Classical states and decoherence

[lucas_]

It is stated that classical states are robust against decoherence.. what would happen if classical states can decohere too? Or how do you imagine it for example occurring to a table.. How would the table look like if it suffers decoherence too? Would you fall down if you sit on one?

 

[StevieTNZ]

I think you have misunderstood what decoherence is. Decoherence is where a sufficiently large quantum object interacts with its environment. Because of the nature of the interaction the resulting state describing the system looks like classical probabilities -- the interference vanishes (although in principle the quantum system + environment remain in superposition).

 

[bhobba]

It is stated that classical states are robust against decoherence.. what would happen if classical states can decohere too?

Classical states are decohered by the environment. For that not to happen some quite advanced technology needs to be used - but when that's done some very strange effects occur:
http://physicsworld.com/cws/article/news/2010/mar/18/quantum-effect-spotted-in-a-visible-object

Thanks
Bill

 

[lucas_]

StevenTNZ and Bhobba.. I was referring to Einselection (Environment-Induced Superselection).

http://cnls.lanl.gov/~dalvit/Publications_files/PRA-72-062101-2005.pdf

"Persistent monitoring of an open quantum system by its
environment can single out a preferred set of states, known
as pointer states. Pointer states are the most robust in spite of
the interaction with the environment. That is, they entangle
least with the environment, and, hence, are least perturbed by
it. This is the essence of environment-induced superselection.

Hence the pointer states, or classical states are robust against decoherence. Contrary to Bill statement that "Classical states are decohered by the environment".

Can someone describe what really is Einselection (Environment-induced superselection). I'm confused by it and can't connect it with standard QM. What is its counterpart in the standard QM. Again. What would happen if classical states decohere too. Then perhaps we won't have an observable of position in our daily life but momentum? Is this what it's saying? It's like particles can choose either position or momentum.. and if decoherence occur even to classical or pointer states, then we should have observable of momentum and not position. so we won't have two feet to walk in position basis but momentum (whatever or how-ever it is).

 

[bhobba]

Hence the pointer states, or classical states are robust against decoherence. Contrary to Bill statement that "Classical states are decohered by the environment".

Its not contrary to it - its an example of it.

Can someone describe what really is Einselection (Environment-induced superselection)

Its simple. Decoherence is an interaction between systems, usually the environment, that transforms a pure state into a mixed state in a particular basis. Most of the time its in the position basis. And that basis is stable meanting it does not change as the interaction evolves. The technical detains of why you can find in page 83 of:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

Its got to with most interactions are of the radial type.

The whole issue is examined in chapter two of the above reference which, if it interests you, I strongly suggest you get a copy of.

First though do you understand the difference between a pure state and a mixed state?

Thanks
Bill

 

[lucas_]

Its not contrary to it - its an example of it.
Its simple. Decoherence is an interaction between systems, usually the environment, that transforms a pure state into a mixed state in a particular basis. Most of the time its in the position basis. And that basis is stable meanting it does not change as the interaction evolves. The technical detains of why you can find in page 83 of:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

Its got to with most interactions are of the radial type.

The whole issue is examined in chapter two of the above reference which, if it interests you, I strongly suggest you get a copy of.

First though do you understand the difference between a pure state and a mixed state?

Thanks
Bill

I own the book. Have just reread page 83 and got the points but it speaks of particles. I also know the difference between a pure state and mixed state. I'm talking of macroscopic object and specifically the following passage:

http://www.nature.com/news/2004/041223/full/news041220-12.html

"The difficulty arises because directly finding out something about a quantum system by making a measurement inevitably disturbs it. "After a measurement," say Wojciech Zurek at Los Alamos National Laboratory in New Mexico and his colleagues, "the state will be what the observer finds out it is, but not, in general, what it was before."

Because, as Zurek says, "the Universe is quantum to the core," this property seems to undermine the notion of an objective reality. In this type of situation, every tourist who gazed at Buckingham Palace would change the arrangement of the building's windows, say, merely by the act of looking, so that subsequent tourists would see something slightly different."

Bhobba. What the above is implying is that if Einselection is temporary switched off, the Buckingham Palace window would keep changing depending on the gaze of each tourist. Here the position observable is still used, but I'm thinking the billions of atoms in the windows is decohered by the environment, so position is already fixed.. so if Einselection is suppressed, how would it make the windows rearrange every time a different tourist look at it? This is what I couldn't understand for years.

 

[bhobba]

Bhobba. What the above is implying is that if Einselection is temporary switched off, the Buckingham Palace window would keep changing depending on the gaze of each tourist

Exactly how do you do that?

Its inherent in the interaction Hamiltonian.

QM does undermine the notion of objective reality. Its related to the problem of outcomes which is also discussed in that book. However decoerence is observer independant.

Thanks
Bill

 

[lucas_]

Exactly how do you do that?

Its inherent in the interaction Hamiltonian.

QM does undermine the notion of objective reality. Its related to the problem of outcomes which is also discussed in that book. However decoerence is observer independant.

Thanks
Bill

the interaction Hamiltonian is in the levels of particles... here positions or energy or momentum can be chosen. But in the Buckingham Palace, it is in the positions of each particles.. but how does the window rearrange when you are not changing position to momentum but just positions. So even without Einselection, the positions of each millimeter of the window is still decohered. Is the window a valid example or a wrong example of the application of Einselection?

 

[bhobba]

but how does the window rearrange when you are not changing position to momentum but just positions.

Come again. Windows and typical macro objects are decohered to be in eigenstates of position - that's the exact import of the page number I gave. Most Hamilitonians are radial.

Thanks
Bill

 

[lucas_]

Come again. Windows and typical macro objects are decohered to be in eigenstates of position - that's the exact import of the page number I gave. Most Hamilitonians are radial.

Thanks
Bill

I was wondering if the Nature author gave a vague example. In the book particles can be eigenstates of position or momentum or energy. But in the article. The palace window is rearranging itself.. you are saying this is still a good example of eigenstates of positions being controlled by Einselection?

 

[bhobba]

In the book particles can be eigenstates of position or momentum or energy

I am saying that because of the the radial nature of virtually all interactions encountered in practice (ie interacting with the air, stray photons etc) a window will be in eigenstates of position. The palace window rearranging itself? I have zero idea why you would think such would happen.

Thanks
Bill

 

[lucas_]

I am saying that because of the the radial nature of virtually all interactions encountered in practice (ie interacting with the air, stray photons etc) a window will be in eigenstates of position. The palace window rearranging itself? I have zero idea why you would think such would happen.

Thanks
Bill

Didnt you read the article

http://www.nature.com/news/2004/041223/full/news041220-12.html

it says without quantum darwism, the palace window would rearrange after each tourist stares at it. my main question is... without quantum darwism or how we get information from reflected photon and not directly interacting with it.. it is indeed possible the window rearrange itself after each tourist gaze?

 

[bhobba]

it says without quantum darwism, the palace window would rearrange after each tourist stares at it.

That's wrong.

From decoherence the position basis is singled out and we have an improper mixed state in it. The general interpretation is that the mixed state is a proper one which means it is actually in that state - but we don't know which one.

I am not an expert on Quantum Darwinism but my limited knowledge of it is its trying to give a purely quantum explanation of that interpretative assumption.

Added Later:
That's a lay article - to disentangle it you need to get the professional paper its based on. I reread the bit on Quantum Darwinism in Schlosshauer and it seems to be saying simply what I said above. We want a fully quantum explanation of how the improper mixed state becomes a proper one.

Thanks
Bill

 

[lucas_]

That's wrong.

From decoherence the position basis is singled out and we have an improper mixed state in it. The general interpretation is that the mixed state is a proper one which means it is actually in that state - but we don't know which one.

I am not an expert on Quantum Darwinism but my limited knowledge of it is its trying to give a purely quantum explanation of that interpretative assumption.

Added Later:
That's a lay article - to disentangle it you need to get the professional paper its based on. I reread the bit on Quantum Darwinism in Schlosshauer and it seems to be saying simply what I said above. We want a fully quantum explanation of how the improper mixed state becomes a proper one.

Thanks
Bill

The Nature layman article is based Zurek paper http://arxiv.org/abs/quant-ph/0105127
Basically Quantum Darwism is as the paper quotes it "Intercepting fragments of the environment allows observers to find out (pointer) state of the system without perturbing it". So the nature layman article is saying that because of quantum darwism, the Buckingham Palace window can't be perturbed by the stare of each tourist. But let's say there was no quantum darwism, can the palace window be perturbed if we send a photon to look at it (say a flashlight) such that the window can change shape? But the window is not in pure state, the positions of each particle is in improper mixed state which looks like proper mixed state (apparent collapse). Can a proper mixed state still be perturbed by the environment and re-prepare to pure state and back to another improper mixed state? I just want to know how accurate is that specific article about the palace window being able to change shape if tourist stares at it (if there was no quantum darwism). Let's just focus on the window thing accuracy.

 

[atyy]

The Nature layman article is based Zurek paper http://arxiv.org/abs/quant-ph/0105127
Basically Quantum Darwism is as the paper quotes it "Intercepting fragments of the environment allows observers to find out (pointer) state of the system without perturbing it". So the nature layman article is saying that because of quantum darwism, the Buckingham Palace window can't be perturbed by the stare of each tourist. But let's say there was no quantum darwism, can the palace window be perturbed if we send a photon to look at it (say a flashlight) such that the window can change shape? But the window is not in pure state, the positions of each particle is in improper mixed state which looks like proper mixed state (apparent collapse). Can a proper mixed state still be perturbed by the environment and re-prepare to pure state and back to another improper mixed state? I just want to know how accurate is that specific article about the palace window being able to change shape if tourist stares at it (if there was no quantum darwism). Let's just focus on the window thing accuracy.

Yes, the window analogy is more or less accurate. Let's go with the simplistic version of collapse just for the idea. A measurement P collapses the wave function randomly into an eigenstate of P. Then if a different measurement Q is made the wave function will randomly collapse into an eigenstate of Q. So for example if I measure position, the wave function will collapse into a narrow peak. Now if I measure momentum, the wave function will collapse into a spread out wave. If I alternate between position and momentum measurements, the wave function will keep jumping between being peaked and spread out. So in Zurek's analogy, each tourist is making a different measurement and so collapsing into an eigenstate of the respective measurements, so reality will be all jumpy.

In addition to Zurek's approach, other lines to explaining the conditions under which repeated or continuous measurements give classical results are:
http://arxiv.org/abs/1305.2517
http://arxiv.org/abs/1407.8090

I think in those papers, one does get a stochastic differential equation describing a jumpy reality. But as long as the jumps are "small", one will have recovered classical trajectories.

 

[lucas_]

Yes, the window analogy is more or less accurate. Let's go with the simplistic version of collapse just for the idea. A measurement P collapses the wave function randomly into an eigenstate of P. Then if a different measurement Q is made the wave function will randomly collapse into an eigenstate of Q. So for example if I measure position, the wave function will collapse into a narrow peak. Now if I measure momentum, the wave function will collapse into a spread out wave. If I alternate between position and momentum measurements, the wave function will keep jumping between being peaked and spread out. So in Zurek's analogy, each tourist is making a different measurement and so collapsing into an eigenstate of the respective measurements, so reality will be all jumpy.

In addition to Zurek's approach, other lines to explaining the conditions under which repeated or continuous measurements give classical results are:
http://arxiv.org/abs/1305.2517
http://arxiv.org/abs/1407.8090

I think in those papers, one does get a stochastic differential equation describing a jumpy reality. But as long as the jumps are "small", one will have recovered classical trajectories.

First of all, it was not Zurek's analogy, the Nature article was written by Philip Ball. Secondly, let me clarify, are you saying macroscopic object can change shape by perturbing it if quantum darwism is suppressed? But thermal vibrations can make each atom classical, so how do you make the whole object change shape? Or does it only work for system in pure state? not macroscopic object? or since a macroscopic object are improper mixed state, then you can make improper mixed state jumpy such that the window can really change shape?

 

[atyy]

First of all, it was not Zurek's analogy, the Nature article was written by Philip Ball. Secondly, let me clarify, are you saying macroscopic object can change shape by perturbing it if quantum darwism is suppressed? But thermal vibrations can make each atom classical, so how do you make the whole object change shape? Or does it only work for system in pure state? not macroscopic object? or since a macroscopic object are improper mixed state, then you can make improper mixed state jumpy such that the window can really change shape?

No, it is not that quantum darwinism can be suppressed. Rather, the emergence of the pointer states via decoherence is just one aspect of how classicality emerges from the quantum formalism. One still has to understand what happens when a sequence of measurements occurs after decoherence. Quantum darwinism is a different analysis of the same quantum formalism, trying to understand the role of repeated measurements for the emergence of classicality.

 

[lucas_]

No, it is not that quantum darwinism can be suppressed. Rather, the emergence of the pointer states via decoherence is just one aspect of how classicality emerges from the quantum formalism. One still has to understand what happens when a sequence of measurements occurs after decoherence. Quantum darwinism is a different analysis of the same quantum formalism, trying to understand the role of repeated measurements for the emergence of classicality.

So why doesn't the window rearrange itself everytime a tourists passes by it? Note in the article, it is arguing that because of quantum darwism, quantum barrier to perturbation seems to exist so we can't change the window. This is why I concluded that if there is no quantum darwism, the window can rearrange itself. Please confirm if the window is just analogy for microscopic system or it is also valid for macroscopic system. If so, how come we don't have experiment where window can change shape or how do we do the experiment to show it?

 

[atyy]

So why doesn't the window rearrange itself everytime a tourists passes by it? Note in the article, it is arguing that because of quantum darwism, quantum barrier to perturbation seems to exist so we can't change the window. This is why I concluded that if there is no quantum darwism, the window can rearrange itself. Please confirm if the window is just analogy for microscopic system or it is also valid for macroscopic system. If so, how come we don't have experiment where window can change shape or how do we do the experiment to show it?

Your question doesn't make any sense. There is no distinction between microscopic and macroscopic systems. They are both governed by quantum mechanics. Under some circumstances, quantum mechanics can be well approximated by classical mechanics. Deocherence and quantum darwinism are ways to explain under what circumstances the classical approximation is good.

 

[lucas_]

Your question doesn't make any sense. There is no distinction between microscopic and macroscopic systems. They are both governed by quantum mechanics. Under some circumstances, quantum mechanics can be well approximated by classical mechanics. Deocherence and quantum darwinism are ways to explain under what circumstances the classical approximation is good.

Your question doesn't make any sense. There is no distinction between microscopic and macroscopic systems. They are both governed by quantum mechanics. Under some circumstances, quantum mechanics can be well approximated by classical mechanics. Deocherence and quantum darwinism are ways to explain under what circumstances the classical approximation is good.

So how do you do the experiment. Let's take the case of a painting. If we put it inside a totally sealed box and no photons can get inside and we installed a camera and one active emitter. How do we make the painting change shape such that the picture in the painting would move? The article says quantum darwism acts as shield to avoid perturbing the object, so with the sealed box, no photons are being reflected off that object (hence suppressing quantum darwism). What must you transmit in the emitter to make the painting rearrange itself (just like the window in the article)?

 

[atyy]

So how do you do the experiment. Let's take the case of a painting. If we put it inside a totally sealed box and no photons can get inside and we installed a camera and one active emitter. How do we make the painting change shape such that the picture in the painting would move? The article says quantum darwism acts as shield to avoid perturbing the object, so with the sealed box, no photons are being reflected off that object (hence suppressing quantum darwism). What must you transmit in the emitter to make the painting rearrange itself (just like the window in the article)?

It's the same as asking how one does a Schroedinger cat experiment.

 

[lucas_]

It's the same as asking how one does a Schroedinger cat experiment.

Schroedinger cat can only occur in Many Worlds. It doesn't exist in Copenhagen nor Bohmian because classicality is Bohr's (or Bohms) terrain. So the Buckingham palace window would be different shapes in different branches of many worlds but fixed shape in Copenhagen or Bohmian.

Anyway. Thank you and Bill. I have tried to read most of references you gave in this and other messages and so would conclude your thoughts (answers and unanswers) are the same as in the books and papers..

Maybe 200 years from now. We'll have clearer answers.

 

[atyy]

Schroedinger cat can only occur in Many Worlds. It doesn't exist in Copenhagen nor Bohmian because classicality is Bohr's (or Bohms) terrain. So the Buckingham palace window would be different shapes in different branches of many worlds but fixed shape in Copenhagen or Bohmian.

Anyway. Thank you and Bill. I have tried to read most of references you gave in this and other messages and so would conclude your thoughts (answers and unanswers) are the same as in the books and papers..

Maybe 200 years from now. We'll have clearer answers.

No, that isn't true. Schroedinger's cat can occur "in principle" in any interpretation, and is a fundamental part of quantum mechanics. However, at present we only have the technology to perform "Schroedinger's furball" experiments. There is no fundamental difference between Schroedinger's furball experiments which have already been realized, and Schroedinger's cat experiments which have not. There is no sharp dividing line between microscopic and macroscopic. It is true that as things become more macroscopic, the classical approximation is usually more and more accurate. It is decoherence and quantum darwinism which attempt to explain why that is the case. But you have to bear in mind that even when decoherence and quantum darwinism lead to the classical approximation being good, the underlying quantumness is never suspended, and this underlying quantumness includes wave function collapse, which causes the observed reality to be jumpy. Decoherence and quantum darwinism explain why these jumps become small enough for the classical approximation to hold. The part that is interpretation dependent in what I wrote is that it is Copenhagen that has collapse, not Bohmian Mechanics or Many-Worlds. However, any successful interpretation must derive Copenhagen, so that is a lingua franca in quantum mechanics.

Also, decoherence is well established, but I am not so sure about quantum darwinism. My main point is that the problem Zurek raises as background to the quantum darwinism approach is the problem of reality being jumpy as a result of wave function collapse. The fundamental idea behind the window analogy is wave function collapse, which is an established part of quantum mechanics. As I mentioned in a previous post, there are other approaches that explain why the classical approximation is good, and quantum darwinism is just one of them.

 

[atyy]

If you would like to read for yourself to see that the window analogy is just a fanciful way of the talking about the jumpiness due to wave function collapse and sequential measurements of non-commuting observables, you can take a look at

http://arxiv.org/abs/quant-ph/0307229
"By contrast, an attempt to discover the state of a quantum system through a direct measurement generally leads to a collapse: after a measurement,
the state will be what the observer finds out it is, but not—in general—what it was before. Thus, it is difficult to claim that quantum states exist objectively in the same sense as their classical counterparts."

 

[lucas_]

If you would like to read for yourself to see that the window analogy is just a fanciful way of the talking about the jumpiness due to wave function collapse and sequential measurements of non-commuting observables, you can take a look at

http://arxiv.org/abs/quant-ph/0307229
"By contrast, an attempt to discover the state of a quantum system through a direct measurement generally leads to a collapse: after a measurement,
the state will be what the observer finds out it is, but not—in general—what it was before. Thus, it is difficult to claim that quantum states exist objectively in the same sense as their classical counterparts."

Ok. Thanks. Well. A separate inquiry.
It is said that we can't differentiate experimentally between a proper mixed state (collapse) vs. improper mixed state in decoherence (apparent collapse). Why, how many Planck length are the smeared out delocalization in improper mixed state vs proper. Is the smeared region smaller than the vacuum fluctuations or larger. If larger, and given technological progress.. can we probe what is the case, whether improper or proper mixed state (collapse)?

 

[atyy]

Ok. Thanks. Well. A separate inquiry.
It is said that we can't differentiate experimentally between a proper mixed state (collapse) vs. improper mixed state in decoherence (apparent collapse). Why, how many Planck length are the smeared out delocalization in improper mixed state vs proper. Is the smeared region smaller than the vacuum fluctuations or larger. If larger, and given technological progress.. can we probe what is the case, whether improper or proper mixed state (collapse)?

Forget about vacuum fluctuations, which don't really have a consensus definition. Proper and improper mixed states cannot be distinguished by "local" measurements, ie. measurements on subsystems. However, they can be distinguished by "global" measurements. Within quantum mechanics, global measurements can in principle be performed, even if in practice they cannot be.

 

[lucas_]

Forget about vacuum fluctuations, which don't really have a consensus definition. Proper and improper mixed states cannot be distinguished by "local" measurements, ie. measurements on subsystems. However, they can be distinguished by "global" measurements. Within quantum mechanics, global measurements can in principle be performed, even if in practice they cannot be.

Or let's just talk of the localization of a particle surrounded or perturbed by photons all over it (picture in one of the papers).. without collapse, the particle is decohered into position because of the dozens (or hundreds) of photons impinging all over it.. in this case, is there still a smearing of the localization and how would it compared to the localization of pure collapse where the particle is just classical?

 

[lucas_]

Or let me give numerical example if you can't understand what I meant by localization above. In collapse, say there is a position eigenvalue of 2.0mm localized from x-axis. In decoherence, it looks like a "collapse" that emulate an eigenvalue of say between 1.8mm to 2.2mm smeared.. something like this.. what is the actual smearing percentage of apparent collapse vs actual collapse in position?

 

[atyy]

Or let me give numerical example if you can't understand what I meant by localization above. In collapse, say there is a position eigenvalue of 2.0mm localized from x-axis. In decoherence, it looks like a "collapse" that emulate an eigenvalue of say between 1.8mm to 2.2mm smeared.. something like this.. what is the actual smearing percentage of apparent collapse vs actual collapse in position?

Whether or not there is collapse or just decoherence, each measurement outcome is (in principle) a perfectly localized point.

However, there is the question of whether the improper mixture from decoherence and the proper mixture from the projection postulate are identical. I don't know - probably should take a look at some of these reviews:
http://arxiv.org/abs/quant-ph/0312059
http://arxiv.org/abs/1404.2635

 

[bhobba]

However, there is the question of whether the improper mixture from decoherence and the proper mixture from the projection postulate are identical. I don't know - probably should take a look at some of these reviews:

They aren't - and that is exactly why decoherence by itself does not solve the measurement problem.

Thanks
Bill

 

[lucas_]

They aren't - and that is exactly why decoherence by itself does not solve the measurement problem.

Thanks
Bill

What is your evidence they aren't. Atty said "collapse or just decoherence, each measurement outcome is (in principle) a perfectly localized point"... meaning there is not even a smeared out difference of one Planck length between collapse and apparent collapse localization...

 

[lucas_]

I was able to tract bhbba reasoning and the plot thickens:

http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

page 39: "Postulating that although the system-apparatus is in an improper mixed
state, we can interpret it as a proper mixed state superficially solves the
problem of outcomes, but does not explain why this happens, how or when.
This kind of interpretation is sometimes called the ensemble-, or ignorance
interpretation. Although the state jSAi is supposed to describe an individual
quantum system, one claims that since we can only infer probabilities
from multiple measurements, the reduced density operator SA is supposed
to describe an ensemble of quantum systems, of which each member is in a
definite state."

I never like the Ignorance interpretation because it is just that, ignorance.
So we are forced to choose other interpretations. I prefer MWI, but in MWI, does one can no longer say that an improper mixed state can be interpretated as a proper mixed state? But still localization are still similar in improper mixed state and proper mixed state in MWI. Or not?

 

[atyy]

They aren't - and that is exactly why decoherence by itself does not solve the measurement problem.

I wasn't talking about whether collapse can be derived from decoherence (it cannot). The question was whether the distribution of outcomes following decoherence with a realistic environment matches the distribution of outcomes of a projective measurement.

 

[lucas_]

I was able to tract bhbba reasoning and the plot thickens:

http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

page 39: "Postulating that although the system-apparatus is in an improper mixed
state, we can interpret it as a proper mixed state superficially solves the
problem of outcomes, but does not explain why this happens, how or when.
This kind of interpretation is sometimes called the ensemble-, or ignorance
interpretation. Although the state jSAi is supposed to describe an individual
quantum system, one claims that since we can only infer probabilities
from multiple measurements, the reduced density operator SA is supposed
to describe an ensemble of quantum systems, of which each member is in a
definite state."

I never like the Ignorance interpretation because it is just that, ignorance.
So we are forced to choose other interpretations. I prefer MWI, but in MWI, does one can no longer say that an improper mixed state can be interpretated as a proper mixed state? But still localization are still similar in improper mixed state and proper mixed state in MWI. Or not?

In Many Worlds, the different Eigenvalues of say position has each own worlds.. coherence may have segregate them. Is this corret? In Copenhagen or even Ensemble/Ignorance, the other branches just vanish. So the main question to ask naturally is.. why is this branch selected and not others? is it right to think that the improper mixed state of this branch is indistinguishable from proper mixed state hence apparent collapse.. and is it valid (or correct) to ask what happened to the other branches.. like did they just disappear? I just want to grasp some bird's eye view of this before delving into the technical papers (because if one understand the concept, it is much easier to understand papers). Thanks.

 

[atyy]

In Copenhagen or even Ensemble/Ignorance, the other branches just vanish. So the main question to ask naturally is.. why is this branch selected and not others? is it right to think that the improper mixed state of this branch is indistinguishable from proper mixed state hence apparent collapse.. and is it valid (or correct) to ask what happened to the other branches.

Copenhagen cannot answer this question as to why the other branches disappear. If one does not postulate that all branches exist as in Many-Worlds, then one has to introduce hidden variables to explain why a particular branch is selected, as eg. Bohmian Mechanics does.

Basically, with Bohmian Mechanics, collapse of the wave function can be derived, ie. the transition from an improper mixture to a proper mixture can be derived.