Monthly Archives: February 2022

The superposition language

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classical language

~ all particles are distinguishable

~ every particle has an objective identity

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quantum language

~ some particles are identical

~ some particles are indistinguishable

~ Not every particle has an objective identity

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[guess]

When you insist on using all-particles-are-distinguishable language on the maybe-indistinguishable particles, you get the superposition language.

[guess]

— Me@2022-02-05 09:26:26 PM

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2022.02.10 Thursday (c) All rights reserved by ACHK

Photon dynamics in the double-slit experiment, 6.2

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A wave function is used for calculating probability, but itself is not a probability.

However, like probability, a wave function is not a physical wave, which is located in physical space-time.

Like probability, a wave function is a mathematical tool that exists only in the conceptual space.

So, like probability, a wave function cannot be measured by any device.

— Me@2022-02-02 6:48 AM

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2022.02.09 Wednesday (c) All rights reserved by ACHK

心懷混亂 7

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Even in the noisiest system, errors can be reliably corrected and accurate information transmitted, provided that the transmission is sufficiently redundant. That is, in a nutshell, how Wikipedia works. … Science is the sum total of a great multitude of mysteries. It is an unending argument between a great multitude of voices. It resembles Wikipedia much more than it resembles the Encyclopaedia Britannica.

— Freeman Dyson

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2022.02.09 Wednesday ACHK

冰心鎖

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超時空接觸 3.2

這段改編自 2021 年 12 月 5 日的對話。

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即係我自己有個經驗就係呢

我同我男朋友呢

係識咗成年之後

先喺埋一齊 o既

因為有時候

…

當初我自己諗

我想要男朋友 ABCDE

咁樣樣係度諗啦

咁但真係好搞笑囉

望住我而家呢個男朋友

係冇一樣可以達成架喎

咁但係發現一齊咗 o既時候呢

原來佢個性格，係可以同我好夾 o既

— Knetawonggg

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尋尋覓覓，並不是刻意要選，所謂「條件最好」的那一位女士。

比喻說，你家裡有一個夾萬（保險箱）。你現在想打開它。但是，你不記得鑰匙放在哪兒。所以，你需要花一點時間去尋找。

你這「尋找鑰匙的故事」的主旨，並不是要覓得，一把完美的鑰匙；亦不是要覓得，世間上最好的那一把鑰匙；而是要奪回，你夾萬的鑰匙。

又例如，將來你有孩子後，你會在放學時段，到學校門口等待他。

你所守候的並不是，學校裡「最好的」那一名孩子；你要迎接的是，你的孩子；

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尋尋覓覓，並不是要找到，「最好的」女朋友，而是要找到，你的太太。

認為愛情是要找到「條件最好的那一位」的人，不會從一而終，因為永遠可能有，亦必定有，條件更好的另一位。

— Me@2022-02-08 11:50:35 PM

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2022.02.09 Wednesday (c) All rights reserved by ACHK

Ex 1.22 Driven pendulum, 2.2

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Structure and Interpretation of Classical Mechanics

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Derive the equations of motion using the Newtonian constraint force prescription, and show that they are the same as the Lagrange equations.

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[guess]


(let* ((U (U-gravity 'g 'm))
       (x_s (literal-function 'x_s))
       (y_s (literal-function 'y_s))
       (L (L-driven-free 'm 'l x_s y_s U))
       (q-rect (up (literal-function 'x)
                   (literal-function 'y)
                   (literal-function 'F))))
  (show-expression
   (((Lagrange-equations L) q-rect) 't)))

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\displaystyle{ \begin{aligned} mD^2x(t) + \frac{F(t)}{l} \left[x(t) - x_s(t)\right] &= 0 \\ mg + m D^2y(t) + \frac{F(t)}{l} [y(t) - y_s(t)] &= 0 \\ -l^2 + [y(t)-y_s(t)]^2 + [x(t)-x_s(t)]^2 &= 0 \\ \end{aligned}}

[guess]

— Me@2022-02-08 10:04:45 AM

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2022.02.08 Tuesday (c) All rights reserved by ACHK

Sharp, 2

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The beauty of doing nothing is that you can do it perfectly. Only when you do something is it almost impossible to do it without mistakes.

Therefore people who are contributing nothing to society, except their constant criticisms, can feel both intellectually and morally superior.

— Thomas Sowell

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2022.02.07 Monday ACHK

友情演義

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無拍之拖, 1.3 | 原來是你, 2.4 | 相聚零刻 2.6 | 尋覓 2.2.3.6.6

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魔術雖是大話，但卻是極少數，合乎道德的大話，因為，魔術師在表演前，已知會觀眾，魔術是假的。

魔術作為假話幻覺，不在欺騙誤導，只為娛樂無窮。

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愛情，就是在友情上，對方知道和同意情況下，加上浪漫情節。

浪漫者，虛構情節也。

友情加上，來自雙方的魔法，就是愛情。

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例如，扮邂逅，由攝影師記錄，以作紀念。

故事，就是誇大現實，剪接歷史。

「愛情故事」是故事，不是事實全部真相。

愛情故事，是在雙方明許或默許下，浪漫化歷史。

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古語有云，相愛容易相處難。

相愛剪接包裝，斷章取義；相處鉅細無遺，全部細節。

魔鬼在細節中，天使也是。

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相愛有如《三國演義》，重故事，作娛樂。

相處有如《三國志》，重史實，作紀錄。

《三國演義》的英文是 Romance of the Three Kingdoms，即《浪漫三國》。

浪漫者，虛構情節也。

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浪漫情節，必有綵排、預演。

例如，扮求婚，由攝影師記錄，以作紀念。

浪漫者，魔法也；

魔法者，馬後砲也。

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「求婚」必為事先同意，或「雖則未必知悉，但必早已預期」，才合乎禮儀。

精確而言，無表之白，不求之婚，才是真正愛情。

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在對方「既不知，亦不期」的情況下求婚，十分失體，十二分愚蠢。

求婚不應是公開在眾目之下，因為，那是情感勒索。對方會受到，從來不應存在的群眾壓力；她會十分尷尬，不能隨心所欲地，接受或拒絶。

不唐突，無勉強，相戀才可長久；

理天命所歸，情人心所向，相愛方能永久。

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「愛情誠可貴，自由價更高」的原因，全在邏輯方面：

只有出於雙方，自由意志下的愛情，才能穿梭時空。

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— Me@2022-01-28 01:43:04 PM

— Me@2022-02-07 10:29:03 AM

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2022.02.07 Monday (c) All rights reserved by ACHK

Photon dynamics in the double-slit experiment, 6

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Why don’t we see superposition states for macroscopic objects?

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A superposition state is not any “overlapping” of multiple physical states.

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A superposition state is a wave function, which is not a physical wave located in physical space.

Instead, it is a mathematical tool to calculate probability distributions.

— Me@2022-02-01

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EM waves are not photon wave functions because EM waves are physical, while wave functions are mathematical.

— Me@2022-02-01

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In addition, the electromagnetic fields are observable (e.g. with an oscilloscope) while Schroedinger wave functions are not observable, even in principle. Clearly, then, the fields are not wavefunctions, are physical, observable fields, rather than merely what you take the modulus-square of to obtain the probability of finding a photon somewhere. The existence of some “wavefunction of the photon” is not a fully settled issue.

— Wikipedia on Photon dynamics in the double-slit experiment

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2022.02.06 Sunday (c) All rights reserved by ACHK

Square root of probability, 3.2.3

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Eigenstates 3.3.2.3

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2.2

Decoherence is not a physical process.

Instead, it is a logical process of replacing one physical system (an experimental setup design) with another.

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Sometimes, it seems to be a physical process when we perform physical operations based on its logic. For example, when we want to execute our plan of replacing a physical system with another one which is identical but with detectors activated.

We do not really need to create another physical system to achieve that. We just have to switch on the not-yet-activated detectors already installed in the original experimental setup. The effect is identical to replacing the original.

— Me@2022-02-04 08:27:23 PM

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But for simplicity, we use the common quantum mechanics language for the time being:

The system has already decohered long before the radioactive trigger’s effect has reached the cat. Since radioactive atom touched the environment, the quantum state of the system has decohered.

Better language:

The behaviour of any macroscopic (aka observable) objects, before cat in the operation chain, has already provided the physical definitions of whether the atom has decayed and not.

— Me@2022-02-04 11:23:49 PM

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Before opening the box, the cat is not in a superposition state. Instead, it is in a mixed state.

The uncertainty is classical probability, which is due to lack of detailed knowledge, not quantum probability, which is due to lack of definition (in terms of physical phenomena difference).

— Me@2022-01-29 10:38:19 PM

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Most people will accept quantum mechanics once they realize that it follows the classical logic.

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Wrong:

1.  go-left   

2.  not-go-left   

3.  both go-left and not-go-left

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Correct but misleading:

1.  go-left   

2.  not-go-left   

3.  “go-left” and “not-go-left” are meaningless

because they are

not defined by physical observable events;

in other words, not defined in terms of physical phenomena yet

That is still misleading because it acts as if we have to use 3-valued logic.

But actually, 3-valued logic is not needed at all. 3-valued logic will appear only if we insist on using the one-layer presentation to represent the actually two-layered logic structure. It is actually binary logic all along:

1.  “go-left” and “not-go-left” are defined

“Going-left” and “not-going-left” are physically distinguishable, because detectors are allowed in the experimental setup.

1.1  go left

1.2  not go left

2.  “go left” and “not go left” are undefined

“Going-left” and “not-going-left” are physically indistinguishable, because detectors of any kind are not allowed in the experimental setup definition; so “going-left” and “non-going-left” are logically meaningless.

On any layer, there are only 2 cases:

For any proposition A, either A is true or \text{NOT}~A is true, but not both.

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Most people will accept quantum mechanics once they realize that, in a sense, it actually creates the classical logic by making the world consistent.

— Me@2022-01-12 12:40:12 PM

— Me@2022-01-29 04:03:53 PM

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2022.02.05 Saturday (c) All rights reserved by ACHK

Final Fantasy X

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深淵 4

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Shortly before arriving, Tidus learns that he, Jecht, and the Zanarkand they hail from are summoned entities akin to aeons based on the original Zanarkand and its people. Long ago, the original Zanarkand battled Bevelle in a machina war, in which the former was defeated. Zanarkand’s survivors became “fayth” so that they could use their memories of Zanarkand to create a new city in their image, removed from the reality of Spira. Once they reach Zanarkand, Yunalesca—the first summoner to defeat Sin and unsent ever since—tells the group that the Final Aeon is created from the fayth of one close to the summoner. After defeating Sin, the Final Aeon kills the summoner and transforms into a new Sin, which has caused its cycle of rebirth to continue. The group decides against using the Final Aeon, due to the futile sacrifices it carries and the fact that Sin would still be reborn. Yunalesca tries to kill Tidus’ group, but she is defeated and vanishes, ending hope of ever attaining the Final Aeon.

— Wikipedia on Final Fantasy X

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2022.02.04 Friday ACHK

Spinoza 3.2

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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

Square root of probability, 3.2.2

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Eigenstates 3.3.2.2

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Actually, quantum mechanics does NOT allow any violation of these logical laws. A quantum superposition state is NOT any “overlapping” of multiple physical states. A quantum superposition state is ONE single physical state.

Contrary to popular belief, Schrödinger created the thought experiment to illustrate that a quantum superposition state should NOT be regarded as any “overlapping” of multiple physical states.

To explain that, we should use the most basic quantum experiment, the double-slit experiment, instead of the cat experiment, because:

1.

…

And more fundamentally:

2.1

The cat-alive state is a well-defined state. The cat-dead state also.

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A quantum state must be a superposition state when in (the definition of) the experiment setup, some definitions of trajectories are missing.

The “definitions” here must be in terms of physical phenomena, because “trajectories” have no objective existence, due to the fact that fundamentally particles have no objective identities; fundamentally, identical particles are indistinguishable.

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“Which trajectory has a particle travelled along” is a hindsight story.

“The electron at location x_1 at time t_1 and the electron at location x_2 at a later time t_2 are actually the same particle” is also a hindsight story.

These kinds of post hoc stories do not exist when some definitions of trajectories are missing in the overall definition of the experiment setup. In such a case, we can only use a superposition state to describe the state of the physical system.

Since such a situation has never happened in a classical (or macroscopic) system, it gives a probability distribution that has never existed before. Such a new kind of probability distribution can only be deduced by the mathematical representation of a superposition state. In other words, such a new kind of probability distribution is encoded in and only in the mathematical language of superposition state.

For example, in the double-slit experiment, if the experiment setup definition disallows any kinds of detectors (that can distinguish particle-go-left and particle-go-right), then tautologically, “go-left” and “go-right” are logically indistinguishable; “go-left” itself and “go-right” itself are both physically meaningless. So the system is actually in ONE single state, namely the superposition state.

Since “go-left” and “go-right” both have no physical meanings, “it is in a superposition state of going-left state and going-right state” means neither “the particle goes left and goes right” nor “the particle goes left or goes right“. Instead, it means that

2.11   going-left and going-right are logically indistinguishable so the system is actually logically ONE single physical state;

2.121   the probability distribution is not that of going-left nor that of going-right;

2.122   so this new kind of state requires a never-seen-before probability distribution,

2.123   which can be calculated from the mathematical expression of the superposition state, aka the wave function.

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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

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Quantum indeterminacy is not due to physical limitations. Quantum indeterminacy is a definitional indeterminacy–some necessary definitions are not precise enough or even missing altogether.

It occurs when you do not allow installing any measuring devices (for some variables) in the experiment. It occurs when you define an experiment in such a way that you cannot define, for example, the difference between trajectories based on the difference between possible physical phenomena.

However, since the difference between the cat-alive state and cat-dead state is well-defined, there is no indeterminacy-due-to-undefined-difference (aka quantum indeterminacy). So there is no so-called “quantum superposition of cat-alive and cat-dead“. In other words, the cat itself is already a measuring device for the particle state.

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For simplicity, assuming that in the box, there were no measuring devices. So before putting the cat there, the atom was in a superposition of decayed and not-decayed-yet.

That does not mean that the atom is physically in two states at the same time. Instead, it actually means that there is logically no difference between decayed and not-yet-decayed, because there is no existence of a measuring device that can make the definitional physical difference.

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

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

However, while you are designing the experiment, once you allow the cat to be inside, you have actually provided a physical definition of “the atom has decayed” and “the atom has not decayed yet“. The cat is actually the measuring device whose existence provides that physical definition. That is the so-called “wave function collapse”.

The “wave function collapse” itself is not a physical process. It is actually a change of probability distribution due to the change of experimental design. The experiment with measurement device and that without measurement device are actually two distinct experiments with distinct probability distributions.

wave function collapse

~ probability distribution change (replacement) due to replacing “the experiment without measurement device” with “the experiment with measuring device“

2.2

…

— Me@2022-01-31 08:33:01 AM

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Although the final device in the chain of measurement needs to be macroscopic for a human being to read, the “measuring device” does not have to be macroscopic.

It even can be only one particle, as long as it can store the result of “going left” or “going right”.

In other words, if by adding an object in the experiment during the experiment design process, “go left” and “go right” acquire their physical definitions (physical meanings) by being distinguishable, then that object is a “measuring device”.

measuring device

~ logical case differentiator during the experiment design process

~ physical case differentiator during the experiment

— Me@2022-02-01 11:02:20 AM

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2022.02.01 Tuesday (c) All rights reserved by ACHK