Category Archives: neither AND nor OR

A Non-classical Feature

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What makes the interference pattern of electrons in the double-slit experiment a non-classical feature?

The probability pattern of every electron being a particle and that of being a wave are different.

For the particle pattern, the left-slit part and the right-slit part of the probability wave do not overlap. The quantum superposition does not cause a (interference) pattern.

This is why the interference pattern is a non-classical feature of the electron double-slit experiment.

— Me@2016-10-06 09:53:07 AM

2016.10.07 Friday (c) All rights reserved by ACHK

Truth values in Quantum Mechanics

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It’s pretty much the same mistake that all the “realists” are doing all the time. They are imagining that they can assign truth values to all questions that could be in principle answered by experiments. (In some way, they give answers “No” or “zero” to all the other questions that were actually not addressed by the measurement.) But quantum mechanics prohibits that. If one assigns classical truth values (or real values) to some operators, one can no longer assign truth values (or real values) to “complementary” (not mutually commuting) operators and questions they represent. Instead of the correct statement that “the value of \(N_a\) isn’t determined if one measures \(L\) instead”, they say that it is zero which is just wrong.

— No particle upon a quantum field means no information

— Lubos Motl

2015.06.03 Wednesday ACHK

Eigenstates 2.3

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So, after all, what is the meaning of “a quantum eigenstate”?

One way to resolve the circular definition is to define

a definite state

as

a state whose measurement result can be predicted with 100% certainty provided that the initial condition is given with 100% accuracy

Another way to resolve the circular definition is to realize that

1. a classical state, as a macroscopic definite state, is experimental or observational;  

2. a quantum eigenstate, as a microscopic definite state, is conceptual.

A classical state is what we, as macroscopic observers, can see directly.

A quantum eigenstate is what we cannot see. Moreover, it is not absolute. For the same system, there are more than one choice of state vector bases, in the sense that different sets of measurements can get different sets of eigenstates.

The concept of “quantum eigenstates” exists because we insist to express quantum states in terms of daily-life (classical (macroscopic) physics) language.

— Me@2013.06.22

2013.06.22 Saturday (c) All rights reserved by ACHK

Schrodinger’s cat

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You should not apply a single-particle wavefunction to Schrodinger’s cat. Instead, you should either use classical physics or use a wavefunction for all the particles of the cat.

— Me@2013-01-23 10:25:00 AM

The uncertainty in Schrodinger’s cat’s life or death problem is classical uncertainty, not quantum uncertainty. For an observer outside the box, the cat is in a mixed state, not just a superposition of quantum eigenstates. The probability in a mixed state is classical, not quantum.

— Me@2013-01-27 09:59:13 AM

2013.01.27 Sunday (c) All rights reserved by ACHK

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

Wheeler’s delayed choice experiment

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Quantum decoherence 5.3
 
 
In the delayed choice experiment, the wave function of the system (the photons and the environment) is also in a superposition of eigenstates, not just the wave functions of the individual photons are.

All the past is there, but our present measurement “chooses” which part to see. 

— Me@2011.10.21
 
 
The chosen part must be a consistent story, according the quantum mechanics.

The chosen part is what we called “an observer”.

— Me@2018-01-22 09:35:02 PM
 
 
 
2011.11.20 Sunday (c) All rights reserved by ACHK

Make a difference, 2

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Verification principle

Verificationism is the view that a statement or question is only legitimate if there is some way to determine whether the statement is true or false, or what the answer to the question is.

Verification principle: That meaningful statements should be analytic, verifiable or falsifiable.

— Wikipedia on Verificationism

檢證原則

一句句子要有意思，你要講得出，至少在原則上，它在什麼情況下為之真、在什麼情況下為之假。換句話說，你要講得出，至少在原則上，如何證明或者否證它。否則，那句句子就沒有意義。

檢證原則 –> 印證原則

但是，有時即使一些句子明明是有意義的，在原則上，也沒有可能百分百證明，它們是正確的。

例如，科學理論句子的特性是，只要有一個妥當執行的實驗，和它的預測不相符，就足以否證它。相反，無論有多少次實驗的結果，和該個科學理論的預測吻合，你也不能保證，下一次的實驗結果，仍然會是那樣。換句話說，無論你做多少次實驗，也不能百分百證明，那句科學理論句子是正確的。

所以，我們放寬了「檢證原則」的要求，把它改編為「印證原則」。一句句子即使不能通過「檢證原則」，如何能夠通過「印證原則」的話，我們仍然可以視之為有意義。

印證原則

一句句子即使不能通過「檢證原則」，如果你可以講得出，至少在原則上，如何提高它的可信度，我們仍然可以視之為有意義。

— Me@2011.09.15

2011.09.15 Thursday (c) All rights reserved by ACHK