Decoherence, Coherence, Pure State, Mixed State

[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.