Square-root-of-probability wave

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The 4 bugs, 1.9

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The common quantum mechanics paradoxes are induced by 4 main misunderstandings.

1.  A wave function is of a particle. Wrong.

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2.1  A system's wave function exists in physical spacetime. Wrong.

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2.2  A superposition state is a physical superposition of a physical state. Wrong.

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3.1  Probability value is totally objective. Wrong.

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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):

1. 

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2.  Although used for calculating probabilities, a wave function \displaystyle{\phi(x)} itself is not probability.

Instead, we have to calculate its squared modulus \displaystyle{ \left| \phi \right|^2} in order to get a probability density; and then do an integration

\displaystyle{ \int_a^b \left| \phi(x) \right|^2 dx }

in order to get a probability, assuming in this case, the physical variable is a particle’s location \displaystyle{ x }.

At best, a wave function is the (complex) square root of probability (density) only.

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In our double slit experiment, the wave function

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

is for calculating the probabilities of passing through the double-slit-plate, without specifying which slit a particle has gone through, since the possible answers are physically-undefined.

Probability is in some sense “partial reality” before getting a result. Since a wave function (representing a quantum state) is not probability, we cannot regard the wave function as a “partial reality”. So, although \displaystyle{| \psi \rangle } is expressed as a sum of \displaystyle{| \psi_L \rangle } and \displaystyle{| \psi_R \rangle}, it cannot be regarded as a physical superposition.

1.  It is not the case that the particle is split into 2 halves; one half goes left and another goes right.

2.1  It is not an overlapping of 2 physical states.

2.2  It is not an overlapping of 2 realities, or partial realities.

2.3  It is not an overlapping of 2 different universes.

An overlapping of classical results will also give you a classical result; will not give you interference patterns.

Particles that go through the left slit will be part of the left fringe. Particles that go through the right slit will be part of the right fringes. So even if the reality (or half-reality) of a particle going left and the reality of it going right overlap, the particle will reach where the left or the right fringe will be, not where the interference pattern will be.

In other words, any simple overlapping a no-interference reality with another no-interference reality will give you also no interference patterns.

The fundamentals of this kind of errors are:

1.  Consider the electron version of the double-slit experiment.

Even if each electron in some sense really has passed through both slits, its two halves (or two realities) will never annihilate each other when they meet, because they are not anti-particle pair. No destructive interference will happen.

2.  The probability of any possible reality (component physical state, parallel universe) is always not less than 0 and not bigger than 1, because it is the nature of any probability \displaystyle{p}:

\displaystyle{0 \le p \le 1}.

In other words, the “superposition” of any two probabilities (possible realities, component physical states, parallel universes) will not give you the zero probability that is needed for destructive interference to happen.

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A major cause of this kind of errors is the wave function’s misleading name “probability wave”.

A wave function is not probability. At best, a wave function is the (complex) square root of probability (density) only. So at most, we can call it “complex-square-root-of-probability wave” only.

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

“A wave function is not probability” (or “a superposition of wave function is not (simple) overlapping of realities“) is the exact reason for the existence of interference patterns.

Also, the mathematical superposition of eigenstates is exactly for calculating those interference patterns.

\displaystyle{ \begin{aligned} \psi &= \psi_1 + \psi_2 \\ \\ P &= \left| \psi \right|^2 \\ &= \psi^* \psi \\ &= (\psi_1^* + \psi_2^*)(\psi_1 + \psi_2) \\ &= \left| \psi_1 \right|^2 + \left| \psi_2^* \right|^2 + \psi_1^* \psi_2 + \psi_2^* \psi_1 \\ \end{aligned} }

This is not totally technically correct; for example, the normalization has not been done. However, the formula is still true schematically.

Exactly since “a wave function is not probability”, we have to “square” it in order to get the probability (density). This “squaring” step creates the cross terms \displaystyle{ \psi_1^* \psi_2 + \psi_2^* \psi_1 }. These cross terms are corresponding to the interference effects.

In other words, the interference effects exist exactly because quantum superposition is a mathematical superposition, not a physical superposition of possible worlds.

If the quantum position was a simple overlapping of possible worlds,

\displaystyle{ \begin{aligned} P &= P_1 + P_2 = \left| \psi_1 \right|^2 + \left| \psi_2^* \right|^2 \\ \end{aligned} }.

There would have been no cross terms, and then no interference patterns.

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3. 

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— Me@2022-02-22 07:01:40 PM

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— Me@2022-02-25 04:27:37 PM

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2022.02.25 Friday (c) All rights reserved by ACHK

The 4 bugs, 1.8

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3.2

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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:

physical definition

~ define 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

— Me@2022-01-31 08:33:01 AM

In the experiment-setup design, when no detector (that can record which slit the particle has gone through) is allowed, the only measurement device remains is the final screen, which records the particle’s final position.

If you ask for the wave function \displaystyle{| \phi \rangle} for the variable representing for the particle’s final position on the screen, then \displaystyle{| \phi \rangle} is in one of the eigenstates, where each eigenstate represents a particular location on the final screen.

The wave function \displaystyle{| \phi \rangle} must be an eigenstate because your experiment design has provided a physical definition for different values of \displaystyle{| \phi \rangle}.

When we see a dot appear at a point on the screen, we say that the particle has reached that location.

However, if you ask which of the 2 slits the particle has gone through, it is impossible to answer, not because of our lack of knowledge (of the details of the experiment-setup physical system), but because of our lack of definition of the case “go-left” and that of the case “go-right” (in terms of observable physical phenomena).

In other words, due to the lack of physical definition, “go-left” and “go-right” are actually logically indistinguishable due to being physically indistinguishable. They should be regarded as identical, thus one single case. We represent that one single case by the wave function

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

a physical variable X is in a superposition state

~ X is a physically-undefined property (of the physical system)

For example, the system does not have the statistical property of “go-left“, nor that of “go-right“. The intended possible values of X, “go-left” and “go-right“, do not exist. Only the value “go-through-double-slit-plate” (without mentioning left and right) exists.

— Me@2022-02-23 07:49:47 AM

~ in the experiment-setup design, no measurement device is allowed to exist to provide a definition of different possible values of X

— Me@2022-02-18 02:04:45 PM

The wave function

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

is for calculating the probabilities of passing through the double-slit-plate, without specifying which slit a particle has gone through. This is what \displaystyle{| \psi \rangle} actually means.

“Passing through the double-slit-plate” is one single physical state. This physical state is not related to the physical state “go-left“, nor the physical state “go-right“, because those two physical cases do not exist in the first place.

The wave function \displaystyle{| \psi \rangle} represents one single physical case. So \displaystyle{| \psi \rangle} is one state. In other words, \displaystyle{| \psi \rangle} is a pure state, not a mixed state.

In this physical case, 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}

“And” and “or” only exist when there are more than one cases. The physical case “go-left” and the physical case “go-right” do not exist in the experiment-setup. So applying “and” or applying “or” are both impossible in this case.

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):

1. The component eigenstates \displaystyle{| \psi_L \rangle } and \displaystyle{| \psi_R \rangle} are logically indistinguishable (due to the lack of physical definition). They should be regarded as one single physical case.

In other words, the plus sign, \displaystyle{+}, can be directly translated to “is indistinguishable from”.

\displaystyle{+}

~ “is indistinguishable from”

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

~ \displaystyle{| \psi_L \rangle} and \displaystyle{| \psi_R \rangle} are indistinguishable; so they form one single state \displaystyle{| \psi \rangle}.

In a quantum superposition, all component eigenstates have to be indistinguishable. In other words, for the Schrödinger’s cat thought experiment, the cat superposition that some popular science text writes,

\displaystyle{| \text{cat} \rangle = \sqrt{0.5}~| \text{cat-alive} \rangle + \sqrt{0.5}~| \text{cat-dead} \rangle},

is actually illegitimate, because \displaystyle{| \text{cat-alive} \rangle} and \displaystyle{| \text{cat-dead} \rangle} are observable physical events; they are distinguishable states (physical cases).

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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, 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:

…

— 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.

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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:

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— 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

The 4 bugs of quantum mechanics popular, 1.5

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3.1 Probability value is totally objective. Wrong.

A probability value is not only partially objective, but also partially subjective. When you get a probability value, you have to specify which observer the value is with respect to. Different observers can get different probabilities for the “same” event.

Also, the same observer at 2 different times should be regarded as 2 different observers.

For example, for a fair dice, before rolling, the probability of getting an 2 is \displaystyle{\frac{1}{6}}. However, after rolling, the probability of getting an 2 is either \displaystyle{0} or \displaystyle{1}, not \displaystyle{\frac{1}{6}}. So the same person before and after getting the result should be regarded as 2 different observers.

A major fault of the many-worlds interpretation of quantum mechanics is that it uses an unnecessarily complicated language to state an almost common sense fact that any probability value is partially subjective and thus must be with respect to an observer. There is no “god’s eye view” in physics.

— Me@2017-05-10 07:45:36 AM

— Me@2022-02-14 10:36:52 AM

Wave functions encode probabilities. So each wave function is partially objective and partially observer-dependent. In other words, a wave function encodes the relationship between a physical system and an observer/experimenter.

— Me@2022-02-20

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2022.02.22 Tuesday (c) All rights reserved by ACHK

The 4 bugs of quantum mechanics popular, 1.4

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A misnomer collection:

2.2.1.

Wave function is not a wave. It is not a physical wave.

2.2.2.

Uncertainty principle is not about uncertainty. It is not directly related to uncertainty.

Uncertainty principle is not a principle. It is not even a physical law. Instead, it is a statistical relation. It is an inequality about the standard deviations of two conjugate variables.

2.2.3.

Superposition state is not a superposition. It is not a physical superposition. It is not a superposition of physical waves.

Superposition state is not a state. Instead, it is a property of a physical system. It is a statistical property of a variable of an experimental setup.

2.2.4.

Quantum mechanics is not quantum. It is not just about quantum (particle of energy).

Quantum mechanics is not mechanics. It is not just about mechanics. It is not just physical laws. Instead, it is a set of meta-laws, laws that physical laws themselves need to follow. It is an operating system on which physical laws can run.

— Me@2022-02-20 06:44:32 AM

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2022.02.21 Monday (c) All rights reserved by ACHK

The 4 bugs of quantum mechanics popular, 1.3

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The common quantum mechanics “paradoxes” are induced by 4 main misunderstandings.

1.  A wave function is of a particle. Wrong.

…

2.1  A system's wave function exists in physical spacetime. Wrong.

…

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

— Me@2022-01-31 08:33:01 AM

superposition

~ lack of the existence of measuring device to provide the physical definitions for the (difference between) microscopic events

— Me@2022-02-12 10:22:09 AM

a physical variable X is in a superposition state

~ X has no physical definition

~ in the experiment-setup design, no measurement device is allowed to exist to provide a definition of different possible values of X

— Me@2022-02-18 02:04:45 PM

2.2   A superposition state is a physical superposition of a physical state. Wrong.

“Quantum state” is a misnomer. It is not a (physical) state. It is a (mathematical) property. It is a system property (of a physical variable) of an experimental-setup design.

“State” and “property” have identical meanings except that:

State is physical. It exists in physical time. In other words, a system's state changes with time.

Property is mathematical. It is timeless. In other words, a system's property does not change. (If you insist on changing a system's property, that system will become, actually, another system.)

For example, “having two wheels” is a bicycle’s property; but the speed is a state, not a property of that bicycle.

superposition state

~ physically-undefined property

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In the phrase “superposition state”, the word “superposition” is also a misnomer.

A superposition state is not of physical waves, nor of physical states. Instead, it is a superposition of physical meanings of some variables in a physical system.

a physical variable X is in a superposition state

~ X is a physically-undefined property (of the physical system)

— Me@2022-02-18 02:04:45 PM

— Me@2022-02-20 06:44:32 AM

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2022.02.21 Monday (c) All rights reserved by ACHK

The 4 bugs of quantum mechanics popular, 1.2

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The common quantum mechanics “paradoxes” are induced by 4 main misunderstandings.

1.  A wave function is of a particle. Wrong.

…

2.1  A system's wave function exists in physical spacetime. Wrong.

…

So a wave function (for a particular variable) is an intrinsic property of a system. It is a mathematical property, not a physical state, of the physical system (the experimental setup). It does not evolve in time.

A wave function looks like evolving in physical time because it is a (mathematical) function of time.

But being a mathematical function of time only means that you can use the wave function to calculate the probabilities of a physical variable having different particular values at different times.

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An electromagnetic wave mathematical equation, which does not exist in physical spacetime, has its corresponding physical wave—-electromagnetic wave, which exists in physical spacetime.

However, a quantum wave function mathematical equation has no corresponding physical wave.

A wave function encodes a probability distribution; it can only correspond to a probability distribution, which is also a mathematical entity only.

A probability distribution can be a function of space and time. But that does not mean that the probability distribution exists in physical spacetime.

Any wave physical, such as electromagnetic wave, can be measured by a physical device.

In a sense, you cannot change a wave function; you can only replace it with another by replacing the physical system with another.

So whether the wave function of a variable is in superposition is an intrinsic property of a system, decided by the experiment’s designer.

Also, because of the existence of incompatible variable pairs, for any system, there must be some variables in a superposition, while others not.

— Me@2022-02-20 06:44:32 AM

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2022.02.20 Sunday (c) All rights reserved by ACHK

The 4 bugs of quantum mechanics popular

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The “para” in “paradox” means “meta”. The original meaning of the word “paradox” is

an error due to mixing language levels—-the object level and the meta level.

However, people have misused the word “paradox” a lot, using it to label anything unexpected. For example, in quantum mechanics, there are many so-called “paradoxes” that may be not really paradoxes.

However, among those quantum mechanics “paradoxes”, some of them are really paradoxes, whose existences are really due to mixing the object time level and the meta-time level.

The time within a story is called the “object time”. The time of the story’s writer or reader is called the “meta-time”.

The physical time in which an experiment is conducted is the object time. The time in which an experiment is designed is the meta-time. The meta-time of an experiment is its designer’s time level.

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“Wave function collapse” is not a physical process. Instead, it is mathematical. It just means that we have to replace the wave function with another if we replace the system with another.

In other words, it is not a physical event that happens during the operation of the experiment. Instead, it “happens” when you replace one experiment design with another. In this sense, “wave function collapse” happens not in the experiment’s time, but in the experiment’s meta-time, the time level of the experiment designer.

wave function collapse

~ probability distribution change (replacement) due to replacing “the experiment without measurement device” with “the experiment with measuring device“ (for a particular physical variable)

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The common quantum mechanics “paradoxes” are induced by 4 main misunderstandings.

1.  A wave function is of a particle. Wrong.

Instead, it is of the system (the experiment setup). It is of a variable of the physical system.

Actually, a system has more than one wave functions. Each physical variable of that system has its own wave function.

2.1  A system's wave function exists in physical spacetime. Wrong.

Instead, the wave function exists in the mathematical abstract space. With respect to an individual physical variable, different physical systems give different probability distributions, which are encoded in different wave functions.

So a wave function (for a particular variable) is an intrinsic property of a system. It is a mathematical property, not a physical state, of the physical system (the experimental setup). It does not evolve in time.

In a sense, you cannot change a wave function; you can only replace it with another by replacing the physical system with another.

— Me@2022-02-19 04:21:38 PM

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2022.02.19 Saturday (c) All rights reserved by ACHK

天線化磁石

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這段改編自 2010 年 10 月 14 日的對話。

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今年三月時，我和一位朋友，想為這個原理，起一個簡潔的名字，因為沒有的話，每次要提起它時，也十分麻煩。

一個可能可用的名字是「天線原理」。

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例如，如果要「搞 gag」（弄笑話）的話，不刻意去弄，就不會有笑話。但是，如果刻意去弄的話，又只會弄到冷笑話。那怎樣辦呢？

那就唯有要，開著「靈感天線」，將自己的心理狀態，調節到適當的天界頻道，企圖去接收，來自未來的訊息。有時接收得到，有時接收不到，不可強求。

你在作其他事情時，就有時會接收到。相反，如果不作他事，專心弄笑話的話，大概可以保證，一定接收不到。

弄巧反拙，寧拙無巧。創意呢家嘢，可遇不可求——沒法勇敢爭取，只能大方接收。

然後，你可以試試，把這個結構，改編成愛情的版本。

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例如，如果要愛情的話，不刻意去找，就不會有對象。但是，如果刻意去找的話，又只會令到自己的行為舉止，十分唐突，令人厭惡。那怎樣辦呢？

那就唯有要，開著「愛情天線」，將自己的心理狀態，調節到適當的天界頻道，企圖去接收，來自未來的緣份。有時接收得到，有時接收不到，不可強求。

你在作其他事情時，就有時會接收到。

不斷作有意義的事情，就自然創造到，內在緣份和外在緣份。

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內在緣份，即是一個不斷升級的自己。記住，你是你另一半的另一半。

升級了的自己，即是一個嶄新的世界。記住，一人一世界。

現在，你只是世界中的一人，但是將來，你這一人卻會化身成，你另一半的幾乎全部世界。

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外在緣份，就是一個相遇的巧合，相戀的機會。

愛情在於吸引，不在追求。

愛情，在於雙方吸引，不在單向追求。

愛情，在於雙方魅力的互相吸引，不在一方企圖的單向追求。

愛情本應為，兩塊磁石的運作。要麼相吸，要麼相斥，沒有第三個可能。

「失戀」這術語，有如「第二次初戀」，都是自相矛盾的詞匯。

失，是單向；戀，是雙向。

相反，如果不作他事，專心找愛情的話，大概可以保證，一定接收不到。

「專心找愛情」會令你完美地消滅，內在姻和外在緣。

弄巧反拙，寧拙無巧。緣份呢家嘢，可遇不可求——沒法勇敢爭取，只能大方接收。

— Me@2022-02-19 06:34:31 AM

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2022.02.19 Saturday (c) All rights reserved by ACHK

Logical arrow of time, 6.4.3

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Logical arrow of time, 6.1.3

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The source of the macroscopic time asymmetry, aka the second law of thermodynamics, is the difference between prediction and retrodiction.

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In a prediction, the deduction direction is the same as the physical/observer time direction.

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In a retrodiction, the deduction direction is opposite to the physical/observer time direction.

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In other words:

In a prediction, the meta-time direction is the same as the object-time direction.

In a retrodiction, the meta-time direction is opposite to the object-time direction.

— Me@2022-02-18 06:52:27 AM

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— guess —

If a retrodiction is done by a time-opposite observer, he will see the entropy increasing. For him, he is really making a prediction.

— guess

— Me@2013-10-25 3:33 AM

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How to create a time-inverted observer?

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Just invert the retrodiction direction.

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Retrodiction to a backward-time observer is just equivalent to retrodiction-for-backward-time to a forward-time observer.

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However, retrodiction-for-backward-time is just prediction.

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In other words, retrodiction to a backward-time observer is equivalent to a prediction for a normal time direction observer.

That’s why

— guess —

If a retrodiction is done by a time-opposite observer, he will see the entropy increasing. For him, he is really making a prediction.

— guess

— Me@2013-10-25 3:33 AM

— Me@2022-02-18 06:37:59 AM

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2022.02.18 Friday (c) All rights reserved by ACHK

EPR paradox, 11.8

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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

— Me@2022-01-31 08:33:01 AM

The second clue:

If in your experimental design, you have planned to activate a detector when each particle is still on its path, then this activation action itself is already part of your experimental design.

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

Superposition is a property for some wave functions (quantum states). So superposition is not a physical phenomenon. Instead, it is a mathematical property of some physical variables of your experimental-setup design.

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, whether a system is in superposition or not (with respect to a particular variable) is an intrinsic property of your experimental setup design, which includes not just objects and devices, but also operations.

“Wave function collapse” is not a physical event that happens during the operation of the experiment. Instead, it “happens” when you replace one experiment design with another.

— Me@2022-02-16 10:45:01 AM

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@2022-02-14 10:35:27 AM

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An experiment-setup design is composed of not only objects and devices, but also operations. A different experiment-setup design will give a different probability distribution for any particular physical variable.

Also, a different observer will see a different probability distribution for any particular physical variable. The same observer at different times actually should be regarded as different observers.

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.

— Me@2022-02-18 07:40:14 AM

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2022.02.18 Friday (c) All rights reserved by ACHK

EPR paradox, 11.7

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…

Even in this stranger case, all experimental results are still consistent with special relativity (aka causality), because wave functions are not physical quantities. Instead, they are mathematical quantities for calculating probabilities, which themselves are also mathematical quantities, for predicting experimental results.

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

— Me@2022-01-31 08:33:01 AM

(Me@2022-02-17 03:34:27 PM: I think I have the answer now. I plan to publish it soon. But I keep the following as a record of thoughts.)

A further strangeness is that

~ How come the results are always consistent when the EPR pair has no definite states before measurement the activation of at least one detector?

~ How does the universe to do such bookkeeping for a system exists across several light-years when the physical variables are still in superposition when the pair is emitted from the source?

~ … when the difference of possible values (such as the difference of spin-up and spin-down) still have no physical definition yet?

~ … when the difference of possible values have not yet defined by the difference of possible readings of a detector (before any detector is allowed to be installed-and-activated)

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However, this kind of strangeness also happens in classical physics, for example:

1. How come energy is always conserved? How is energy conservation “executed”?

2. How does probability work? How does the universe work to fulfill the predicted probability patterns?

— Me@2022-02-11 12:47:14 AM

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A clue (but not yet the whole final solution) is that probability is with respect to observers.

— Me@2022-02-11 10:13:36 AM

A probability is partially objective and partially subjective. So a wave function, which is used for calculating probabilities, is also partially objective and partially subjective.

A major fault of the many-worlds interpretation of quantum mechanics is that it uses an unnecessarily complicated language to state an almost common sense fact that any probability value is partially subjective and thus must be with respect to an observer.

— Me@2022-02-14 10:36:52 AM

— Me@2022-02-14 10:35:27 AM

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2022.02.17 Thursday (c) All rights reserved by ACHK