Daily Archives: February 23, 2022

The 4 bugs, 1.7

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3.2

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In an accurate language, that design has already given the experiment-setup a property that “X is in a mixed state”, meaning that the probabilities assigned to different possible values of X are actually classical probabilities.

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In the most basic double-slit experiment, assume that the probability of the going to either slit is \displaystyle{\frac{1}{2}}.

In the standard quantum mechanics language:

When no detector installed or no detector is activated, the particle’s position variable is in a superposition state

\displaystyle{| \psi \rangle = \sqrt{0.5}~| \psi_L \rangle + \sqrt{0.5}~| \psi_R \rangle},

where \displaystyle{|\psi_L \rangle} and \displaystyle{| \psi_R \rangle} are eigenstates of going-left and that of going-right respectively. The particle is not in any of the following states:

1.  \displaystyle{| \psi_L \rangle}

2.  \displaystyle{| \psi_R \rangle}

3.  \displaystyle{| \psi_L \rangle} or \displaystyle{| \psi_R \rangle}

4.  \displaystyle{| \psi_L \rangle} and \displaystyle{| \psi_R \rangle}

Instead, mathematically, the particle’s position variable is in the state \displaystyle{| \psi \rangle}, which is a pure state, which is one single state, not a statistical mixture.

\displaystyle{| \psi \rangle = \sqrt{0.5}~| \psi_L \rangle + \sqrt{0.5}~| \psi_R \rangle}

Physically, it means that although, before measurement, the position variable of the particle is in the state, after measurement, the state will have a probability of \displaystyle{0.5} to become \displaystyle{| \psi_L \rangle}; and a probability of \displaystyle{0.5} to become \displaystyle{| \psi_R \rangle}.

In short, the wave function \displaystyle{| \psi \rangle } will collapse to either \displaystyle{| \psi_L \rangle} or \displaystyle{| \psi_R \rangle}.

Note that this standard language is a useful shortcut. However, it is for the convenience of daily-life calculations only. In case you want not only to apply quantum mechanics, but also to understand it (in order to avoid common conceptual paradoxes), you can translate the common language to a more accurate version:

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— Me@2022-02-22 07:01:40 PM

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2022.02.23 Wednesday (c) All rights reserved by ACHK

The 4 bugs of quantum mechanics popular, 1.6

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3.1  Probability value is totally objective. Wrong.

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3.2

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.

In other words, “where and when an observer should do what during the experiment” is actually part of your experimental-setup design, defining what probability distribution (for any particular variable) you (the observer) will get.

If the experimenter does not follow the original experiment design, such as not turning on the detector at the pre-defined time, then he is actually doing another experiment, which will have a completely different probability distribution (for any particular variable).

— Me@2022-02-18 07:40:14 AM

— Me@2022-02-14 10:35:27 AM

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Note that with respect to the physical variable X you are going to measure, the system is always classical, because you have to activate the detector in order to measure that variable.

Once “activating the detector” is part of the experimental-setup, in a non-accurate but easier to understand language, that variable is already in a mixed state since the beginning of the experiment.

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

In an accurate language, that design has already given the experiment-setup a property that “X is in a mixed state”, meaning that the probabilities assigned to different possible values of X are actually classical probabilities.

.

In the most basic double-slit experiment, assume that the probability of the going through either slit is \displaystyle{\frac{1}{2}}.

In the standard quantum mechanics language:

…

— Me@2022-02-22 07:01:40 PM

— Me@2022-02-21 07:17:28 PM

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2022.02.23 Wednesday (c) All rights reserved by ACHK