I did), but there was virtually no correlation between what I thought was quality work and what I actually got rewarded for. The vast majority of my publications were minor tweaks on previous work that were specifically engineered to get past the program committees of key conferences. My best work (by my own quality metric) either went unnoticed, or could not get accepted for publication at all. When it got to the point where I was faced with a very stark choice between continuing to produce bullshit and get rewarded for it, or to do what I thought was good work and eventually get fired, I quit.

   
Evbn 4 days ago | link

Industry isn’t so different. My salary is determined by 2 days of interviews and negotiations, and only slightly perturbed by my performance over the next several years.

— Hacker News

2013.01.11 Friday ACHK

比喻

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Dimension 1.2

這段改編自 2010 年 4 月 3 日的對話。

該片的另一個問題是，它只用了一些比喻作為 argument（論據）。

「比喻」的作用，在於輔助理解，加深記憶。但是，「比喻」本身，並不可以作為論據。所以，我們要清楚知道，「以比喻來輔助解釋」和「以比喻本身作為解釋」的分別。前者合理，後者荒謬。

當一個所謂的「科學作品」，只提供一些比喻，而背後卻沒有提供，實質的內容和具體的論據時，那就只可算是「偽科學」和「偽作品」。

— Me@2013.01.09

2013.01.09 Wednesday (c) All rights reserved by ACHK

Digital physics, 3.2

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… what changes continuously is not the eigenvalue, namely the quantity that you measure, but rather the probabilities of measuring one or the other of those eigenvalues.

— Jan 26 ’11 at 23:51

— Carlo Rovelli

2013.01.08 Tuesday ACHK

Information lost, 3.3

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Unitarity 3

The laws of Quantum Mechanics are very subtle — so subtle that they allow randomness to coexist with both energy conservation and information conservation.

— The Black Hole War, p.89

— Leonard Susskind

2013.01.06 Sunday ACHK

Dimension 1.1

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這段改編自 2010 年 4 月 3 日的對話。

（安：你上次電郵了一段有關「dimension（次元）」的短片給我，內容講述何謂「第四個次元」或以上。但是，你在電郵中又提及，那段短片的講法不盡正確，有所遺漏。它錯在哪裡呢？）

「量數」（counting number）不同於「序數」（ordering number）。以下請留意，「一個」（one）和「第一」（first）的分別；「二個」（two）和「第二」（second）的分別；如此類推。

「點」是零次元；「線」是一次元；「面」是二次元；「立體」是三次元。「時間」，在物理的「相對論」中，可以看成「第四個次元」。「三次元空間」加「一次元時間」，形成我們宇宙的「四次元時空」。

該段影片的錯處是，它假設了，「第四個次元」一定是「時間次元」。它彷彿不知道，在理論上，「第四個次元」可能都是「空間次元」。所以，那段影片有「以偏概全」之嫌。

雖然，根據現時的實驗結果，宇宙的次元數目，的確是「三加一」，即是「『三次元空間』加『一次元時間』」；但是，該段短片的主題是，理論上，「更高次元」的「樣子」是怎麼樣。所以，它完全沒有提及，「第四個次元」是「空間次元」的那個情況，並不是因為作者刻意的剪接。

— Me@2013.01.05

2013.01.06 Sunday (c) All rights reserved by ACHK

Coherent quantum superpositions 1.2

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remain secret = is not lost to the environment yet

— Me@2013-01-03 11:07:30 AM

The no-cloning theorem is a result of quantum mechanics that forbids the creation of identical copies of an arbitrary unknown quantum state.

— Wikipedia on No-cloning theorem

[guess]

conservation of information

= you can only move, but not copy, a piece of information

Classical information can be copied because “identical” classical systems are not really identical if we consider their microscopic details. One macrostate can be corresponding to a lot of microstates, e.g.

4 = 1 + 1 + 2

4 = 1 + 3 + 0

copy one macrostate = find another microstate which is corresponding to the same macrostate

Whether two states are “identical” depends on the resolution of the observer.

[guess]

— Me@2013-01-03 11:07:30 AM

2013.01.04 Friday (c) All rights reserved by ACHK

Coherent quantum superpositions

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Decoherence was worked out in great detail by Los Alamos scientist Wojciech Zurek, Zeh and others over the following decades. They found that coherent quantum superpositions persist only as long as they remain secret from the rest of the world.

— from Max Tegmark; John Archibald Wheeler (2001). “100 Years of the Quantum”. Scientific American 284 (2003): 68–75

— Wikipedia on Quantum entanglement

That means the superposition information is not lost to the environment yet.

— Me@2012.12.31

2013.01.03 Thursday (c) All rights reserved by ACHK

Light cone

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Light-like is between space-like and time-like.

Light is the boundary between space and time.

[guess]

“Nothing can be faster than light” may be a tautology due to the definitions of the words “mass“, “speed of light“, “space” and “time“.

— Me@2013.01.01

2013.01.02 Wednesday (c) All rights reserved by ACHK

EPR paradox, 9

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In an EPR experiment, once you have measured one particle’s spin, you know the spin of the opposite particle instantaneously.

Your ability of getting the total information at once is due to the fact that you know partial information in advance. Since the time of the separation of the two particles, you have already known that “the opposite particle must have an opposite spin”. 

Let

A = the spin of your particle

B = the fact that the opposite particle must have an opposite spin

C = the spin of the opposite particle

knowing A + knowing B = knowing C

There are no superluminal (faster-than-light) communications between the two particles. So the whole EPR experiment is compatible with classical locality, aka special relativity.

The strange thing is the quantum non-locality part.

— Me@2012-04-04 5:21:25 PM  

2013.01.01 Tuesday (c) All rights reserved by ACHK

Single-world interpretation, 7.2

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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

2012.12.28 Friday (c) All rights reserved by ACHK

Gravity as an entropic force, 2

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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

EPR paradox, 8

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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

Quantum entanglement 2

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EPR paradox, 7

Some people have interpreted this as telling us that “everything is connected to everything else” or that “quantum mechanics entangles us all in one universal whole.”

After all, the reasoning goes, at the big bang everything emerged from one place since, we believe, all places we now think of as different were the same place back in the beginning.

— p.122

— The Fabric of the Cosmos

— Brian Greene

2012.12.22 Saturday ACHK

EPR paradox, 6

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The claim that EPR effects violate the principle that information cannot travel faster than the speed of light have been countered by noting that they cannot be used for signaling because neither observer can control, or predetermine, what he observes, and therefore cannot manipulate what the other observer measures.

— Wikipedia on Copenhagen interpretation

2012.12.17 Monday ACHK