Category Archives: quantum probability

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

Bayesian probability

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Bayesian probability is one of the most popular interpretations of the concept of probability. The Bayesian interpretation of probability can be seen as an extension of logic that enables reasoning with uncertain statements. To evaluate the probability of a hypothesis, the Bayesian probabilist specifies some prior probability, which is then updated in the light of new relevant data. The Bayesian interpretation provides a standard set of procedures and formulae to perform this calculation. Bayesian probability interprets the concept of probability as “a measure of a state of knowledge”, in contrast to interpreting it as a frequency or a physical property of a system.

— Wikipedia on Bayesian probability

2010.09.02 Thursday ACHK

Probability theory

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In fact, the spectrum of interpretations in quantum mechanics has a close analogue in probability theory.

Note that anyone who acted that way would be silly, and that their error would have little to do with QUANTUM MECHANICS, but mainly with PROBABILITY THEORY. Probability theory is the special case of quantum mechanics in which ones algebra of observables is commutative. (This becomes a theorem in the context of C*-algebra theory.) Quantum mechanics has special features due to the noncommutativity, but probability theory already exhibits certain subtleties of interpretation, which I believe are a large part of what’s at stake here.

— John C. Baez

2009.12.02 Wednesday ACHK