Relational quantum mechanics

EPR paradox, 10

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Relational quantum mechanics (RQM) is an interpretation of quantum mechanics which treats the state of a quantum system as being observer-dependent, that is, the state is the relation between the observer and the system. This interpretation was first delineated by Carlo Rovelli in a 1994 preprint, and has since been expanded upon by a number of theorists. It is inspired by the key idea behind special relativity, that the details of an observation depend on the reference frame of the observer, and uses some ideas from Wheeler on quantum information.

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Relational solution

In RQM, an interaction between a system and an observer is necessary for the system to have clearly defined properties relative to that observer. Since the two measurement events take place at spacelike separation, they do not lie in the intersection of Alice’s and Bob’s light cones. Indeed, there is no observer who can instantaneously measure both electrons’ spin.

The key to the RQM analysis is to remember that the results obtained on each “wing” of the experiment only become determinate for a given observer once that observer has interacted with the other observer involved. As far as Alice is concerned, the specific results obtained on Bob’s wing of the experiment are indeterminate for her, although she will know that Bob has a definite result. In order to find out what result Bob has, she has to interact with him at some time {\displaystyle t_{3}} in their future light cones, through ordinary classical information channels.

The question then becomes one of whether the expected correlations in results will appear: will the two particles behave in accordance with the laws of quantum mechanics? Let us denote by {\displaystyle M_{A}(\alpha )} the idea that the observer {\displaystyle A} (Alice) measures the state of the system {\displaystyle \alpha} (Alice’s particle).

So, at time {\displaystyle t_{2}}, Alice knows the value of {\displaystyle M_{A}(\alpha )}: the spin of her particle, relative to herself. But, since the particles are in a singlet state, she knows that

{\displaystyle M_{A}(\alpha )+M_{A}(\beta )=0,}

and so if she measures her particle’s spin to be {\displaystyle \sigma }, she can predict that Bob’s particle ( {\displaystyle \beta } ) will have spin {\displaystyle -\sigma }. All this follows from standard quantum mechanics, and there is no “spooky action at a distance” yet. From the “coherence-operator” discussed above, Alice also knows that if at {\displaystyle t_{3}} she measures Bob’s particle and then measures Bob (that is asks him what result he got) — or vice versa — the results will be consistent:

{\displaystyle M_{A}(B)=M_{A}(\beta )}

Finally, if a third observer (Charles, say) comes along and measures Alice, Bob, and their respective particles, he will find that everyone still agrees, because his own “coherence-operator” demands that

{\displaystyle M_{C}(A)=M_{C}(\alpha )} and {\displaystyle M_{C}(B)=M_{C}(\beta )}

while knowledge that the particles were in a singlet state tells him that

{\displaystyle M_{C}(\alpha )+M_{C}(\beta )=0.}

Thus the relational interpretation, by shedding the notion of an “absolute state” of the system, allows for an analysis of the EPR paradox which neither violates traditional locality constraints, nor implies superluminal information transfer, since we can assume that all observers are moving at comfortable sub-light velocities. And, most importantly, the results of every observer are in full accordance with those expected by conventional quantum mechanics.

— Wikipedia on Relational quantum mechanics

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2018.10.22 Monday ACHK

The Sixth Sense, 3

Mirror selves, 2 | Anatta 3.2 | 無我 3.2

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You cannot feel your own existence or non-existence. You can feel the existence or non-existence of (such as) your hair, your hands, etc.

But you cannot feel the existence or non-existence of _you_.

— Me@2018-03-17 5:12 PM

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Only OTHER people or beings can feel your existence or non-existence.

— Me@2018-04-30 11:29:08 AM

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2018.04.30 Monday (c) All rights reserved by ACHK

Logical arrow of time, 6.2

Source of time asymmetry in macroscopic physical systems

Second law of thermodynamics

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Physics is not about reality, but about what one can say about reality.

— Bohr

— paraphrased

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Physics should deduce what an observer would observe,

not what it really is, for that would be impossible.

— Me@2018-02-02 12:15:38 AM

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1. Physics is about what an observer can observe about reality.

2. Whatever an observer can observe is a consistent history.

observer ~ a consistent story

observing ~ gathering a consistent story from the quantum reality

3. Physics [relativity and quantum mechanics] is also about the consistency of results of any two observers _when_, but not before, they compare those results, observational or experimental.

4. That consistency is guaranteed because the comparison of results itself can be regarded as a physical event, which can be observed by a third observer, aka a meta observer.

Since whenever an observer can observe is consistent, the meta-observer would see that the two observers have consistent observational results.

5. Either original observers is one of the possible meta-observers, since it certainly would be witnessing the comparison process of the observation data.

— Me@2018-02-02 10:25:05 PM

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2018.02.03 Saturday (c) All rights reserved by ACHK

The Dunning–Kruger effect

想不出來 1.2.2

The Dunning–Kruger effect is a cognitive bias in which low-ability individuals suffer from illusory superiority, mistakenly assessing their ability as much higher than it really is. Dunning and Kruger attributed this bias to a metacognitive incapacity, on the part of those with low ability, to recognize their ineptitude and evaluate their competence accurately. Their research also suggests corollaries: high-ability individuals may underestimate their relative competence and may erroneously assume that tasks which are easy for them are also easy for others.

Dunning and Kruger have postulated that the effect is the result of internal illusion in those of low ability, and external misperception in those of high ability: “The miscalibration of the incompetent stems from an error about the self, whereas the miscalibration of the highly competent stems from an error about others.”

— Wikipedia on Dunning–Kruger effect

I’ve found that people who are great at something are not so much convinced of their own greatness as mystified at why everyone else seems so incompetent.

— Paul Graham

2017.02.17 Friday ACHK

E1.2

Do not be too timid and squeamish about your actions. All life is an experiment. The more experiments you make the better.

— Emerson

One experience [almost] always helps another, because the first experience betters you, to deal with the second experience; even if the first experience is unpleasant.

— Me@2011.07.16

— Me@2015.11.19

2015.11.19 Thursday (c) All rights reserved by ACHK

Quantum Indeterminacy

注定外外傳 1

Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics.

Indeterminacy in measurement was not an innovation of quantum mechanics, since it had been established early on by experimentalists that errors in measurement may lead to indeterminate outcomes. However, by the later half of the eighteenth century, measurement errors were well understood and it was known that they could either be reduced by better equipment or accounted for by statistical error models. In quantum mechanics, however, indeterminacy is of a much more fundamental nature, having nothing to do with errors or disturbance.

— Wikipedia on Quantum indeterminacy

Quantum indeterminacy is the inability to predict the behaviour of the system with 100% accuracy, even in principle.

If everything is connected

, quantum indeterminacy is due to the logical fact that, by definition, a “part” cannot contain (all the information of) the “whole”.

An observer (A) cannot separate itself from the system (B) that it wants to observe, because an observation is an interaction between the observer and the observed

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In order to get a perfect prediction of a measurement result, observer (A) must have all the information of the present state of the whole system (A+B). However, there are two logical difficulties.

First, observer A cannot have all the information about (A+B).

Second, observer A cannot observe itself to get (all of) its present state information, since an observation is an interaction between two entities. Logically, it is impossible for something to interact with itself directly. Just as logically, it is impossible for your right hand to hold your right hand itself. 

So the information observer A can get (to the greatest extent) is all the information about B, which is only part of the system (A+B) it (A) needs to know in order to get a prefect prediction for the evolution of the system B.

— Me@2015-09-14 08:12:32 PM

2015.09.15 Tuesday (c) All rights reserved by ACHK

Replay

stephengillie 64 days ago

In gaming, the concept is called a “replay”, where instead of recording the pixels on the screen in every frame, they instead record all inputs processed on every frame, and just replay them thru the same engine. The action is technically idempotent in the game world.

Where this breaks down is when features get updated between revisions. If your game patched the “jump” function to increase upward momentum from 1.1 m/s to 1.13 m/s, the Replay would be incorrect. You would be jumping onto platforms you couldn’t get up to before, moving faster, maybe even dodging enemy attacks that hit you when you played that match.

The human neuroprocessor is always changing and growing, always revising itself. Thus memories replay incorrectly. You apply old feelings to new mental patterns, and sometimes they lead to weird places. Or sometimes you mistake something easy for being difficult, because your memory data is out-of-date for your current processes. 

— Hacker News

2015.04.16 Thursday ACHK

What Is it Like to Be a Bat?

Feeling is a relationship between a particular observer and a particular observed.

So the question of “whether the color red I see is the same as the color red you see” is logically meaningless.

— Me@2015-04-06 1:13 PM

If observer B can get the memory of observer A, it is logically possible to feel another mind’s feelings (to a certain extend).

In that situation, the question of “whether B’s feeling of seeing the color red is the same as A’s” is meaningful.

— Me@2015-04-07 03:58:46 PM

2015.04.09 Thursday (c) All rights reserved by ACHK

Open Source MindOS

這段改編自 2010 年 4 月 10 日的對話。

(安:我發覺我都有一個,大部人也沒有的優點。我這類性格的人,又真的很少。)

什麼優點?

(安:我比較容易受教。我舉一個例子:

有一次,我和朋友甲討論一個邏輯問題。我的心目中一直以為,因為「先決條件」和「充份條件」,是兩個不同的概念,所以沒有關係。但是,甲指出「充份條件」其實即是,「所有先決條件」的總和。

經過他的解釋,我發覺原本「兩者沒有關係」的想法是錯的。我就自然立刻承認。我不單不會因為發現自己錯,有絲毫不高興;我反而會十分開心,因為,「發現自己原本錯」,其實就即是「發現了真正的答案」。

換句話說,「發現自己錯」的那一刻,正正是我知識增長,和智力提升的那一刻。)

那就即是話,你腦中的作業系統,是 Open Source 的 —— 容許別人修改。

(安:但是,我發覺大部分人,也不是那樣的。他們不單不會因為,發現「真正答案」而高興,甚至會全盤否定它,為的只是要「自己不會錯」。

這是我不能理解的。直到學到你的「心靈作業系統」理論,加上哲學家羅素的那一句,我才開始理解到,為何大部地球人,無論在過去、現在、將來,也「不可能有錯」。)

— Me@2014.06.26

A stupid man’s report of what a clever man says is never accurate, because he unconsciously translates what he hears into something that he can understand.

— A History of Western Philosophy

— Bertrand Russell

2014.06.27 Friday (c) All rights reserved by ACHK

康德

這段改編自 2010 年 4 月 10 日的對話。

根據李生的描述,哲學家康德講過,在「現象世界」中沒有自由,一切皆受物理定律的支配。但是,那樣的話,康德就不能建構其道德理論,因為人根本沒有「自由意志」。沒有「自由意志」,就沒有所謂的「道德責任」。

所以,為了可以建構道德理論,康德又說,雖然人在「現象世界」中沒有自由,但在「本體世界」中卻有自由。

李生批評,那是一個博懵(鑽空子)的講法,因為,在邏輯上,我們只能透過「現象」,去觀察「本體」。「本體」有自由,「現象」就會有自由;「現象」沒有自由,「本體」就沒有自由。

假設有人說:「雖然我壞事做盡,但我本性善良。」

我就會回應:「既然你本性善良,為何會壞事做盡?」

但是,如果用我以下的詮釋,康德的講法,就可能有意義。你的身體是一件物件,所以會受物理定律的支配,不會自由;但是,你的思想並不是物件,所以可能有自由。簡言之,動作不自由,意志有自由。

例如,根據物理定律,你的手指遇到火燒時,會立刻彈開,防止自己受傷。這是你不能控制的。但是,當你經歷這個動作時,心裡感受是什麼,或者腦中思想是怎樣,卻有一定的自由度,只要你那些不同的思想感受,不會干擾到,物理世界的運行就可以。

但是,我後來發覺,我這個詮釋並不成立,因為,不同的感受,對應著身體的不同物理狀態。所以,間接地,心理感受也會受,物理定律的影響支配。

比喻說,假設你用墨水筆寫一篇文章。不同的文章,對應著墨水在紙上的不同排列分佈。你並沒有可能,在不影響到墨水分佈的情況下,修改到該篇文章的內容。

同理,修改一部電腦儲存的資料時,其實即是在改變其硬件的狀態。在這個意思之下,同一部電腦的「軟件」和「硬件」,並不是該電腦的兩個部分,而是同一樣東西的兩個方面。你並不能拆開那部電腦,把它分成兩部分,然後介紹:「這部分是電腦的『軟件』;而那部分則是電腦的『硬件』。」

— Me@2014.03.25

— Me@2014.03.31

2014.04.01 Tuesday (c) All rights reserved by ACHK

Universe 7

The universe as a whole is an un-observable for two reasons, one physical and one logical.

The physical reason is that the speed of light, while being the maximum possible signal transmission speed, is finite. However, the expansion of the universe, in a sense, is faster than the speed of light. So the light rays emitted by some objects can never reach your eyes, no matter how long you wait. You cannot observe everything at once at any particular moment of time.

The logical reason is that, for any observer, at least one thing in this universe it cannot observe: itself. You can never see yourself directly, just as a camera can never take a picture of itself directly.

— Me@2012-10-18 12:47:32 PM

— Me@2014-02-25 01:57:06 PM

2014.02.26 Wednesday (c) All rights reserved by ACHK

Universe | I

Onion self 9 | 洋蔥自我 9 | Inner and outer, 7

Universe is not something you can observe directly, but a logical implication.

Whatever you can observe, it is only part of the universe, not the universe itself. 

“I” is also a logical implication or logical limit.

Whatever you can observe, belongs to your “I”, but is not your “I”.

For example, you can see your right hand.

It is part of you.

It is yours, but it is not you.

— Me@2012.10.18

— Me@2014.02.09

2014.02.10 Monday (c) All rights reserved by ACHK

千年往事

這段改編自 2010 年 4 月 10 日的對話。

(安:我們現在以為的知識,一千年後看回來,會發覺很多也是不正確,或者是不全面的。)

那亦都很正常。但是,原則性的東西,而又不牽涉具體細節,如果我們現在的理解正確,就沒有時間性。原則不會隨時間改變,永世正確。

例如我們上次討論,二千多年前所寫的《心經》,之中提及的「色即是空,空即是色」,其實就是想講出「本體」和「現象」的關係。試想想,「本體現象」這組概念和對應的理論,是哲學家康德於一百多年發揚光大的。而二千多年前的《心經》,竟然可以連接到,那就是所謂的「英雄所見略同」。

「色」,就即是「現象」;而「空」,就即是「本體」。

— Me@2013.12.03

2013.12.03 Tuesday (c) All rights reserved by ACHK