Decoherence, Coherence, Pure State, Mixed State

[rodsika]

If the cat could be kept totally isolated then according to the rules of the Copenhagen interpretation there should be no "collapse" due to observation, so it should evolve into macroscopic superpositions--that was exactly why Schroedinger thought up this example, to try to suggest there was a problem with the Copenhagen idea that isolated quantum systems have wavefunctions that evolve according to the deterministic Schroedinger equation until they are "observed".

Hi, you wrote in the other thread the following:

"Sure, even in the Copenhagen interpretation you could have decoherence if you could keep a sufficiently complex system consisting of both a subsystem and its "environment" in isolation for a little while, so there'd be no external system to "collapse" it (like Schroedinger's cat, or a simulation on a large quantum computer)."

and you wrote above that "If the cat could be kept totally isolated then according to the rules of the Copenhagen interpretation there should be no "collapse" due to observation, so it should evolve into macroscopic superpositions"

Now a question that has been haunting me the whole day.

Decoherence can occur inside the cat body (subsystem of the whole which is what decoherence is all about). This means the cat bloodstream or bones can become classical with definite positions (a result of decoherence). So how could the cat suffer macroscopic superposition when part of its internal body had become classical?

This is what I meant in message #7 here where I asked:

"Supposed you have a buckyball composing of 430 atoms prepared in pure state. It means a total superposition exists. Now if one just considers say interaction of 50 atoms inside the buckyball and ignores the rest, decoherence occurs?? How could that be."

Your reply was:

I don't really know what kind of answer you're looking for when you say "how could that be". Apparently it just follows from the math of QM when you calculate a reduced density matrix for the 50 atoms, I don't see why you think this should be so problematic?

And I asked (in the same message)

"Or why doesn't the decoherence inside the system spread to the whole?"

Your reply was:

Don't know what "spread to the whole" would mean, the rules of wavefunction evolution don't allow for a pure state to evolve into anything but another pure state, but the reduced density matrix for a subsystem would I think be calculated from this very pure state of the whole system.

What I meant by spread was this. Since decoherence occurs in the 50 atoms in the 430 atom buckyball, the 50 atoms become classical. Why didn't the classicality spread to the entire buckyball such that it the position become definite and classical?? This is similar to the question why the cat in macroscopic superposition has the internal organ like liver suffer decoherence which becomes classical and yet it didn't spread to the entire cat making the whole cat classical. It's like seeing a smeared image of the cat with a solid liver inside.

Note very important that we are talking about Copenhagen in this message where before things are measured, they are in superposition. So pls don't mention Many Worlds because in Many worlds one can argue there are many branches and all are classical. I'm focusing on Copenhagen where before measurements things exist in smeared out superposition but decoherence can exist internally inside the smeared superposition just like you said in message #2:

As for decoherence, as I understand it this only applies to some subsystem of a larger system. So if you have the contents of the box in a pure state at the moment the box is sealed, then the complete state vector of everything in the box should remain in a pure state forever as long as the box remains isolated...but if you consider the state of the cat subsystem as separate from the state of the remaining contents of the box (air molecules, cat toys, etc.), then the interaction of the cat with the environment will cause the cat subsystem to go to a mixed state, with the interference terms approaching zero.

Here the same question can be asked why decoherence in a region (say cat liver) inside the pure state didn't spread the region of classicality (classical liver) to the entire object (in smeared out superposition) preventing or killing the superposition.

And lastly. How complex must be the thing inside the 100% isolated box before this spreading of region of decoherence spread to the entire making turning it classical (in position).

Thanks.

 

[JesseM]

Decoherence can occur inside the cat body (subsystem of the whole which is what decoherence is all about). This means the cat bloodstream or bones can become classical with definite positions (a result of decoherence).

Decoherence means that the reduced density matrix for a bone, say, would come to be a mixed state where the amplitude is concentrated on position eigenstates and the interference terms were close to zero. But that's not quite the same as saying the particles have become "classical with definite positions", the mixed state would still look like a statistical ensemble of different position eigenstates, each of which would feature the particles in different sets of positions. So for example one position eigenstate might involve a given leg bone being upright because the cat is in a standing position, another might involve it being horizontal because the cat is in a sleeping position, the reduced density matrix would include both. Decoherence doesn't provide a "collapse" that selects one of the many position eigenstates, it just means that it's approximately correct to treat it as a statistical mixture of these different states rather than a superposition where you have to worry about interference effects.

What I meant by spread was this. Since decoherence occurs in the 50 atoms in the 430 atom buckyball, the 50 atoms become classical.

I think it's misleading to say they "become classical", as I said they don't go to any single definite set of positions, and it's only approximately correct to treat them as a regular statistical ensemble if you're just looking at those 50 particles and ignoring the other 380, you would still find interference effects if you looked at all 430 at once. Again think of the delayed choice quantum eraser, where if you just look at the probability distribution for signal photons ignoring correlations with idlers, you find a non-interference pattern on the screen behind the double slit, but if you consider the conditional probability that a signal photon landed at various positions given that the idler was detected at some detector, then here there may be an interference pattern.

Note very important that we are talking about Copenhagen in this message where before things are measured, they are in superposition. So pls don't mention Many Worlds because in Many worlds one can argue there are many branches and all are classical. I'm focusing on Copenhagen where before measurements things exist in smeared out superposition but decoherence can exist internally inside the smeared superposition

Copenhagen is just sort of agnostic about what's "really" going on in the box before measurement, it just says that we model the inside of the box as a big superposition in order to figure out the probabilities of various outcomes when we open it. In terms of Copenhagen, say you could prepare some vast number of boxes with the identical cats measured to be in identical initial pure states at the moment the box was sealed, and then for each one you opened the box after some fixed time and made another exhaustive measurement of all the particles, and then you looked at the statistical patterns in all these different experiments, constructing a probability distribution on different final outcomes. In that case, the probability distribution for different final outcomes involving all the particles would show interference effects (akin to how the probability distribution for signal and idler shows interference), but if you just looked at "reduced" final outcomes which only involved paying attention to a particular subsystem of particles in each final measurement, here the probability distributions for different possible outcomes would show virtually no interference (akin to how the probability distribution for signal photon alone, throwing out information about the idler, doesn't show interference).

 

[rodsika]

Decoherence means that the reduced density matrix for a bone, say, would come to be a mixed state where the amplitude is concentrated on position eigenstates and the interference terms were close to zero. But that's not quite the same as saying the particles have become "classical with definite positions", the mixed state would still look like a statistical ensemble of different position eigenstates, each of which would feature the particles in different sets of positions. So for example one position eigenstate might involve a given leg bone being upright because the cat is in a standing position, another might involve it being horizontal because the cat is in a sleeping position, the reduced density matrix would include both. Decoherence doesn't provide a "collapse" that selects one of the many position eigenstates, it just means that it's approximately correct to treat it as a statistical mixture of these different states rather than a superposition where you have to worry about interference effects.

I think it's misleading to say they "become classical", as I said they don't go to any single definite set of positions, and it's only approximately correct to treat them as a regular statistical ensemble if you're just looking at those 50 particles and ignoring the other 380, you would still find interference effects if you looked at all 430 at once. Again think of the delayed choice quantum eraser, where if you just look at the probability distribution for signal photons ignoring correlations with idlers, you find a non-interference pattern on the screen behind the double slit, but if you consider the conditional probability that a signal photon landed at various positions given that the idler was detected at some detector, then here there may be an interference pattern.

Copenhagen is just sort of agnostic about what's "really" going on in the box before measurement, it just says that we model the inside of the box as a big superposition in order to figure out the probabilities of various outcomes when we open it. In terms of Copenhagen, say you could prepare some vast number of boxes with the identical cats measured to be in identical initial pure states at the moment the box was sealed, and then for each one you opened the box after some fixed time and made another exhaustive measurement of all the particles, and then you looked at the statistical patterns in all these different experiments, constructing a probability distribution on different final outcomes. In that case, the probability distribution for different final outcomes involving all the particles would show interference effects (akin to how the probability distribution for signal and idler shows interference), but if you just looked at "reduced" final outcomes which only involved paying attention to a particular subsystem of particles in each final measurement, here the probability distributions for different possible outcomes would show virtually no interference (akin to how the probability distribution for signal photon alone, throwing out information about the idler, doesn't show interference).

About this whole density matrix thing. A week ago I posted a thread called "Predictivity Sieves questions" asking something about it but no one answered so hopefully you can answer it (reproduced in the following) so I can understand better this density matrix as it pertains to decoherence, many thanks.

I wrote in that thread the following:

There is something that escapes my understanding about decoherence and the so called predictivity sieves. In Max Tegmark paper:

http://arxiv.org/abs/quant-ph/0101077"The second unanswered question in the Everett picture was more subtle but equally important: what physical mechanism picks out the classical states — face up and face down for the card — as special? The problem was that from a mathematical point of view, quantum states like "face up plus face down" (let’s call this "state alpha") or "face up minus face down" ("state beta", say) are just as valid as the classical states "face up" or "face down".

So just as our fallen card in state alpha can collapse into the face up or face down states, a card that is definitely face up — which equals (alpha + beta)/2 — should be able to collapse back into the alpha or beta states, or any of an infinity of other states into which "face up" can be decomposed. Why don’t we see this happen?

Decoherence answered this question as well. The calculations showed that classical states could be defined and identified as simply those states that were most robust against decoherence. In other words, decoherence does more than just make off-diagonal matrix elements go away. If fact, if the alpha and beta states of our card were taken as the fundamental basis, the density matrix for our fallen card would be diagonal to start with, of the simple form

density matrix = [1 0]
--------------------[0 0]

since the card is definitely in state alpha. However, decoherence would almost instantaneously change the state to

density matrix = [1/2 0]
--------------------[0 1/2]

so if we could measure whether the card was in the alpha or beta-states, we would get a random outcome. In contrast, if we put the card in the state "face up", it would stay "face up" in spite of decoherence. Decoherence therefore provides what Zurek has termed a "predictability sieve", selecting out those states that display some permanence and in terms of which physics has predictive power."

---------------------------

Inquiries about the above:

1. What does it mean "if the alpha and beta states of our card were taken as the fundamental basis, the density matrix for our fallen card would be diagonal to start with"? What does becoming "diagonal" mean?

2. How come if the card is in alpha state, decoherence would amost instantaneously change the state to the 2nd density matrix?

3. And why if the card was in alpha state, one would get a random outcome? What random outcome is it talking about?

 

[JesseM]

About this whole density matrix thing. A week ago I posted a thread called "Predictivity Sieves questions" asking something about it but no one answered so hopefully you can answer it (reproduced in the following) so I can understand better this density matrix as it pertains to decoherence, many thanks.

As I said I haven't studied the technical details of decoherence and that goes for density matrices as well, what I know about them is from nontechnical explanations from physicists, for example the basic idea that a density matrix is just a statistical ensemble of different possible pure states. Probably it's possible to figure out the basics from the definitions in http://qis.ucalgary.ca/quantech/443/chapter_five.pdf though. For a 2x2 density matrix as in Tegmark's example, they would write the four entries as:

\left[ \begin{matrix}<br /> \rho_{11} &amp; \rho_{12}\\ <br /> \rho_{21} &amp; \rho_{22}\\ <br /> \end{matrix}<br /> \right]<br />

And define the entries as follows:

\rho_{11} = \sum_i p_i \langle a_1 \mid \psi_i \rangle \langle \psi_i \mid a_1 \rangle
\rho_{12} = \sum_i p_i \langle a_1 \mid \psi_i \rangle \langle \psi_i \mid a_2 \rangle
\rho_{21} = \sum_i p_i \langle a_2 \mid \psi_i \rangle \langle \psi_i \mid a_1 \rangle
\rho_{11} = \sum_i p_i \langle a_2 \mid \psi_i \rangle \langle \psi_i \mid a_2 \rangle

Where here \mid a_1 \rangle and \mid a_1 \rangle would be the measurement basis, so they'd be the states Tegmark called "alpha" and "beta" respectively since he said that's what was being measured, in terms of bra-ket notation it would be clearer to write them as |alpha> and |beta>. Then \mid \psi_1 \rangle and \mid \psi_2 \rangle would be the pure states in the statistical ensemble, assigned probabilities p1 and p2, I think Tegmark's point was that decoherence would drive the card into a statistical ensemble of classical states, in this case "face up" which he defined as (|alpha> + |beta>)/2 and "face down" which I guess would be (|alpha> - |beta>)/2 (normally superpositions like this involve a factor of 1/sqrt(2), not 1/2, I wonder if he wrote it incorrectly here). So if there's an equal probability of either, meaning p1=1/2 and p2=1/2, then I think if you plug all this into the above (keeping in mind that products <alpha|beta> and <beta|alpha> are equal to zero, while <alpha|alpha> and <beta|beta> should be 1) you will find that the matrix ends up being

\left[<br /> \begin{matrix}<br /> \frac{1}{2} &amp; 0\\ <br /> 0 &amp; \frac{1}{2}\\ <br /> \end{matrix}<br /> \right]<br />

Seems to work for me if we assume the "face up" and "face down" terms have a factor of 1/sqrt(2), not 1/2...

1. What does it mean "if the alpha and beta states of our card were taken as the fundamental basis, the density matrix for our fallen card would be diagonal to start with"? What does becoming "diagonal" mean?

As seen by the equations in the tutorial it looks like you need a set of basis vector (corresponding to the possible outcomes of whatever you plan to measure, in this case alpha or beta) to define \mid a_i \rangle in the density matrix. Diagonal just means that only the elements of the matrix along the line from upper left to lower right are nonzero, in this case only \rho_{11} and \rho_{22}, the other terms are zero. When he said "the density matrix for our fallen card would be diagonal to start with", he was taking as the "starting" condition that the card had just been measured in the |alpha> state, so here I guess you could have a statistical ensemble where \mid \psi_1 \rangle = |alpha> and \mid \psi_2 \rangle = |beta>, in which case measuring it to be in |alpha> would mean p1=1 and p2=0. If you plug that into the above equations you do get

\left[<br /> \begin{matrix}<br /> 1 &amp; 0\\ <br /> 0 &amp; 0\\ <br /> \end{matrix}<br /> \right]<br />

which qualifies as diagonal.

2. How come if the card is in alpha state, decoherence would amost instantaneously change the state to the 2nd density matrix?

From the above, I think it's because decoherence drives the system into a statistical mixture of position eigenstates, in this case a 1/2 probability of face-up and a 1/2 probability of face-down.

3. And why if the card was in alpha state, one would get a random outcome? What random outcome is it talking about?

In that statement he was talking about what would happen when the card was no longer in the alpha state, but had been driven by decoherence into a statistical mixture of face-up and face-down...in that case if you measured again in the alpha/beta basis, it'd be random whether you got alpha or beta. Here were his words:

...the card is definitely in state alpha. However, decoherence would almost instantaneously change the state to

density matrix = \left[<br /> \begin{matrix}<br /> \frac{1}{2} &amp; 0\\ <br /> 0 &amp; \frac{1}{2}\\ <br /> \end{matrix}<br /> \right]<br />

so if we could measure whether the card was in the alpha or beta-states, we would get a random outcome.

 

[rodsika]

Decoherence means that the reduced density matrix for a bone, say, would come to be a mixed state where the amplitude is concentrated on position eigenstates and the interference terms were close to zero. But that's not quite the same as saying the particles have become "classical with definite positions", the mixed state would still look like a statistical ensemble of different position eigenstates, each of which would feature the particles in different sets of positions. So for example one position eigenstate might involve a given leg bone being upright because the cat is in a standing position, another might involve it being horizontal because the cat is in a sleeping position, the reduced density matrix would include both. Decoherence doesn't provide a "collapse" that selects one of the many position eigenstates, it just means that it's approximately correct to treat it as a statistical mixture of these different states rather than a superposition where you have to worry about interference effects.

You said that "Decoherence doesn't provide a "collapse" that selects one of the many position eigenstates".. but isn't it what the Preferred Basis is all about.. where it selects one of the many position eigenstates. This is why I equate decoherence with classicality. So why do we experience classical world while that 50 atoms in the 430 atom buckyball don't.

I think it's misleading to say they "become classical", as I said they don't go to any single definite set of positions, and it's only approximately correct to treat them as a regular statistical ensemble if you're just looking at those 50 particles and ignoring the other 380, you would still find interference effects if you looked at all 430 at once. Again think of the delayed choice quantum eraser, where if you just look at the probability distribution for signal photons ignoring correlations with idlers, you find a non-interference pattern on the screen behind the double slit, but if you consider the conditional probability that a signal photon landed at various positions given that the idler was detected at some detector, then here there may be an interference pattern.

Let's take the case of this universe. Our universe can be said to be totally isolated in a 100% isolation box. Decoherence has produced classical Earth with definite positions and this classicality is all over the entire universe (which becomes classical) or to put it in another form. How come the universe is classical when it supposedly should experience macroscopic superposition just like the cat as both are 100% isolated. The cat is like the universe enclosed in 100% hypothetical isolation box too. How come the cat is in superposition with no definite classical region like a classical liver organ, while this universe has a classical Earth and galaxy and so on. This was what I meant in my previous message. Again let's ignore Many worlds for now because Many worlds are all classical in the branches.

Copenhagen is just sort of agnostic about what's "really" going on in the box before measurement, it just says that we model the inside of the box as a big superposition in order to figure out the probabilities of various outcomes when we open it. In terms of Copenhagen, say you could prepare some vast number of boxes with the identical cats measured to be in identical initial pure states at the moment the box was sealed,[ and then for each one you opened the box after some fixed time and made another exhaustive measurement of all the particles, and then you looked at the statistical patterns in all these different experiments, constructing a probability distribution on different final outcomes. In that case, the probability distribution for different final outcomes involving all the particles would show interference effects (akin to how the probability distribution for signal and idler shows interference), but if you just looked at "reduced" final outcomes which only involved paying attention to a particular subsystem of particles in each final measurement, here the probability distributions for different possible outcomes would show virtually no interference (akin to how the probability distribution for signal photon alone, throwing out information about the idler, doesn't show interference).

 

[JesseM]

You said that "Decoherence doesn't provide a "collapse" that selects one of the many position eigenstates".. but isn't it what the Preferred Basis is all about.. where it selects one of the many position eigenstates.

No...again, a "basis" is a set of vectors, not a single vector! Decoherence selects the position basis as the "preferred basis" (or comes very close to doing so) for macroscopic systems, but the position basis is a set of different position eigenstates.

Let's take the case of this universe. Our universe can be said to be totally isolated in a 100% isolation box. Decoherence has produced classical Earth with definite positions and this classicality is all over the entire universe (which becomes classical) or to put it in another form. How come the universe is classical when it supposedly should experience macroscopic superposition just like the cat as both are 100% isolated. The cat is like the universe enclosed in 100% hypothetical isolation box too. How come the cat is in superposition with no definite classical region like a classical liver organ, while this universe has a classical Earth and galaxy and so on. This was what I meant in my previous message. Again let's ignore Many worlds for now because Many worlds are all classical in the branches.

How can you say "decoherence has produced classical earth" if you want to "ignore Many worlds"? Again, decoherence does not provide a collapse onto a single classical state, it provides no help for those who want a Copenhagen-like interpretation where there is only a single definite outcome.

 

[rodsika]

No...again, a "basis" is a set of vectors, not a single vector! Decoherence selects the position basis as the "preferred basis" (or comes very close to doing so) for macroscopic systems, but the position basis is a set of different position eigenstates.

How can you say "decoherence has produced classical earth" if you want to "ignore Many worlds"? Again, decoherence does not provide a collapse onto a single classical state, it provides no help for those who want a Copenhagen-like interpretation where there is only a single definite outcome.

Here's entry of Decoherence in Wikipedia:

"Decoherence does not provide a mechanism for the actual wave function collapse; rather it provides a mechanism for the appearance of wavefunction collapse. The quantum nature of the system is simply "leaked" into the environment so that a total superposition of the wavefunction still exists, but exists — at least for all practical purposes — beyond the realm of measurement."

That is.. the other branches are simply beyond the realm of measurement... which could really vanish if one won't want to accept Many Worlds. Actually. Majority of scientists who believe in Decoherence don't believe in Many Worlds. You describe the situation as:

In practice though I think most physicists who work on the issue of decoherence would reject the idea that any special "collapse" happens on measurement, even for a non-isolated system, regardless of whether they accept all the ideas associated with the MWI (they might accept the mathematical formalism of the MWI but be agnostic about whether other versions of the same human experimenters besides the ones they experience can really be considered 'real' for example...some might also prefer other no-collapse interpretations like Bohmian mechanics).

Of course they reject the idea that any special collapse occurs in decoherence. Instead. They believe that the quantum nature of the system is simply "leaked" into the environment so that a total superposition of the wavefunction still exists. But that doesn't necessarily mean believing in Many Worlds.

So in the buckyball double slit experiment. What really happens in between emission and detection. If we don't accept Many Worlds. We can say the buckyball is literally in superposition or smeared out. Can this be refuted? If not. This actual superposition without Many Worlds is possible.

Going to the universe in isolation which should supposed to be in superposition. You can't argue that just because it is not in macroscopic superposition mean Many World is true. Who knows. There may be something outside the universe like inflationary bubble universes that can serve as environment and our classical world is a result of decoherence. Remember that the whole programme of Decoherence is to help explain why the world is classical. Are you saying that either one has to accept Many Worlds or just treat this whole decoherence thing as mere calculational aid similar to Copenhagen treatment of the wave function as for calculational purpose only? But this is possible too.. that decoherence works but only in calculational sense as far as wave function and Born rule is concerned. Why does decoherence automatically entail real Many Worlds in the branches? Why can't decoherence just be pure math like calculational aid for how the wave function behave that doesn't use the collapse concept?

 

[JesseM]

Here's entry of Decoherence in Wikipedia:

"Decoherence does not provide a mechanism for the actual wave function collapse; rather it provides a mechanism for the appearance of wavefunction collapse. The quantum nature of the system is simply "leaked" into the environment so that a total superposition of the wavefunction still exists, but exists — at least for all practical purposes — beyond the realm of measurement."

That is.. the other branches are simply beyond the realm of measurement... which could really vanish if one won't want to accept Many Worlds.

If you don't accept MWI, then what determines which one is "your" branch and which are the "other branches" that are "beyond the realm of measurement"? Decoherence alone provides no help with this, you would have to add something akin to the Born rule to randomly select one of the members of the statistical ensemble produced by decoherence. So, you're still incorrect to suggest that decoherence alone could provide something like a "collapse" into a single classical state where everything has a single well-defined position.

Majority of scientists who believe in Decoherence don't believe in Many Worlds.

What does "believe in Decoherence" mean? Decoherence just follows from the QM, but you can accept the math without believing it somehow solves the measurement problem. If you're claiming that most of the scientists who think decoherence provides a solution to the measurement problem don't accept many worlds (or some variant like decoherent histories), I don't think you're necessarily correct about that.

Of course they reject the idea that any special collapse occurs in decoherence. Instead. They believe that the quantum nature of the system is simply "leaked" into the environment so that a total superposition of the wavefunction still exists. But that doesn't necessarily mean believing in Many Worlds.

Can you provide any quotes from scientists who believe that "a total superposition of the wavefunction still exists" but don't believe in many-worlds? That position doesn't really make much sense to me.

Going to the universe in isolation which should supposed to be in superposition. You can't argue that just because it is not in macroscopic superposition mean Many World is true. Who knows. There may be something outside the universe like inflationary bubble universes that can serve as environment and our classical world is a result of decoherence. Remember that the whole programme of Decoherence is to help explain why the world is classical. Are you saying that either one has to accept Many Worlds or just treat this whole decoherence thing as mere calculational aid similar to Copenhagen treatment of the wave function as for calculational purpose only? But this is possible too.. that decoherence works but only in calculational sense as far as wave function and Born rule is concerned. Why does decoherence automatically entail real Many Worlds in the branches? Why can't decoherence just be pure math like calculational aid for how the wave function behave that doesn't use the collapse concept?

Even those who do make use of the "collapse concept" (the Born rule) can still use the math of decoherence to describe how a complex quantum system evolves before we measure it. For example I imagine you could use it to explain why, in the double-slit experiment with an electron, if the electron is traveling through a gas rather than a vacuum, then when we measure its position on the screen the probability distribution won't show interference, much like if we had measured which slit it went through (even though we didn't). Decoherence could explain why the electron's interactions with the gas molecules acted in a way similar to a measurement, even though we didn't measure it and it would be impossible in practice for us to deduce which slit it went through by measuring all the gas molecules.

But note that in this example there'd still be assumed a final measurement when the electron hit the screen, where the Born rule applied to the wavefunction of the whole system would be used to get probabilities the electron would be measured at different positions. If you want to make use of decoherence with no uses of the Born rule, I think you'd have trouble for exactly the same reason that it's problematic to derive probabilities from the many-worlds interpretation. How would your hypothetical physicist using it as a "calculational aid" actually get any predictions about the results of real-world experiments if he couldn't use the Born rule to get probabilities? The data we get from real-world experiments consists of statistics, not complex amplitudes.

 

[rodsika]

Here's entry of Decoherence in Wikipedia:

"Decoherence does not provide a mechanism for the actual wave function collapse; rather it provides a mechanism for the appearance of wavefunction collapse. The quantum nature of the system is simply "leaked" into the environment so that a total superposition of the wavefunction still exists, but exists — at least for all practical purposes — beyond the realm of measurement."

That is.. the other branches are simply beyond the realm of measurement... which could really vanish if one won't want to accept Many Worlds. Actually. Majority of scientists who believe in Decoherence don't believe in Many Worlds. You describe the situation as:



Of course they reject the idea that any special collapse occurs in decoherence. Instead. They believe that the quantum nature of the system is simply "leaked" into the environment so that a total superposition of the wavefunction still exists. But that doesn't necessarily mean believing in Many Worlds.

So in the buckyball double slit experiment. What really happens in between emission and detection. If we don't accept Many Worlds. We can say the buckyball is literally in superposition or smeared out. Can this be refuted? If not. This actual superposition without Many Worlds is possible.

Going to the universe in isolation which should supposed to be in superposition. You can't argue that just because it is not in macroscopic superposition mean Many World is true. Who knows. There may be something outside the universe like inflationary bubble universes that can serve as environment and our classical world is a result of decoherence. Remember that the whole programme of Decoherence is to help explain why the world is classical. Are you saying that either one has to accept Many Worlds or just treat this whole decoherence thing as mere calculational aid similar to Copenhagen treatment of the wave function as for calculational purpose only? But this is possible too.. that decoherence works but only in calculational sense as far as wave function and Born rule is concerned. Why does decoherence automatically entail real Many Worlds in the branches? Why can't decoherence just be pure math like calculational aid for how the wave function behave that doesn't use the collapse concept?

Are you saying there are 2 kinds of Decoherence...

1. Decoherence that still make use of "collapse concept" (the Born rule)

2. Decoherence that doesn't use the collapse concept.

　

You said "Even those who do make use of the "collapse concept" (the Born rule) can still use the math of decoherence to describe how a complex quantum system evolves before we measure it."

　

In the famous experiment by Anton Zeilinger and company depicted graphically in

http://www.mpipks-dresden.mpg.de/~klh/research/decoherence/thermodeco/index.html

Decoherence was said to be proven. But do they mean Collapse is refuted by the experiment, or is it like your example of the electron moving in the cloud of gas? Does Zeilinger experiment still need the Born rule?

Also I assume that Born rule automatically mean the concept of collapse, right? In the web site, you can see graphically that the interference disappears slowly. But in collapse model, any initial contact with the outside world should immediately collapse the wave function. Is the experiment proving that collapse didn't occur and does the experiment refute the idea of wavefunction collapse?

I first heard of the experiment years ago and thought it had proven the concept of Decoherence.

Yesterday I kinda got an idea from your message that proof of Decoherence automatically mean proof of Many Worlds? Are you saying this?

If not. What's the distinction or how to distinguish between the Decoherence that proves Many Worlds and Decoherence that still use the Born rule?

Maybe Decoherence in Many Worlds involves Universal Wavefunction that decohere versus Decoherence in Born rule that involves just messing up the coherence? But doesn't this latter automaticaly imply the branches got split off in the Zeilinger buckyball decoherence experiment? and branches splitting off mean Many Worlds? If not. How can there be two branches or more (I assume the buckyball decohering means there are branches that got split off) and not involve Many Worlds?

This is all quite confusing.

Many thanks for your assistance.

 

[JesseM]

Are you saying there are 2 kinds of Decoherence...

1. Decoherence that still make use of "collapse concept" (the Born rule)

2. Decoherence that doesn't use the collapse concept.

Decoherence itself just deals with an aspect of how the wave function for a complex system evolves, but any time you have a wave function you can use the Born rule to get probabilities of different measurement outcomes from that.

In the famous experiment by Anton Zeilinger and company depicted graphically in

http://www.mpipks-dresden.mpg.de/~klh/research/decoherence/thermodeco/index.html

Decoherence was said to be proven. But do they mean Collapse is refuted by the experiment, or is it like your example of the electron moving in the cloud of gas? Does Zeilinger experiment still need the Born rule?

Still needs the Born rule, seems to be fairly similar to the idea of the electron moving through gas, except he's showing for lower-temperature environment the fullerene's probability distribution (found using the Born rule) does show interference, then this is destroyed for a higher-temperature environment.

Also I assume that Born rule automatically mean the concept of collapse, right? In the web site, you can see graphically that the interference disappears slowly. But in collapse model, any initial contact with the outside world should immediately collapse the wave function. Is the experiment proving that collapse didn't occur and does the experiment refute the idea of wavefunction collapse?

No, the only "collapse" is the final measurement of the fullerene's position, the model wouldn't assume any collapse due to decoherence with the environment on its way to the detector. The probability distribution for it to be found at various final positions shows interference if the temperature is lower, then the interference in this same probability distribution gradually disappears if the temperature is raised, showing that a hot environment has effects similar to a measurement of the fullerene as it traveled even though no actual collapse due to measurement was invoked until the very end when its position was measured at the final detector.

Yesterday I kinda got an idea from your message that proof of Decoherence automatically mean proof of Many Worlds? Are you saying this?

No, of course not, why would I specifically talk about how decoherence can be used in combination with the "collapse" concept if I was saying that?

If not. What's the distinction or how to distinguish between the Decoherence that proves Many Worlds and Decoherence that still use the Born rule?

Decoherence can't "prove" the MWI, it's just invoked by MWI advocates to try to explain why you wouldn't expect any macroscopic superpositions of different position states in the MWI. The math of decoherence itself is exactly the same in terms of what it says about the evolution of the reduced density matrix for a given subsystem, it's just that if you use the Born rule you can then use this reduced density matrix to get a probability distribution for different measurement outcomes when you measure the subsystem, with the MWI you're not supposed to invoke such a collapse due to measurement and the reduced density matrix is just seen as a sort of ensemble of different parallel versions of the subsystem which are all equally real.

Maybe Decoherence in Many Worlds involves Universal Wavefunction that decohere versus Decoherence in Born rule that involves just messing up the coherence?

I don't understand what this means. Again, the actual math would be exactly the same up until the moment the Born rule is invoked to get a probability distribution for various outcomes (like the buckyball being found at various positions by the final detector, after already having passed through the three gratings).

But doesn't this latter automaticaly imply the branches got split off in the Zeilinger buckyball decoherence experiment? and branches splitting off mean Many Worlds? If not. How can there be two branches or more (I assume the buckyball decohering means there are branches that got split off) and not involve Many Worlds?

What do you mean "branches that got split off"? The reduced density matrix for the buckyball would look like something close to an ensemble of classical states without interference between them, in the MWI you might call these different states "branches" but there'd be no reason to do so in the Copenhagen interpretation, instead the reduced density matrix would just be used to calculate the probabilities for which state would actually be found on measurement, there'd be no reason to view them as a set of equally real "branches".

Do you understand that decoherence is really just a derived consequence of the standard QM rules for wavefunction evolution applied to complex systems, it isn't some fundamentally new law?

 

[rodsika]

For years I was under the impression that decoherence was supposed to replace the idea of wave function collapse. If you will read the wikipedia article on "quantum decoherence", you will see it direclty gives the impression that collapse no longer occurs. For example, one part reads:

"Before an understanding of decoherence was developed the Copenhagen interpretation of quantum mechanics treated wavefunction collapse as a fundamental, a priori process. Decoherence provides an explanatory mechanism for the appearance of wavefunction collapse"

Are you sure collapse still occurs?

In a typical electron double slit experiment, any photon that disturbs it will dephase the phase coherence and give the appearance of wavefunction collapse. They often explain it that the wave function is still there and not really collapsed (even after final measurement). This was the idea in my mind for some 5 years.

Are you saying wave function collapse still happens? Try to read the whole wikipedia article. Maybe you are mistaken? The start of that article says:

"In quantum mechanics, quantum decoherence (also known as dephasing) is how quantum systems interact with their environments to exhibit probabilistically additive behavior. Quantum decoherence gives the appearance of wave function collapse (the reduction of the physical possibilities into a single possibility as seen by an observer) and justifies the framework and intuition of classical physics as an acceptable approximation: decoherence is the mechanism by which the classical limit emerges out of a quantum starting point and it determines the location of the quantum-classical boundary."

It says "Quantum decoherence gives the appearance of wave function collapse ". It means wave function collapse didn't happen at all.

You will say what determines the probability if not the born rule which assumes collapse. But no. Decoherence automatically goes in hand with environment selection of the preferred basis (like if it is fast, position basis is chosen, if slow, energy basis is chosen). This means no collapse really occurs at all! So I think you are mistaken to think that collapse occurs in the general idea of Quantum Decoherence.

 

[JesseM]

For years I was under the impression that decoherence was supposed to replace the idea of wave function collapse. If you will read the wikipedia article on "quantum decoherence", you will see it direclty gives the impression that collapse no longer occurs. For example, one part reads:

"Before an understanding of decoherence was developed the Copenhagen interpretation of quantum mechanics treated wavefunction collapse as a fundamental, a priori process. Decoherence provides an explanatory mechanism for the appearance of wavefunction collapse"

Are you sure collapse still occurs?

In the Copenhagen interpretation it is still a necessary part of deriving the final probability distribution for various outcomes (like the probability distribution for the buckyball to be detected at various positions by the final detector, a probability distribution that shows interference effects if the temperature was lower but no interference effects if the temperature was higher). That doesn't mean Copenhagen advocates necessarily believe the collapse really "occurs" in an ontological sense, just that it's a necessary part of our human models for making predictions.

Are you saying wave function collapse still happens? Try to read the whole wikipedia article. Maybe you are mistaken? The start of that article says:

"In quantum mechanics, quantum decoherence (also known as dephasing) is how quantum systems interact with their environments to exhibit probabilistically additive behavior. Quantum decoherence gives the appearance of wave function collapse (the reduction of the physical possibilities into a single possibility as seen by an observer) and justifies the framework and intuition of classical physics as an acceptable approximation: decoherence is the mechanism by which the classical limit emerges out of a quantum starting point and it determines the location of the quantum-classical boundary."

It says "Quantum decoherence gives the appearance of wave function collapse ". It means wave function collapse didn't happen at all.

It "gives the appearance of wave function collapse" at a stage before our model actually includes any collapse, for example in my electron passing through a gas example, it means the probability distribution for the electron to show up at various positions on the screen doesn't show interference, just as if it was measured going through the slits and its wavefunction had collapsed then, even though in fact we did not apply a "collapse" to the electron/gas wavefunction until the moment the electron was detected at the screen.

Again it seems as if you don't understand that decoherence changes nothing about the basic formalism of QM, in the Copenhagen interpretation you still have a quantum state vector that evolves according to the Schroedinger equation between measurements, and then on measurement you derive probabilities from the state vector at that moment using the Born rule. Are you familiar with the basic mathematical formalism here, or is your understanding based only on verbal summaries?

You will say what determines the probability if not the born rule which assumes collapse. But no. Decoherence automatically goes in hand with environment selection of the preferred basis (like if it is fast, position basis is chosen, if slow, energy basis is chosen). This means no collapse really occurs at all! So I think you are mistaken to think that collapse occurs in the general idea of Quantum Decoherence.

Yes, it selects a preferred basis for a given subsystem (or comes very close to doing so, the interference terms never entirely disappear), but again remember that a basis is a set of different states, not a single one. Decoherence alone doesn't provide for any sort of collapse into a single position eigenstate, nor is there any obvious way for it to assign probabilities to the different eigenstates without invoking the Born rule. Anytime you see physicists using decoherence to make probabilistic predictions about what will actually be observed in a given experiment, their calculations always involve using the Born rule at the very end, even if decoherence may make the final probability distribution for the end state mirror the probability that would be expected if an earlier "collapse" had happened (like in the electron/gas experiment where the final probability distribution for the electron looks just like the one you'd expect if the electron had been measured going through the slits and collapsed then, even though the calculations involved no such earlier collapse).

 

[rodsika]

No...again, a "basis" is a set of vectors, not a single vector! Decoherence selects the position basis as the "preferred basis" (or comes very close to doing so) for macroscopic systems, but the position basis is a set of different position eigenstates.

Thanks. I understood how I miunderstood it all these years. Anyway. Going back to the above we discussed yesterday (message #36)

You said that "Decoherence selects the position basis as the "preferred basis" (or comes very close to doing so) for macroscopic systems, but the position basis is a set of different position eigenstates." In our classical world. We have exact value of the position eigenstates. So in our classical world what selects one of the many position eigenstates in this concept of Preferred Basis in Decohrence in MWI that doesn't use the Born Rule?

 

[JesseM]

Thanks. I understood how I miunderstood it all these years. Anyway. Going back to the above we discussed yesterday (message #36)

You said that "Decoherence selects the position basis as the "preferred basis" (or comes very close to doing so) for macroscopic systems, but the position basis is a set of different position eigenstates." In our classical world. We have exact value of the position eigenstates. So in our classical world what selects one of the many position eigenstates in this concept of Preferred Basis in Decohrence in MWI that doesn't use the Born Rule?

Well, in the MWI nothing selects one of them, they're all seen as equally real, but naturally they each include different classical states for my brain so each version of my brain is only experiencing one version of the world around it (again, in an approximate sense since decoherence does not lead interference terms in the density matrix with a position basis to go exactly to zero). But defining what it means to have different "probabilities" for different outcomes is problematic in the MWI.

 

[JesseM]

Hi, You think a MWI-less and Born Rule-less Decoherence -> Preferred Basis -> Selection of one of the many position eigenstates via stochastic processes in the vacuum or Planck scale (see details below) is possible?

No, I don't know of any way decoherence without the Born rule can select a particular position out of eigenstates out of many. That was why in post #36 I said:

No...again, a "basis" is a set of vectors, not a single vector! Decoherence selects the position basis as the "preferred basis" (or comes very close to doing so) for macroscopic systems, but the position basis is a set of different position eigenstates.

How can you say "decoherence has produced classical earth" if you want to "ignore Many worlds"? Again, decoherence does not provide a collapse onto a single classical state, it provides no help for those who want a Copenhagen-like interpretation where there is only a single definite outcome.

and in post #38 I said:

If you don't accept MWI, then what determines which one is "your" branch and which are the "other branches" that are "beyond the realm of measurement"? Decoherence alone provides no help with this, you would have to add something akin to the Born rule to randomly select one of the members of the statistical ensemble produced by decoherence. So, you're still incorrect to suggest that decoherence alone could provide something like a "collapse" into a single classical state where everything has a single well-defined position.

The quote by Mulhauser that you mention appears in section 6.7 on p.13 of this paper, he's a philosopher and I don't think these speculations are justifiable in terms of any existing theory or interpretation of QM, I don't know why he thinks that "interactions of hidden variables in the so-called quantum vacuum" would "explain fluctuations in the quantum vacuum" or "offer deterministic predictions about which of several actual states a decohering system might enter." Without more detail I have no idea what he's talking about, and I definitely don't think these are mainstream ideas.