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.

 

[lucas_]

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.

I searched for "apparent collapse" in the archive, read it the whole night and would like to ask something for clarification and want to get to the bottom of this. I know what Bhobba meant about improper mixed state with born rule being indistinguishable from proper mixture or collapse hence called apparent collapse. But he added that since you can insert collapse anywhere in the von Neumann chain, he inserts it after improper mixed state decoherence. Does this mean that when nobody look.. he insert the collapse (since he digs into ensemble/ignorance interpretation).. meaning without true collapse, the improper mixed state won't have definite outcome even if it looks and smell like a proper mixed state??

Another thing. Isn't it that waves can overlap so if all are waves, and the air molecules are waves and photons are waves, and you all have wave interacting.. how would they give rise to particles at all. So even with such apparent collapse, you need actual collapse (by inserting it when nobody looks) to give rise to definite outcome (give rise to solid matter)?

 

[atyy]

Does this mean that when nobody look.. he insert the collapse (since he digs into ensemble/ignorance interpretation).. meaning without true collapse, the improper mixed state won't have definite outcome even if it looks and smell like a proper mixed state??

Essentially yes, in the following sense. For any local observable, the proper and improper mixed states will give a definite classical outcome even without wave function collapse. The important question is whether we also get a definite quantum outcome which is labelled by a definite classical outcome. This is important if one makes successive measurements. Unless one introduces hidden variables or uses the Many-Worlds approach, this definite quantum outcome that is labelled by a definite classical outcome does not happen without wave function collapse.

 

[lucas_]

Essentially yes, in the following sense. For any local observable, the proper and improper mixed states will give a definite classical outcome even without wave function collapse. The important question is whether we also get a definite quantum outcome which is labelled by a definite classical outcome. This is important if one makes successive measurements. Unless one introduces hidden variables or uses the Many-Worlds approach, this definite quantum outcome that is labelled by a definite classical outcome does not happen without wave function collapse.

What is the difference between "definite quantum outcome" and definite classical outcome"? Any example.. anything to do with pointer states?

But without collapse, waves are still waves.. and wave that interact with wave still produce wave.. so how can particles even occur? Note born rule doesn't imply collapse, born rule just produce the probability...

 

[atyy]

What is the difference between "definite quantum outcome" and definite classical outcome"? Any example.. anything to do with pointer states?

Let's work in the Copenhagen interpretation, where there is the classical measuring apparatus and the quantum system. When one makes a measurement, one gets a definite reading of the classical measuring apparatus, which is the classical outcome. Also, after the measurement, the wave function collapses to produce a new state of the quantum system, which is the definite quantum outcome. So with a measurement one gets a definite classical outcome and a definite quantum outcome. The definite quantum outcome is used to predict the joint distribution of the classical outcomes of successive measurements.

But without collapse, waves are still waves.. and wave that interact with wave still produce wave.. so how can particles even occur? Note born rule doesn't imply collapse, born rule just produce the probability...

Well, it is still a "wave" after collapsing. The main point of collapse is that the time evolution is random, whereas the Schroedinger equation is deterministic. Forget about what a classical particle is, a quantum particle is a new thing in quantum mechanics that is different from the classical particle with a definite position and momentum. If a quantum particle has a trajectory, it cannot be a classical trajectory, but must be a Bohmian trajectory. The new quantum concept of a particle is more fundamental, and the classical particle is emergent as an approximation to the quantum particle.

 

[lucas_]

Let's work in the Copenhagen interpretation, where there is the classical measuring apparatus and the quantum system. When one makes a measurement, one gets a definite reading of the classical measuring apparatus, which is the classical outcome. Also, after the measurement, the wave function collapses to produce a new state of the quantum system, which is the definite quantum outcome. So with a measurement one gets a definite classical outcome and a definite quantum outcome. The definite quantum outcome is used to predict the joint distribution of the classical outcomes of successive measurements.
Well, it is still a "wave" after collapsing. The main point of collapse is that the time evolution is random, whereas the Schroedinger equation is deterministic. Forget about what a classical particle is, a quantum particle is a new thing in quantum mechanics that is different from the classical particle with a definite position and momentum. If a quantum particle has a trajectory, it cannot be a classical trajectory, but must be a Bohmian trajectory. The new quantum concept of a particle is more fundamental, and the classical particle is emergent as an approximation to the quantum particle.

Ok. Thanks. I'd like to understand the context of Bhobba "Apparent Collapse" which has hundreds of hits in the search box. In his view, observation needs collapse but in your view observation can occur without collapse, what is the subtle difference. Bhobba stated in the thread regarding Zurek's that:

Decoherence explains what is called APPARENT collapse. What it meant is that the system is in what is called an improper mixed state. A mixed stated is where you have a number of systems prepared in a definite state and present one randomly for observation. If an improper mixed state was like that collapse would have occurred - you are observing the system in the state you measured it. But an improper mixed state is different - it has exactly the same mathematical form - and no observation can tell the difference - but it was not prepared that way - an ACTUAL collapse is still required to account for an observation. It has been swept under the carpet so to speak - but its still there.

Bhobba said that "an ACTUAL collapse is still required to account for an observation" while you said that "after the measurement, the wave function collapses to produce a new state of the quantum system". Why is that orders reversed in yours and his case? Maybe by using essemble ignorance interpretation, the order got reverse? this is so subtle that in spite of hundreds of hits of "apparent collapse". I'm still a bit confused. Thanks.

 

[atyy]

Bhobba said that "an ACTUAL collapse is still required to account for an observation" while you said that "after the measurement, the wave function collapses to produce a new state of the quantum system". Why is that orders reversed in yours and his case? Maybe by using essemble ignorance interpretation, the order got reverse? this is so subtle that in spite of hundreds of hits of "apparent collapse". I'm still a bit confused. Thanks.

For projective measurements, it doesn't matter whether the wave function collapses first then you get the classical outcome, or whether you get the classical outcome first then the wave function collapses. However, there are more general sorts of wave function collapse or state reduction possibilities than projective measurements, and in those cases, it is better to state the classical result as being produced by the uncollapsed wave function.

In bhobba's ensemble interpretation, he usually includes decoherence and places the cut after decoherence. If one uses a finite dimensional description, then decoherence can always be followed by a projective measurement, in which case the order doesn't matter. (I think there might be some subtleties if the decoherence is not perfect, as is usually the case.)

The important idea is that collapse is really useful for predicting the results of the *next* measurement conditioned on the outcome of the first. If there is no next measurement, there is no need to postulate collapse.

As far as I understand, the differences between bhobba's ensemble interpretation and an orthodox Copenhagen-style interpretation are extremely minor and not conceptually very important. If bhobba had not called his interpretation "ensemble", I would have called it "Copenhagen".

 

[lucas_]

For projective measurements, it doesn't matter whether the wave function collapses first then you get the classical outcome, or whether you get the classical outcome first then the wave function collapses. However, there are more general sorts of wave function collapse or state reduction possibilities than projective measurements, and in those cases, it is better to state the classical result as being produced by the uncollapsed wave function.

In bhobba's ensemble interpretation, he usually includes decoherence and places the cut after decoherence. If one uses a finite dimensional description, then decoherence can always be followed by a projective measurement, in which case the order doesn't matter. (I think there might be some subtleties if the decoherence is not perfect, as is usually the case.)

The important idea is that collapse is really useful for predicting the results of the *next* measurement conditioned on the outcome of the first. If there is no next measurement, there is no need to postulate collapse.

As far as I understand, the differences between bhobba's ensemble interpretation and an orthodox Copenhagen-style interpretation are extremely minor and not conceptually very important. If bhobba had not called his interpretation "ensemble", I would have called it "Copenhagen".

But in the Kochen Specker theorem.. or even in aspect experiment, properties only exist upon measurement... so before collapse, there is no classical world. So you can't say classical outcome come first then quantum outcome. Unless this is the raw Copenhagen? But after Kochen Specker or Aspect's, Copenhagen is face lifted to the interpretation that reality doesn't exist before measurement (I think the old Copenhagen is everything is just on paper and just calculate). So what interpretations do you base yours or Bill's arguments (distinguishing is important)? Also how would it differ if wavefunctions have ontological existence and not just episthesmological. Would improper mixed state still have classical values or just purely quantum ontological wave functions? In this case, it does need collapse to turn to classical reality, isn't it. This is what I had in mind when I think of them.. so I can imagine them.. like an actual wave from all over impinging on dusts, etc.

 

[atyy]

But in the Kochen Specker theorem.. or even in aspect experiment, properties only exist upon measurement... so before collapse, there is no classical world. So you can't say classical outcome come first then quantum outcome. Unless this is the raw Copenhagen? But after Kochen Specker or Aspect's, Copenhagen is face lifted to the interpretation that reality doesn't exist before measurement (I think the old Copenhagen is everything is just on paper and just calculate). So what interpretations do you base yours or Bill's arguments (distinguishing is important)? Also how would it differ if wavefunctions have ontological existence and not just episthesmological. Would improper mixed state still have classical values or just purely quantum ontological wave functions? In this case, it does need collapse to turn to classical reality, isn't it. This is what I had in mind when I think of them.. so I can imagine them.. like an actual wave from all over impinging on dusts, etc.

Yes, in Copenhagen "reality" only happens when one measures and obtains a classical outcome. The classical outcome is "reality". There are two aspects to collapse: the classical outcome and the quantum outcome. In my language, getting the classical outcome alone is not collapse.

 

[bhobba]

But in the Kochen Specker theorem.. or even in aspect experiment, properties only exist upon measurement

That's not quite true. It doesn't apply to hidden variables eg the position of a particle in Bohmian Mechanics. The subtlety being the property and what is observed - QM is only concerned with observations..

Thanks
Bill

 

[lucas_]

That's not quite true. It doesn't apply to hidden variables eg the position of a particle in Bohmian Mechanics. The subtlety being the property and what is observed - QM is only concerned with observations..

Thanks
Bill

What I was asking was supposed wave function and collapse were real and not just occurring on paper, the entire analysis like apparent collapse in inproper mixed state etc are the same and we still need real collapse after apparent collapse? This is what I'm bit confused. What would be the changes.. if you have previously written about this in old messages... please refer me to them because I couldn't find any about it. Thanks.

 

[bhobba]

What I was asking was supposed wave function and collapse were real and not just occurring on paper, the entire analysis like apparent collapse in inproper mixed state etc are the same and we still need real collapse after apparent collapse?

Wave-function collapse is not part of QM - only some interpretations. For example its not in many worlds.

As far as I can see from what you wrote is if wave-function collapse is real then we will need real collapse after apparent collapse. Of course - but that's tautological.

How an improper mixed state becomes a proper one can be solved in a number of ways. I personally simply face it head on and say - I make no hypothesis.

Thanks
Bill

 

[lucas_]

Wave-function collapse is not part of QM - only some interpretations. For example its not in many worlds.

As far as I can see from what you wrote is if wave-function collapse is real then we will need real collapse after apparent collapse. Of course - but that's tautological.

How an improper mixed state becomes a proper one can be solved in a number of ways. I personally simply face it head on and say - I make no hypothesis.

Thanks
Bill

Yes, in Copenhagen "reality" only happens when one measures and obtains a classical outcome. The classical outcome is "reality". There are two aspects to collapse: the classical outcome and the quantum outcome. In my language, getting the classical outcome alone is not collapse.

you mentioned "in my language".. so it is not a standard thing about there being classical outcome and quantum outcome (any references)? What if in the double slit experiment, the photon or electron emitted doesn't want to collapse, then you won't measure anything, there will be no detection.. here quantum outcome produces classical outcome. I think it is a classical bias to think classical outcome is apriori, but if the photon/electron won't collapse into particle and continued being waves,, then you won't detect anything and no classical outcome at all.

 

[bhobba]

but if the photon/electron won't collapse into particle and continued being waves,, then you won't detect anything and no classical outcome at all.

I am having a bit of difficulty here. Quantum objects are neither particles or waves - that is a myth of QM:
http://arxiv.org/pdf/quant-ph/0609163.pdf

By assuming collapse from waves to particle and similar ideas not really part of QM you will of course run into problems.

I know you have Schlosshauer's book and he states the measurement problem correctly - it has nothing to do with collapse which isn't surprising since its not part of QM anyway. It is, from page 50:

1. The problem of a preferred basis
2. The problem of non-observability of interference.
3. The problem of outcomes.

Decoherence more or less solves the first two - it the third one that is the problem. Its basically how an improper mixed state becomes a proper one. That is the key issue. I am no expert on Quantum Darwinism, I just know about it from what Schlosshauer's writes in his book, but it looks like an attempt to give a purely quantum account of 3. But while Schlosshauer states its promising (page 88) I don't think it has as yet succeeded.

Thanks
Bill

 

[lucas_]

I am having a bit of difficulty here. Quantum objects are neither particles or waves - that is a myth of QM:
http://arxiv.org/pdf/quant-ph/0609163.pdf

By assuming collapse from waves to particle and similar ideas not really part of QM you will of course run into problems.

I know you have Schlosshauer's book and he states the measurement problem correctly - it has nothing to do with collapse which isn't surprising since its not part of QM anyway. It is, from page 50:

1. The problem of a preferred basis
2. The problem of non-observability of interference.
3. The problem of outcomes.

Decoherence more or less solves the first two - it the third one that is the problem. Its basically how an improper mixed state becomes a proper one. That is the key issue. I am no expert on Quantum Darwinism, I just know about it from what Schlosshauer's writes in his book, but it looks like an attempt to give a purely quantum account of 3. But while Schlosshauer states its promising (page 88) I don't think it has as yet succeeded.

Thanks
Bill
Thanks
Bill

But even how a pure state becomes a proper one is problematic, I just realized a while ago that the density matrix is just a statistical tool.. it can't produce outcome on its own.. something separate needed... is this correct way to think?

 

[bhobba]

But even how a pure state becomes a proper one is problematic,

That is the essential rock bottom problem - it's issue 3 I mentioned above.

I just realized a while ago that the density matrix is just a statistical tool.. it can't produce outcome on its own.. something separate needed... is this correct way to think?

IMHO it is. Its how an improper mixed state becomes a proper one. A proper mixed state is where pure states are randomly presented for observation - its in a specific state before observation, we know why we get an outcome - it objectively exists prior to observation - everything is sweet if you can only figure out how that happens. Some interpretations like collapse interpretations or Bohmian Mechanics handle it easily but for most - blank out.

From what I can see Quantum Darwinism tries to give a purely quantum account of it which is a tough ask - I think its doomed - but time will tell.

And then there is the issue of is it really a problem at all. All theories assume things - is assuming an improper mixed state a proper one - somehow - really that bad? It's what I do. Its basically just a slight variation on the ensemble interpretation of Ballentine. Its called the ignorance ensemble for obvious reasons.

Thanks
Bill