Photons in expanding space

If a photon (wave package) redshifts (stretches) travelling in our expanding universe, is its energy reduced?

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Since you say you’re talking about what happens locally (in a small volume), I’ll answer from that point of view. The usual formulation of energy conservation in such a volume is that energy is conserved in an inertial reference frame. In general relativity, there are no truly inertial frames, but in a sufficiently small volume, there are reference frames that are approximately inertial to any desired level of precision. If you restrict your attention to such a frame, there is no cosmological redshift. The photon’s energy when it enters one side of the frame is the same as the energy when it exits the other side. So there’s no problem with energy conservation.

The (apparent) failure of energy conservation arises only when you consider volumes that are too large to be encompassed by a single inertial reference frame.

To be slightly more precise, in some small volume V=L^3 of a generic expanding Universe, imagine constructing the best possible approximation to an inertial reference frame. In that frame, observers near one edge will be moving with respect to observers near the other edge, at a speed given by Hubble’s Law (to leading order in L). That is, in such a frame, the observed redshift is an ordinary Doppler shift, which causes no problems with energy conservation.

If you want more detail, David Hogg and I wrote about this at considerable (perhaps even excessive!) length in an AJP paper.

— Photons in expanding space: how is energy conserved?

— answered Aug 16, 2011 at 15:31

— Ted Bunn

— Physics Stack Exchange

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2022.09.11 Sunday ACHK

Quantum as potential, 2

Only measurement results (aka physical phenomena) form the physical reality.

Quantum Mechanics is a theory of measurement results.

Quantum Mechanics is a theory of reality.

Quantum Mechanics is not a theory of unobservables (undefined-observables).

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Quantum mechanics is a story of reality, not a story of story.

— Me@2022-07-27 10:38:32 AM

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2022.07.29 Friday (c) All rights reserved by ACHK

Quantum as potential

Realist view is wrong.

Before measurement, there are quantum potentials only.

quantum ~ potential

Note that it is NOT the “quantum potential” in the Bohm interpretation.

— Me@2016-08-21 06:13:49 PM

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A wave function encodes the probabilities of different potential measurement results of a physical experiment. It is not a physical wave.

Quantum superposition is NOT a superposition of realities.

Physics should consider only measurement results and their probabilities. Only measurement results are realities.

No measurement result, aka physical phenomenon, is in a superposition.

For example, in the double-slit experiment, the measurement results are (the locations of) the dots on the final screen. Every dot location is not in a superposition.

— Me@2022-07-25 06:43:05 PM

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2022.07.25 Monday (c) All rights reserved by ACHK

Schrodinger’s cat, 3.5

This description is wrong.

Quantum superposition is exhibited in fact in many directly observable phenomena, such as interference peaks from an electron wave in a double-slit experiment.

— Wikipedia on Quantum superposition

Whatever you observe, it is not a superposition.

If no left-right detector is allowed, the moving-left/right variable is an unobservable. What you observe, instead, is the dot on the final screen.

In other words, the observable is the final position of a particle when it reaches the final screen. And the final screen itself acts as the detector for that observable.

Superposition is unobservable due to the lack of definition (of the distinction between different states) of the corresponding physical variable, due to the fact that no corresponding detector, such as the left-right detector, is allowed in the experimental design.

physical phenomena

~ observable events

Superposition

~ logically unobservable, since not yet defined

~ not yet defined, since logically undefinable

~ logically undefinable, since no corresponding detector is allowed

A superposition state is not an observable state. In other words, it is not a physical state. Then what is the point of considering it?

Although a superposition state is not a physical state, it is a mathematical state that can be used to calculate the probabilities of different possible physical-states/observable-events.

— Me@2022-07-06 06:00:55 PM

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2022.07.07 Thursday (c) All rights reserved by ACHK

Schrodinger’s cat, 3.4

A macroscopic system (such as a cat) may evolve over time into a superposition of classically distinct quantum states (such as “alive” and “dead”).

— Wikipedia on Quantum superposition

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The components of a superposition must be indistinguishable states.

A superposition is neither an AND state nor an OR state.

AND or OR are only possible for more than one state.

AND or OR are only possible for at least 2 (distinguishable) states.

The cat is not in a superposition state of “alive” and “dead”.

Instead, it is in a mixed state of “alive” and “dead”.

A mixed state is an OR state (of at least 2 distinguishable states).

— Me@2022-07-03 11:02:24 AM

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2022.07.03 Sunday (c) All rights reserved by ACHK

Schrodinger’s cat, 3.3

The modern view is that this mystery is explained by quantum decoherence.

Quantum decoherence is useful, but NOT necessary.

It is useful for the self-consistency checking of quantum mechanics.

Some microscopic states are expressed as (mathematical) superpositions of macroscopic-indistinguishable-if-no-measuring-device-is-allowed states.

Two states are called “macroscopic-distinguishable” only if they result in two different physical phenomena. In other words, the distinction must be observable.

an eigenstate

~ an observable (at least in principle) state

~ a physical state

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a superposition state

~ an unobservable (even in principle) state

~ a mathematical (but not physical) state

We define microscopic states and events in terms of macroscopic states and events. A consistent theory must be able to deduce (explain or predict) macroscopic states and events from those microscopic states and events.

— Me@2022-06-15 07:40:37 PM

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2022.06.29 Wednesday (c) All rights reserved by ACHK

Eigenstates 3

an eigenstate

~ an state identical to the overall average

In analogy, in the equation

\displaystyle{\frac{12+13+14}{3}=13},

the number 13 appears both on the left (as one of the component numbers) and on the right (as the overall average).

In this sense, the number 13 is an “eigenstate”.

— Me@2016-08-25 01:36 AM

— Me@2022-06-28 08:19 PM

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An eigenstate has a macroscopic equivalence.

— Me@2016-08-29 06:10:21 PM

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An eigenstate is a microstate that has a corresponding macrostate.

An eigenstate is a mathematical state which is also a physical state.

An eigenstate is an observable state.

— Me@2022-06-28 07:36:40 PM

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2022.06.28 Tuesday (c) All rights reserved by ACHK

Schrodinger cat’s misunderstanding

Schrodinger’s cat, 3.2

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In 1935, Erwin Schrödinger devised a well-known thought experiment, now known as Schrödinger’s cat, which highlighted this dissonance between quantum mechanics and classical physics.

The main point of the Schrödinger’s cat thought experiment is NOT to prove that there should also be superposition for macroscopic objects. Instead, the main point of the thought experiment is exactly the opposite—to prove that regarding a superposition state as a physical state leads to logical contradiction.

— Me@2022-06-15 07:19:36 PM

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2022.06.22 Wednesday (c) All rights reserved by ACHK

Schrodinger’s cat, 3.1

It is natural to ask why ordinary everyday objects and events do not seem to display quantum mechanical features such as superposition. Indeed, this is sometimes regarded as “mysterious”, for instance by Richard Feynman. In 1935, Erwin Schrödinger devised a well-known thought experiment, now known as Schrödinger’s cat, which highlighted this dissonance between quantum mechanics and classical physics.

The modern view is that this mystery is explained by quantum decoherence. A macroscopic system (such as a cat) may evolve over time into a superposition of classically distinct quantum states (such as “alive” and “dead”). However, the state of the cat is entangled with the state of its environment (for instance, the molecules in the atmosphere surrounding it). If one averages over the quantum states of the environment—a physically reasonable procedure unless the quantum state of all the particles making up the environment can be controlled or measured precisely—the resulting mixed quantum state for the cat is very close to a classical probabilistic state where the cat has some definite probability to be dead or alive, just as a classical observer would expect in this situation.

Quantum superposition is exhibited in fact in many directly observable phenomena, such as interference peaks from an electron wave in a double-slit experiment. Superposition persists at all scales, provided that coherence is shielded from disruption by intermittent external factors. The Heisenberg uncertainty principle states that for any given instant of time, the position and velocity of an electron or other subatomic particle cannot both be exactly determined. A state where one of them has a definite value corresponds to a superposition of many states for the other.

— Wikipedia on Quantum superposition

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It is natural to ask why ordinary everyday objects and events do not seem to display quantum mechanical features such as superposition. Indeed, this is sometimes regarded as “mysterious”, for instance by Richard Feynman.

Superposition is not “mysterious”. It is “mysterious” only if you regard “a superposition state” as a physical state.

Only observable states are physical states. Any observable, microscopic or macroscopic, is NOT a superposition.

A superposition is NOT observable, even in principle; because the component states of a superposition are physically-indistinguishable mathematical states, aka macroscopically-indistinguishable microscopic states.

(Those component states, aka eigenstates, are observable and distinguishable once the corresponding measuring device is allowed.)

They are indistinguishable because the distinction is not defined in terms of the difference between different potential experimental or observational results.

Actually, the distinction is not even definable, because the corresponding measuring device is not allowed in the experimental design yet.

— Me@2022-06-15 11:51:22 AM

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2022.06.16 Thursday (c) All rights reserved by ACHK

Physically-indistinguishable mathematical states

… that’s not totally correct, because a macroscopic state, even in principle, cannot be a superposition of macroscopic eigenstates.

— Me@2012.12.31

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A macrosopic state is an actual physical state.

A macrosopic state, by definition, cannot be a superposition of different macroscopic states. A superposition must be of different macroscopically-indistinguishable microscopic states.

In other words, a physical state, by definition, cannot be a superposition of different physically-distinguishable physical states. A superposition must be of different physically-indistinguishable mathematical states.

— Me@2022-05-17

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2022.05.17 Tuesday (c) All rights reserved by ACHK

數學教育 7.5.1

Genius 4.2.1 | A Fraction of Algebra, 2.1

這段改編自 2010 年 4 月 24 日的對話。

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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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(安:但是,這個講法可能有一個問題。

雖然,你剛才列舉了數個例子,來示範如何將高深數學,間接應用到人生處世,但是,一般人未必有那種能力。所以我想問,你又是如何去跨過這個難關呢?)

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什麼難關?

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(安:去翻譯那些抽象數學概念,到其他範疇,或者日常生活。)

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那不是「難關」。你的意思是,一般人也沒有那個能力,而我有。所以,那是超能力;我當年一定是,用了一些秘技,才獲取之。

天才之道,點滴累積。其實並沒有所謂的「秘技」。只要一步一步地,學習數學,就自然建構出,一個相對接近完整的數學思考體系,生成「翻譯抽象數學概念到其他範疇」等能力。

所以,我猜想你的疑問是,其實我所講的「點滴累積」,或者「一步一步地」,雖然理想上是,基本的要求,但是現實中是,大部人也做不到。那就代表著,大部人可能也會遇到,一個共通的「難關」。那個「難關」究竟是什麼?我又是如何克服它,而做到「一步一步地」「點滴累積」的呢?

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你問題的最簡化版本是:「如何學習數學,開創人生?」

有起碼以下三個先決條件:

1. 對數學(及其他學問人生),有極大興趣;

2. 遇到合理的老師和書籍:

重點是,數學概念或運算上的主要步驟,亳無違漏。支節可免,但主旨必須。細節可以無師自通,大節必靠前人指點。平地自己行,斜地靠梯級。平地可跳步,梯不可跳級。

3. 極超大量的背誦和練習:

數學是理科,所以其背誦方法,不是「死背」零碎隨機的資料,而是「生背」息息相關的訊息。融匯貫通地背誦的唯一方法是,極超大量的操練。

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你所講的「難關」,就是以上的第二點。老師有分好老師和差老師。大部分也是差老師。而差老師再分兩類:不懂數學和不懂教學。

— Me@2022.05.02 11:48 PM

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2022.05.03 Tuesday (c) All rights reserved by ACHK

Dynamical pictures

Comparison of pictures

The Heisenberg picture is closest to classical Hamiltonian mechanics (for example, the commutators appearing in the above equations directly correspond to classical Poisson brackets). The Schrödinger picture, the preferred formulation in introductory texts, is easy to visualize in terms of Hilbert space rotations of state vectors, although it lacks natural generalization to Lorentz invariant systems. The Dirac picture is most useful in nonstationary and covariant perturbation theory, so it is suited to quantum field theory and many-body physics.

Summary comparison of evolutions

— Wikipedia on Dynamical pictures

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2022.04.05 Tuesday ACHK

Huygens’ principle, 1.1

Why are there no backward secondary wavefronts?

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A secondary wave source is of different nature from a primary wave source. Consider an one dimensional transverse wave on a string:

Primary wave source is activated by the force from above, and then the wave propagates to both directions. Secondary wave source is activated by the particle on the left.

Primary wave source energy is from outside the string. Secondary wave source energy is from an adjacent string molecule.

When the secondary source S reaches its maximum, although it drags both P and Q, they are in different situations. At that moment, while the instantaneous velocity of Q is upward, that of P is downward.

Note that the red arrow at P is the force on P by S. It is not the net force on P.

— Me@2022-03-09 11:14:07 PM

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2022.03.30 Wednesday (c) All rights reserved by ACHK

EPR paradox, 12.2

Experiment C:

What if during Experiment A, the observer changes his mind to turn on the detector before the particle’s arrival?

Explanation X:

We should regard this whole process as an experiment-setup.

The probability patterns encoded in the quantum state is of this experiment-setup, which in this case is equivalent to Experiment B. With respect to this experiment-process/experiment-setup, the variable-to-be-measured is always in a mixed state.

The word “always” here means that a quantum state is not a physical state of a particle in physical spacetime during the experiment. Instead, it is a property (of a physical variable) of the experiment-setup (physical system) itself.

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

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However, for an experiment like Experiment C, doesn't the violation of Bell's inequality have proved that the spin of the particle is still in a superposition before the activation of the detector?

Let’s translate this question to a double-slit experiment version. (The consistency of the left detector and the right detector is as strange as the EPR consistency.)

Experiment C:

What if in the double-slit experiment, the detector is off when the particle is emitted, but the observer changes his mind to turn on the detector before the particle’s passing through of the double-slit plate?

Is the particle in a superposition or not when the detector is still off?

Instead of a superposition pure state, we should regard the particle path state as a mixed state, even before the detector is activated.

The reason is given in Explanation X.

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However, for an experiment like Experiment C, doesn't the violation of Bell's inequality have proved that the path of the particle is still in a superposition before the activation of the detector?

The violation of Bell’s inequality should be interpreted in this way:

Experiment A:

If there is no detector activated throughout the experiment until the particle reaches the final screen, the resulting statistical pattern (aka the interference pattern) is possible only if the particle has no definite path. “An unknown but definite path exists” would not be able to create such statistics.

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Experiment B:

If there is a detector activated since the beginning of the experiment, the particle path is in a mixed state since that beginning, meaning that the path is definite although unknown before measurement.

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Experiment C:

What if in the double-slit experiment, the detector is off when the particle is emitted, but the observer changes his mind to turn on the detector before the particle’s passing through of the double-slit plate?

Is the particle in a superposition or not when the detector is still off?

After the detector is activated, the path is in a mixed state.

Before the detector is activated, regarding the path state as in a superposition or as in a mixed state makes no physical difference, because by definition, there is no measurement before the detector is activated.

Also, a superposition’s coefficients are always about the potential-activation of detectors.

A superposition state has a corresponding mixed state. The superposition coefficients can be modulus-squared to give the mixed state coefficients. That is the exact original meaning of the superposition coefficients. (This is the statistical interpretation given by Born rule.)

In other words, each coefficient in a superposition state by default encodes the probability of each potential measurement result.

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However, in Experiment C, regarding the state as a superposition state before the activation of detector creates conceptual paradoxes, such as:

If the particle path variable has no definite state before measurement, how come the left detector and right detector always give consistent results?

This is the double-slit experiment version of the EPR paradox.

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When the experimenter follows the plan of Experiment A, the particle path variable is always in a superposition, since the beginning of the experiment.

However, when he changes his mind to turn on the detector before the particle’s passing through of the double-slit plate, the particle path variable is always in a mixed state, since the beginning of the experiment.

Wouldn’t that create retro-causality?

It seems to be retro-causality, but it is not, because this description is a language shortcut only. The apparent violation of causality does not exist in the language longcut version, which is provided in Explanation X.

Also, due to the indistinguishability of identical particles, particle identities and thus particle trajectories are post hoc stories only.

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In short, the violation of Bell’s inequality means that:

If there is no path detector activated throughout the experiment until the particle reaches the final screen, the path variable never has a definite value, known or unknown, throughout that experiment.

The violation of Bell’s inequality should not be applied to Experiment C, because it is not the case of “having no detector throughout the experiment”.

Also, note that we do not need the violation of Bell’s inequality to prove that the path variable has no definite state, known or unknown.

Just the interference pattern’s existence is already enough for us to do so.

— Me@2022-03-08 11:56:00 PM

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2022.03.24 Thursday (c) All rights reserved by ACHK

EPR paradox, 12.1

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@2022-02-22 07:01:40 PM

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Note that different observers see different “physical systems”. They see different quantum states, because a quantum state is actually not a “state”, but a (statistical) property of a system, encoded in the superposition coefficients.

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Experiment A:

In an EPR experiment, if it is by design that an observer will not turn on the detector, then the story should be that this experiment-setup is always in a superposition state (with respect to the variable-not-to-be-measured).

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Experiment B:

In an EPR experiment, if it is by design that an observer will turn on the detector before a particle’s arrival, then the story should be that this experiment-setup is always in a mixed state (with respect to the variable-to-be-measured).

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No concept of “wave function collapse” is needed.

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What if during Experiment A, the observer changes his mind to turn on the detector before the particle's arrival?

He has actually replaced experiment-setup A with experiment-setup B.

Then is the experiment always in a superposition state? Or always in a mixed state?

As a language shortcut, you can say that the superposition wave function collapses at the moment of system replacement.

However, it is a language shortcut, a story only.

A story is not reality.

A story is post hoc.

physical definition

~ define unobservable events in terms of observable events

Any story would be fine as long as it is compatible with reality, aka measurement results.

But some stories are better than others.

Here, only the longcut version can avoid common meaningless questions.

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Experiment C:

What if during Experiment A, the observer changes his mind to turn on the detector before the particle’s arrival?

We should regard this whole process as an experiment-setup.

The probability patterns encoded in the quantum state is of this experiment-setup, which in this case is equivalent to Experiment B. With respect to this experiment-process/experiment-setup, the variable-to-be-measured is always in a mixed state.

The word “always” here means that a quantum state is not a physical state of a particle in physical spacetime during the experiment. Instead, it is a property (of a physical variable) of the experiment-setup (physical system) itself.

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

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However, for an experiment like Experiment C, doesn't the violation of Bell's inequality have proved that the spin of the particle is still in a superposition before the activation of the detector?

Let’s translate this question to a double-slit experiment version.

— Me@2022-03-08 11:56:00 PM

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2022.03.09 Wednesday (c) All rights reserved by ACHK

EPR paradox, 11.12

Measuring spin and polarization

In de Broglie–Bohm theory, the results of a spin experiment cannot be analyzed without some knowledge of the experimental setup. It is possible to modify the setup so that the trajectory of the particle is unaffected, but that the particle with one setup registers as spin-up, while in the other setup it registers as spin-down. Thus, for the de Broglie–Bohm theory, the particle’s spin is not an intrinsic property of the particle; instead spin is, so to speak, in the wavefunction of the particle in relation to the particular device being used to measure the spin. This is an illustration of what is sometimes referred to as contextuality and is related to naive realism about operators. Interpretationally, measurement results are a deterministic property of the system and its environment, which includes information about the experimental setup including the context of co-measured observables; in no sense does the system itself possess the property being measured, as would have been the case in classical physics.

— Wikipedia on De Broglie–Bohm theory

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2022.03.06 Sunday ACHK

Bit software; qubit hardware

Quantum information is the information of the state of a quantum system.

— Wikipedia on Quantum information

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\displaystyle{\begin{aligned} |a|^2 + |b|^2 &= 1 \\ \end{aligned}}

For a system with the superposition state

\displaystyle{\begin{aligned} | \psi \rangle &= a~| \psi_L \rangle + b~| \psi_R \rangle \\ \end{aligned}},

quantum information is the information of the superposition coefficients \displaystyle{a} and \displaystyle{b}.

— Me@2022-03-03 07:11:10 PM

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A quantum 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.

— Me@2022-02-20 06:44:32 AM

— Me@2022-03-03 07:53:09 PM

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Quantum information does not exist in physical spacetime. Instead, it exists in the experiment-setup designer’s time. In this sense, it exists in meta-physical time.

It is not information that exists in a physical system. Instead, it is the information about the physical system.

— Me@2022-02-20 11:27:31 PM

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Quantum computers are implemented by using qubits, encoding information in the system property (aka quantum state) itself. A qubit is stored in the property of the system, not just arrangements of particles of the system as in a classical media.

Classical information is stored in microscopic setups, such as the arrangements of microscopic particles, of a system.

Quantum information is stored in macroscopic setups, such as the magnetic field direction for maintaining an electron spin’s superposition state, of a system.

— Me@2022-02-20 11:30:37 PM

— Me@2022-03-03 10:29:53 PM

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quantum information ~ a system property

conservation of quantum information ~ a property of those system properties

— Me@2022-02-20 8:13 AM

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You can locate a piece of classical information in a physical system/information media.

You cannot locate a piece of quantum information in a physical system, because quantum information is stored in the statistical properties of that physical system, which includes objects and experimental processes.

You have to do a large number of identical experiments in order to extract those statistical patterns.

For example, for a fair dice, the numbers on its faces, its weight, etc. are classical information. However, the probability value of getting (such as) 2, which is \displaystyle{\frac{1}{6}}, is quantum information; it does not exist in physical spacetime.

— Me@2022-02-20 11:46:40 PM

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“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.

— Me@2022-02-20 06:44:32 AM

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state ~ the easiest-to-change property of a system

— Me@2022-02-21 08:52:34 PM

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Classical information is stored in the states of a system (information media).

Quantum information is stored in the properties of a system.

— Me@2022-02-21 08:52:34 PM

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A qubit might for instance physically be a photon in a linear optical quantum computer, an ion in a trapped ion quantum computer, or it might be a large collection of atoms as in a superconducting quantum computer. Regardless of the physical implementation, the limits and features of qubits implied by quantum information theory hold as all these systems are mathematically described by the same apparatus of density matrices over the complex numbers.

— Wikipedia on Quantum information

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Note that while a bit is a software object, a qubit is a physical object.

— Me@2022-02-23 05:19:02 PM

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2022.03.04 Friday (c) All rights reserved by ACHK

The particle-trajectory model

The 4 bugs, 1.13

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

4.1  Each particle always has a definite identity. Wrong.

identical particles

~ some particles are identical, except having different positions

~ some particle trajectories are indistinguishable

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trajectory indistinguishability

~ particle identity is an approximate concept

— Me@2022-02-11 12:47:14 AM

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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

4.2  Each particle always has a trajectory. Wrong.

Which trajectory has a particle travelled along” is a hindsight story.

The electron at location x_1 at time t_1 and the electron at location x_2 at a later time t_2 are actually the same particle” is also a hindsight story.

These kinds of post hoc stories do not exist when some definitions of trajectories are missing in the overall definition of the experiment setup. In such a case, we can only use a superposition state to describe the state of the physical system.

Since such a situation has never happened in a classical (or macroscopic) system, it gives a probability distribution that has never existed before.

— Me@2022-01-31 08:33:01 AM

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a trajectory story

~ a hindsight story

~ a post hoc story

reality

~ experimental data

~ observable events

story

~ an optional description of an unobservable event

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Even though the nature of a trajectory story is a hindsight story or a post hoc story, it must be based on observable events, compatible with experiment results.

— Me@2022-03-01 07:33:31 PM

— Me@2022-03-02 10:30:41 AM

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The double slit experiment (and any other experiments that have quantum effects) puts the particle-trajectory model into a stress test and breaks it. The experiment exposes the bug of the particle-trajectory model. For example, the superposition case (aka the no-detector case) cannot be explained by this model.

Another example, even if the two slits on double-slit-plate are all closed, some particles, although not many, will still “go through” the plate.

— Me@2022-02-27 09:17:23 AM

— Me@2022-03-01 11:09:24 PM

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quantum effect

~ an effect that cannot use the particle-trajectory model

~ an effect that does not have a trajectory story

— Me@2022-03-02 12:23:54 PM

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2022.03.02 Wednesday (c) All rights reserved by ACHK

The 4 bugs, 1.12

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.

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):

3. 

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