Dynamical pictures

Comparison of pictures

The Heisenberg picture is closest to classical Hamiltonian mechanics (for example, the commutators appearing in the above equations directly correspond to classical Poisson brackets). The Schrödinger picture, the preferred formulation in introductory texts, is easy to visualize in terms of Hilbert space rotations of state vectors, although it lacks natural generalization to Lorentz invariant systems. The Dirac picture is most useful in nonstationary and covariant perturbation theory, so it is suited to quantum field theory and many-body physics.

Summary comparison of evolutions

— Wikipedia on Dynamical pictures

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2022.04.05 Tuesday ACHK

EPR paradox, 11.1

Black hole information paradox, 2.2.1

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superposition

~ lack of the existence of measuring device in the definition of the experimental setup to define the difference between microscopic events in terms of the difference between observable physical events

— Me@2022-01-31 08:33:01 AM

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Note that superposition is mathematical, not physical. A wave function is not probabilities, nor a physical wave. Superposition applies only to wave functions, not to probabilities, nor to physical realities.

If superposition had been of probabilities or of physical realities, there would have been no interference patterns in the double-slit experiment.

— Me@2022-02-11 03:32:47 PM

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For example, in the double-slit experiment, if no detector is installed, the system is in a quantum superposition state.

It is not that each individual photon is in a superposition, because an individual particle has no 100% objective identity, due to the indistinguishability of identical particles. Instead, it is that the system of the whole experimental setup is in a superposition.

This applies also to other more complicated experimental setups, such the EPR experiment, the delayed-choice experiment, the delayed-choice quantum eraser, etc.

— Me@2021-01-23 12:57 AM

— Me@2022-02-11 03:29 PM

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physical definition

~ define the microscopic events in terms of observable physical phenomena such as the change of readings of the measuring device

~ define unobservable events in terms of observable events

— Me@2022-01-31 08:33:01 AM

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a definite state

~ an eigenstate

~ a state that has given a physical definition

— Me@2022-02-11 01:19:57 PM

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What we do in the present does not change the past, but changes we can see/say about the past. — Wheeler on Delayed choice quantum eraser, paraphrased, Me@2018-02-04 03:40:27 PM

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

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

It is because, tautologically, any state that cannot be physically defined is logically and physically meaningless.

In other words, any state that has no distinguishing observable effects does not make sense. For example, if in a double-slit experiment, no detector is allowed, then it is no point to label the state either as “go-left” or as “go-right”. Instead, we have to label the state as a superposition state.

Some unobservable (aka microscopic) variables are meaningless. It is not because of any philosophical points of view, but because we have not defined those variables in terms of observables or observable events, aka physical phenomena. In other words, those variables have no physical definitions yet.

— Me@2022-02-11 03:50:59 PM

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Quantum mechanics, and physics in general, gives the rules of storytelling about reality. A story is a post hoc description of a physical event. In other words, quantum mechanics, and physics in general, is about phenomena, not noumena.

phenomenon (plural phenomena)

~ thing appearing to view

~ reality with respect to an observer

noumenon (plural noumena)

~ thing-in-itself

~ reality independent of any observers

— Me@2022-02-11 3:00 PM

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2022.02.11 Friday (c) All rights reserved by ACHK

Spinoza 3.2

對牛彈琴 2.2 | 數學教育 6.2 | 大世界 7.2

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Intellect is invisible to those have none.

— Arthur Schopenhauer

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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.

— p.83

— Chapter XI. Socrates

— A History of Western Philosophy (1945)

— Bertrand Russell

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(安:根據羅素的講法,有很多人學習深奧學問時,所謂的「明白」,未必是真正的明白,因為他們會不自覺地,把那些新知識,翻譯成自己明白的版本;即是夾硬用,舊知識的語言,以理解新知識。Paul Graham 說在小時候,曾經用這個方法,去學習數學;即是將數學概念,翻譯成日常生活的概念。)

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他真的有講過嗎?

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(安:我記得是。當然,我可以記錯。但是,有沒有講過,或者誰講過,並不是重點。重要的是,那些講法,有沒有道理。

後來他發現,學數學其實不應,用這個方法。其實,學其他專業,也應先破除,翻譯和簡化等習慣。

有些新概念是,純粹用一堆舊概念組裝而成,就可以用這個方法。但是,如果一個新概念中,有一些全新,即前無古人的元素時,翻譯必然有誤,理解一定有錯。堅持用舊世界的語言,去理解新天地,只會阻礙你,心靈的進化。

Everything which exists, exists either in itself or in something else.

That which cannot be conceived through anything else must be conceived through itself.

— Baruch Spinoza

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另外,他提的另一個,有關學習數學的要點是,即使假設你在大學中,學到的數學,在日常生活中沒有用,單單是為獲取,那些嶄新的元素概念本身,就已經能夠令你有超能力;令你有一些,常人沒有的思考工具、比喻語言。)

— Me@2022-02-03 12:09:36 PM

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2022.02.04 Friday (c) All rights reserved by ACHK

A Whole New World

嶄新的世界 5 | Extraordinary, 3

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Do not ask your children to strive for extraordinary lives. Such striving may seem admirable, but it is the way of foolishness. Help them instead to find the wonder and the marvel of an ordinary life. Show them the joy of tasting tomatoes, apples and pears. Show them how to cry when pets and people die. Show them the infinite pleasure in the touch of a hand. And make the ordinary come alive for them. The extraordinary will take care of itself.

— William Martin

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I can show you the world
Shining, shimmering, splendid
Tell me, princess, now when did
You last let your heart decide?

I can open your eyes
Take you wonder by wonder
Over, sideways and under
On a magic carpet ride

A whole new world
A new fantastic point of view
No one to tell us, “No”
Or where to go
Or say we’re only dreaming

— Aladdin’s A Whole New World

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2022.01.24 Monday ACHK

超時空接觸 3

相聚零刻 1.1.2 | 大世界 10

這段改編自 2021 年 12 月 4 日的對話。

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自己的世界,以自己為中心,並不是「自我中心」;

要求別人的世界,也以你自己為中心,才是「自我中心」。

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地球人竟然會,因為所謂的「失戀」,而不太開心。部分原因是,他自我中心;覺得世界必定要跟他,心目中的劇本來運行。例如:「她是我期待已久的夢中情人,所以,她必定是我,命中注定的未來太太。」

萬一,其實是通常,受到「夢中情人」拒絶的話,他就會覺得,失去了「命中注定的未來太太」,人生就再沒大意義了。

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合理的想法是:「她是我期待已的夢中情人,所以,她有可能是我,命中注定的未來太太。如果不是的話,我仍然會欣賞她,但是,我的注意力,就不再在她身上,而會轉移到(尋找)我的未來太太。我只愛我未來太太一人。」

如果你再,明戀暗戀(肯定不是你未來太太的)其他人的話,那就,是為不忠。

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覺得的夢中情人,不一定是你的未來太太——真正的夢中情人。誰是你「真正的夢中情人」,不會未卜先知。誰是你的「未來太太」,只會未來先知。所以,所謂的「命中注定」,只能事後講,馬後砲。

— Me@2022-01-23 11:34:20 PM

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Your world is your world.

— Ludwig Wittgenstein

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你的主觀世界,並不是客觀世界的全部。

— Me@2009.09.16

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2022.01.24 Monday (c) All rights reserved by ACHK

Logical arrow of time, 6.4.2

Logical arrow of time, 6.1.2

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The source of the macroscopic time asymmetry, aka the second law of thermodynamics, is the difference between prediction and retrodiction.

In a prediction, the deduction direction is the same as the physical/observer time direction.

In a retrodiction, the deduction direction is opposite to the physical/observer time direction.

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— guess —

If a retrodiction is done by a time-opposite observer, he will see the entropy increasing. For him, he is really making a prediction.

— guess —

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— Me@2013-10-25 3:33 AM

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A difference between deduction and observation is that in observation, the probability is updated in real time.

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each update time interval ~ infinitesimal

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In other words, when you observe a system, you get new information about that system in real time.

Since you gain new knowledge of the system in real time, the probability assigned to that system is also updated in real time.

— Me@2020-10-13 11:27:59 AM

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2020.12.04 Friday (c) All rights reserved by ACHK

大腦物理性損毀不是比喻

99.85%的人不會,終身被匪欺騙教育,大腦已經物理性損毀了,假如說匪的謊言灌輸有20層,那麼絕大多數人遭鐵拳之後的反思,最多只能突破一兩層,達到“我愛國所以要說話”的程度,離理解台人港人藏人維人還非常遠,至少還需要十幾個層次的突破。所以覺醒者極少極少,而且沒有力量。很悲哀,但事實如此。

所以匪的滅亡,恐怕不會是由於覺醒後的民眾起來反抗,而是傳統的王朝滅亡現象,天災加人禍造成經濟崩潰,引發統治崩潰,帶來的不是社會進步,而是社會危機。

大腦物理性損毀不是比喻,而是 literally 如此,人腦的神經細胞本身不構成思想,神經細胞之間的連接方式才是,從嬰兒出生到不斷學習成長,就是逐步構建神經細胞連接到過程,連接完成之後,是不可逆的,所以經匪教育的人,99.85%都是終身殘疾,剩下那點點漏網之魚,只是教育失敗而已。

肉體也是一樣,從受精卵、胚胎開始,細胞都是幹細胞,然後分化成各種完全不同的組織細胞,成長為肉體,這個分化、成長、發育的過程是非常可塑的,外界條件可以對肉體發育造成很大影響,但是一旦發育完成,還有可能退回去變成幹細胞,再重新發育一次,變成一個不一樣的肉體嗎?沒有可能的。

所以您國成年人99.85%都是無救的,不要對他們抱任何希望,期待發生什麼什麼事件能夠改變他們的思維,從這個意義上看,他們都是已經死亡的人。唯一的希望恐怕在還沒有受匪教育或受教育不多的小孩子,以及還沒有出生的下一代,只有趕緊跑路,把他們帶離地獄,才有一點點挽救的希望。

所以逃離匪區最大的收穫是什麼,不是自己能賺錢,能自由,而是孩子可以不用再經歷我們曾經經歷的那些毫無意義的痛苦、摧殘、扭曲,孩子可以有機會做個正常人。我們自己每個人都已經多多少少被毀滅了一部分,但是能救孩子,下一代還有新的希望,還有什麼比這更重要的呢。

— 李穎

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People do not change. They die, replaced by other people.

Most people do not change. They die, replaced by a new generation of people.

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You cannot change the people around you, but you can change the people you choose to be around.

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2020.02.15 Saturday ACHK

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

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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

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2019.02.11 Monday (c) All rights reserved by ACHK

Logical arrow of time, 6.4

The source of the macroscopic time asymmetry, aka the second law of thermodynamics, is the difference of prediction and retrodiction.

In a prediction, the deduction direction is the same as the physical/observer time direction.

In a retrodiction, the deduction direction is opposite to the physical/observer time direction.

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— guess —

If a retrodiction is done by a time-opposite observer, he will see the entropy increasing. For him, he is really doing a prediction.

— guess —

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— Me@2013-10-25 3:33 AM

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The existence of the so-called “the paradox of the arrow of time” is fundamentally due to the fact that some people insist that physics is about an observer-independent objective truth of reality.

However, it is not the case. Physics is not about “objective” reality.  Instead, physics is always about what an observer would observe.

— Lubos Motl

— paraphrased

— Me@2019-01-19 10:25:15 PM

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2019.01.19 Saturday (c) All rights reserved by ACHK

宇宙大戰 1.2

PhD, 2.4 | 故事連線 1.1.6 | 碩士 3.4

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(問:我也遇過類似的情境。

我和一位好朋友合作做小組習作時,雖然未至於反目,但總會有很多爭拗。和他合作前,明明和他感情要好。各自有什麼困難時,對方總會杖義相助。

為什麼人類會,那麼奇怪呢?)

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簡單地說,即使是同一個人,其實也有不同方面,各樣性格。

做朋友時,你只需要接受小部分—你可以選擇,只接受他,最好的優點。但是,做工作伙伴時,你卻要接收大部分—你未必可以選擇,不接受他,最壞的缺點。

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(問:那樣,如果要「複雜地說」呢?)

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複雜地說,每個個體也透過自己,在這宇宙間的經歷,形成一個「主觀宇宙」,簡稱「世界觀」。

大部分人,也不自覺地,以為他的主觀宇宙,就是客觀宇宙的全部。這個不幸,源於每個人的主觀宇宙,是他唯一能夠觀察到的「客觀宇宙部分」;每個人當時的主觀宇宙,是他當時唯一能夠,觀察到的「客觀宇宙部分」。

只有一些「被選擇的心靈」,簡稱「半神人」,才會想像到,他的主觀世界,只是客觀世界的極小部分。所以,如果兩個人也不是「半神人」,而又要在工作上合作的話,其實就相當於,把兩個(主觀)宇宙的大部分,重疊在一起。

每個宇宙原本,都有各自的運行法則;貿然要求兩個宇宙,互相干涉對方內政,自然會十分危險。

六千五百萬年前,單單是一個小行星與地球相撞,就足以令大部分恐龍滅絕。試想想,兩個宇宙相撞,殺傷力會大多少倍。

— Me@2019-01-01 11:20:57 PM

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2019.01.01 Tuesday (c) All rights reserved by ACHK

宇宙大戰 1.1

PhD, 2.3 | 故事連線 1.1.5 | 碩士 3.3

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(問:你好似講到,人類那麼危險?)

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因為事實上,人類的確是,那麼危險。

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剛才所講,有關選擇碩士或博士論文導師,所需的技巧,背後的精神,其實是通用的—同時適用於你將來選擇公司、上司、生意合作伙伴、配偶,等等。

選擇錯誤,同樣是有改變一生的後果。

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(問:人類真的那麼危險嗎?)

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你一日未試過,同一個人有工作關係,或者錢銀來往,你也不會知道,他的真面目。

時常會聽到一類故事:

甲和乙是幾十年的要好朋友。他們決定合作創業。不料,一同工作不出幾個月,就反目收場。

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(問:我也遇過類似的情境。

我和一位好朋友合作做小組習作時,雖然未至於反目,但總會有很多爭拗。和他合作前,明明和他感情要好。各自有什麼困難時,對方總會杖義相助。

為什麼人類會,那麼奇怪呢?)

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簡單地說,即使是同一個人,其實也有不同方面,各樣性格。

做朋友時,你只需要接受小部分—你可以選擇,只接受他,最好的優點。但是,做工作伙伴時,你卻要接收大部分—你未必可以選擇,不接受他,最壞的缺點。

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(問:那樣,如果要「複雜地說」呢?)

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— Me@2018-12-20 11:06:49 PM

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2018.12.20 Thursday (c) All rights reserved by ACHK

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.

,,,

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