Daily Archives: March 1, 2022

The 4 bugs, 1.12

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EPR paradox, 11.11

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3.2 (2.3)  In some cases, the wave function of a physical variable of the system is in a superposition state at the beginning of the experiment. And then when measuring the variable during the experiment, that wave function collapses. Wrong.

A wave function (for a particular variable) is an intrinsic property of a physical system.

“Physical system” means the experimental-setup design, which includes not just objects and devices, but also operations.

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The common misunderstanding comes from representing \displaystyle{| \psi \rangle } as a sum of \displaystyle{| \psi_L \rangle } and \displaystyle{| \psi_R \rangle}. But this is not a physical superposition, but a mathematical superposition only.

This mathematical superposition has 3 meanings (applications):

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3. 

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Only the longcut version can avoid such meaningless questions.

If you insist on answering those questions:

How to collapse a wave function?

Replace system \displaystyle{A} with system \displaystyle{B}.

It is not that the wave function \displaystyle{\psi} evolves into \displaystyle{\phi}. Instead, they are just two different wave functions for two different systems.

How long does it take? How long is the decoherence time?

The time needed for the system replacement.

How to uncollapse a wave function?

Replace system \displaystyle{B} with system \displaystyle{A}.

— Me@2022-02-27 12:41:31 AM

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The wave function “collapse” is actually a wave function replacement. It “happens” not during the experiment time, but during the meta-time, where the designer has replaced the experiment-setup design (that without activated device) with another one (that with activated device).

That’s how to resolve the paradoxes, such as EPR.

Anything you are going to measure is always classical, in the sense that it is the experiment designer that decides which variable is classical, by adding the measuring devices and measuring actions to the experiment design.

It is not that the wave collapses during the experiment when you turn on the detector to measure.

The detector and the planned action of activating it have already formed a “physical definition” that makes your experiment design to have a system being in a mixed state, instead of a superposition state, since the beginning of the experiment.

Put it more accurately, since a wave function is a mathematical function, not a physical field, it does not exist in physical spacetime.

In a sense, instead of existing at the time level of the experiment and the observer, a wave function exists at the meta-time level, the time level of the experiment-setup designer.

So it is meaningless to say “the experimental setup is in a superposition state (or not) in the beginning of the experiment”. Instead, we should say:

The detector and the planned action of activating it have already formed a “physical definition” that makes your experiment design to have a system being in a mixed state, instead of a superposition state, since the beginning of the experiment.

— Me@2022-02-14 10:35:27 AM

— Me@2022-02-21 07:17:28 PM

— Me@2022-02-22 07:01:40 PM

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2022.03.01 Tuesday (c) All rights reserved by ACHK

數學教育 7.2

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這段改編自 2010 年 4 月 24 日的對話。

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（安：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。）

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又例如，之前我把向量幾何中的「完備集合」概念，應用到學習知識上，引申成「知識完備集合」。

任何一門學問，雖然在起初時，看似有無盡的細節要駕馭，但是，努力收集零碎資料，到一個程度後，你會發現，細節雖然多，原理卻只有幾個，萬變不離其中。

那就有如，雖然在三度空間中，有無數點，而每一點也可以用，一支向量箭尖去代表；但是，要表達所有點的任何之一，你並毋須在事先，就收集無數支向量箭；因為，在三度空間中，你只要收集齊，三支互相獨立的原始元素向量 \displaystyle{\{ \mathbf i, \mathbf j, \mathbf k \}}，那些任何一點，就可以透過它們的線性組合去代表。

\displaystyle{\mathbf a = a_x \mathbf i + a_y \mathbf j + a_z \mathbf k = (a_x, a_y, a_z)}

Wikipedia image licensed under
the Creative Commons Attribution-Share Alike 2.5 Generic license

年青時閱讀，以為將會有，無數本書要閱讀，時間不會夠用。大約六年多後，發現沒大興趣再閱新書，因為，再不覺那些新書有新知，只覺那些新書抄舊書。原因很簡單，沒有新元素。

\displaystyle{\mathbf a = a_x \mathbf i + a_y \mathbf j + a_z \mathbf k = (a_x, a_y, a_z)}

你在三度空間中，如果要升格，進入四度空間，必須收集到一支，全新的原始基因向量；它必須是完全獨立於，原本的那三支。

\displaystyle{\mathbf a = a_x \mathbf i + a_y \mathbf j + a_z \mathbf k + a_t \mathbf l = (a_x, a_y, a_z, a_t)}

如果讀者未學過「向量」那一課數學的話，那就不易明白。

再幾年後，不再只是沒有興趣閱讀，更要建立防火牆，主動抗拒大部分，只歸平庸的書籍，因為，沒有新元素的資料，會搞亂我當時已大致建立好的，自己知識體系。那是人生必經階段。

自始以後，新知識的原材料，主要只會來自，專題研究 和 自身實證考驗。

— Me@2022-03-01 10:37:07 AM

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2022.03.01 Tuesday (c) All rights reserved by ACHK