Classical states and decoherence

[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

 

[bhobba]

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".

It is.

The difference really has to do with your view of probabilities. The ensemble type interpretations are frequentest like - Copenhagen - Bayesian like:
http://en.wikipedia.org/wiki/Copenhagen_interpretation
'The subjective view, that the wave function is merely a mathematical tool for calculating the probabilities in a specific experiment, has some similarities to the Ensemble interpretation in that it takes probabilities to be the essence of the quantum state, but unlike the ensemble interpretation, it takes these probabilities to be perfectly applicable to single experimental outcomes, as it interprets them in terms of subjective probability.'

There is even supposedly a Bayesian interpretation but for the life of me I can't tell where it departs from Copenhagen - except some Copenhagenists think of the wave function as actually real and you have actual collapse which I find rather strange because its introduces unnecessary problematical assumptions.

Some Copenhagenists have gone over to the Consistent histories view (they describe it as Copenhagen done right) which doesn't even have observations - for them QM is the stochastic theory of histories. Interesting interpretation - but maybe simply trying to define your way out of problems.

Thanks
Bill

 

[lucas_]

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

But a pure state is just vector in Hilbert space, there is no matter or observation is not possible. According to Heisenberg Potentia. Before wave function collapse or if you don't want to use the language of collapse... before the vector choose a basis.. like position or momentum.. it is smeared out and there is no solid object. So how can you connect above when you said that "A proper mixed state is where pure states are randomly presented for observation"? How can you observe something that is smeared out or ghost like?

Is the above a separate problem or issue from the question of how improper mixed state can be thought up of as proper mixed state? Please clafify, thanks.

 

[bhobba]

But a pure state is just vector in Hilbert space, there is no matter or observation is not possible.

Its more than that as the Born Rule tells you.

it is smeared out and there is no solid object.

Precisely why are you prescribing proprieties like smeared to a quantum system when it's not observed?

How can you observe something that is smeared out or ghost like?.

QM is a theory about observations, so, of course you can do it. Observation is a primitive of the theory.

To get a better understnding of exactly what a state is check out post 137:
https://www.physicsforums.com/threads/the-born-rule-in-many-worlds.763139/page-7

The key fundamental axiom is:
An observation/measurement with possible outcomes i = 1, 2, 3 ... is described by a POVM Ei such that the probability of outcome i is determined by Ei, and only by Ei, in particular it does not depend on what POVM it is part of.

Note that an observation is an undefined primitive of the theory, like particle is an undefined primitive of classical mechanics, or point is an undefined primitive of Euclidean geometry etc etc. We have an intuitive idea what they mean and as the theory is developed you get a better idea, but that is typical of physical theories. Mathematicians work to a higher standard and if you go and study a book like Geometry Of Quantum theory by Varadarjan you will find exact mathematical definitions of such things - but how you apply them - that's another matter. As Einstein said - 'As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.' Also that approach is what is euphemistically referred to by mathematicians as non-trivial - meaning its HARD.

Now from that axiom alone we have, via Gleason, Born's Rule. The state is simply a mathematical requirement following from that axiom. It's not real, telling us something is smeared our or anything like that. It, just like probabilities, tells us about the expected value of observations.

What decoherence does is refine the concept of observation. You get a mixed state in the basis of what you are observing ie the state is Σpi |bi><bi| and the observable is Σyi |bi><bi|. Now let's suppose its a proper mixed state then the system is actually, prior to observation, in some state |bi><bi| with probability pi. When you observe it with the observable O = Σyi |bi><bi| the yi you get tells you what |bi><bi| there is. Its not changed by the observation (if its a filtering type observation) and in that sense it can be considered an objective property of the system. Everything is much more classical and common-sense. It reveals something there beforehand - no problem of outcomes - its there before you observe it. But it isn't a proper mixed state - its an improper state - it's observationally indistinguishable from a proper one - but it's not the same. This is the problem of outcomes - why do we get an outcome. The fundamental axiom says we will - but why.

That said I think far too many people get caught up with this. Its simply the fundamental axiom of QM - that observations exist and have outcomes is a primitive of the axiom and the theory. Its no different to other primitives like point particle, point, event, and a myriad of other primitives in physics. Its simply part of the scientific method - every theory has assumed primitives.

Thanks
Bill

 

[lucas_]

Its more than that as the Born Rule tells you.
Precisely why are you prescribing proprieties like smeared to a quantum system when it's not observed?

see this message I read (is there a way you can show it's not true?):https://www.physicsforums.com/threa...hat-is-nature-really-like.117727/#post-965075

Quantum Reality #8. The duplex world of Werner Heisenberg (The world is twofold, consisting of potentials and actualities.) Most physicists believe in the Copenhagen interpretation, which states that there is no deep reality- QR # 1) and observation creates reality QR # 2). What these two realities have in common is the assertion that only phenomena are real; the world beneath phenomena is not.

One question which this position immediately brings to mind is this: "if observation creates reality, what does it create this reality out of? Are phenomena created out of sheet nothingness or out of some more substantial stuff?" Since the nature of unmeasured reality is unobservable by definition, many physicists dismiss such questions as meaningless on pragmatic grounds.

According to Heisenberg, there is no deep reality - nothing down there that's real in the same sense as the phenomenal facts are real... "But the atoms and the elementary particles themselves are not as real; they form a world of potentialities or possibilities rather than one of things or facts . . .

...Heisenberg's two worlds are bridged by a special interaction which physicists call a "measurement." During the magic measurement act, one quantum possibility is singled out, abandons its shadowy sisters, and surfaces in our ordinary world as an actual event. Everything that happens in our World arises out of possibilities prepared for in that other-the world of quantum potentia. In turn, our world sets limits on how far crowds of Potentia can roam. Because certain facts are actual, not everything is possible in the quantum world. There is no deep reality, no deep reality-as-we-know-it...

i'll save the following for deeper and slow analysis. Can you never agree with the above, and why?

QM is a theory about observations, so, of course you can do it. Observation is a primitive of the theory.

To get a better understnding of exactly what a state is check out post 137:
https://www.physicsforums.com/threads/the-born-rule-in-many-worlds.763139/page-7

The key fundamental axiom is:
An observation/measurement with possible outcomes i = 1, 2, 3 ... is described by a POVM Ei such that the probability of outcome i is determined by Ei, and only by Ei, in particular it does not depend on what POVM it is part of.

Note that an observation is an undefined primitive of the theory, like particle is an undefined primitive of classical mechanics, or point is and undefined primitive of Euclidean geometry etc etc. We have an intuitive idea what they mean and as the theory is developed you get a better idea, but that is typical of physical theories. Mathematicians work to a higher standard and if you go and study a book like Geometry Of Quantum theory by Varadarjan you will find exact mathematical definitions of such things - but how you apply them - that's another matter. As Einstein said - 'As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.' Also that approach is what is euphemistically referred to by mathematicians as non-trivial - meaning its HARD.

Now from that axiom alone we have, via Gleason, Born's Rule. The state is simply a mathematical requirement following from that axiom. It's not real, telling us something is smeared our or anything like that. It, just like probabilities, tells us about the expected value of observations.

What decoherence does is refine the concept of observation. You get a mixed state in the basis of what you are observing ie the state is Σpi |bi><bi| and the observable is Σyi |bi><bi|. Now let's suppose its a proper mixed state then the system is actually, prior to observation, in some state |bi><bi| with probability pi. When you observe it with the observable O = Σyi |bi><bi| the yi you get tells you what |bi><bi| there is. Its not changed by the observation (if its a filtering type observation) and in that sense it can be considered an objective property of the system. Everything is much more classical and common-sense. It reveals something there beforehand - no problem of outcomes - its there before you observe it. But it isn't a proper mixed state - its an improper state - it's observationally indistinguishable from a proper one - but it's not the same. This is the problem of outcomes - why do we get an outcome. The fundamental axiom says we will - but why.

That said I think far too many people get caught up with this. Its simply the fundamental axiom of QM - that observations exist and have outcomes is a primitive of the axiom and the theory. Its no different to other primitives like point particle, point, event, and a myriad of other primitives in physics. Its simply part of the scientific method - every theory has assumed primitives.

Thanks
Bill

 

[bhobba]

see this message I read (is there a way you can show it's not true?):https://www.physicsforums.com/threa...hat-is-nature-really-like.117727/#post-965075

To be blunt it's philosophical waffle. You know that when you see stuff like - if observation creates reality what does it create reality out of. The question first is - what is reality - oh and BTW you are going to have to get everyone to agree on it. Good luck with that. Philosophers never seem to agree and science has never found any actual use for an answer. The best answer is - science describes the world with models - but what that world is in a philosophical sense - really who cares. And it has led to some VERY deep insights such as the fundamental role of symmetry, whereas the later has led no-where. In QM observation is a primitive, like event in relativity is a primitive, like tons of other things in science. Accept it and move on or get stuck in a philosophical rut that really is off topic here.

Thanks
Bill

 

[lucas_]

To be blunt it's philosophical waffle. You know that when you see stuff like - if observation creates reality what does it create reality out of. The question first is - what is reality - oh and BTW you are going to have to get everyone to agree on it. Good luck with that. Philosophers never seem to agree and science has never found any actual use for an answer. The best answer is - science describes the world with models - but what that world is in a philosophical sense - really who cares. And it has led to some VERY deep insights such as the fundamental role of symmetry, whereas the later has led no-where. In QM observation is a primitive, like event in relativity is a primitive, like tons of other things in science. Accept it and move on or get stuck in a philosophical rut that really is off topic here.

Thanks
Bill

Ok. I got your point. Pls. go to page 49 of Maximillian Decoherence book.

To be blunt it's philosophical waffle. You know that when you see stuff like - if observation creates reality what does it create reality out of. The question first is - what is reality - oh and BTW you are going to have to get everyone to agree on it. Good luck with that. Philosophers never seem to agree and science has never found any actual use for an answer. The best answer is - science describes the world with models - but what that world is in a philosophical sense - really who cares. And it has led to some VERY deep insights such as the fundamental role of symmetry, whereas the later has led no-where. In QM observation is a primitive, like event in relativity is a primitive, like tons of other things in science. Accept it and move on or get stuck in a philosophical rut that really is off topic here.

Thanks
Bill

Thanks for the clarifications. I finally understood your position and would read every single messages you write at physicsforums. It's really a puzzle that in spite of the fact there is ongoing superposition between system and environment even right now as we speak, there is definite outcome. It's like having superposition and collapse occurring at same time.. we are now in more dire situation than Bohr original Copenhagen interpretation. And without giving up ignorance interpretation, it seems Many worlds is becoming more likely... scary to think that there are other me's out there also typing these messages. Anyways.. thanks for all the assistance. I wonder how long I'd be able to read all your 4000 messages here. If I have question, I may just start a thread or join others..

 

[bhobba]

Ok. I got your point. Pls. go to page 49 of Maximillian Decoherence book.

That's the section I got the 3 measurement sub-problems from.

It's really a puzzle that in spite of the fact there is ongoing superposition between system and environment even right now as we speak, there is definite outcome.

Sure - that's the problem of outcomes - the big issue in QM.

we are now in more dire situation than Bohr original Copenhagen interpretation.

Remember what I said: 'I think far too many people get caught up with this. Its simply the fundamental axiom of QM - that observations exist and have outcomes is a primitive of the axiom and the theory. Its no different to other primitives like point particle, point, event, and a myriad of other primitives in physics. Its simply part of the scientific method - every theory has assumed primitives.'

There are a number of interpretive solutions - take your pick.

Reading my earlier posts - I don't envy you that one - my views have changed considerably since posting here.

Thanks
Bill

 

[atyy]

It is.

The difference really has to do with your view of probabilities. The ensemble type interpretations are frequentest like - Copenhagen - Bayesian like:
http://en.wikipedia.org/wiki/Copenhagen_interpretation
'The subjective view, that the wave function is merely a mathematical tool for calculating the probabilities in a specific experiment, has some similarities to the Ensemble interpretation in that it takes probabilities to be the essence of the quantum state, but unlike the ensemble interpretation, it takes these probabilities to be perfectly applicable to single experimental outcomes, as it interprets them in terms of subjective probability.'

There is even supposedly a Bayesian interpretation but for the life of me I can't tell where it departs from Copenhagen - except some Copenhagenists think of the wave function as actually real and you have actual collapse which I find rather strange because its introduces unnecessary problematical assumptions.

Some Copenhagenists have gone over to the Consistent histories view (they describe it as Copenhagen done right) which doesn't even have observations - for them QM is the stochastic theory of histories. Interesting interpretation - but maybe simply trying to define your way out of problems.

Thanks
Bill

The Copenhagen I was indoctrinated with was agnostic about frequentist or Bayesian probability, since anything that works with Kolmogorov is ok :) I never heard of a Copenhagen in which the quantum state is really real. Of course Copenhagen has the quantum state as fakely real (FAPP), but we know it's fake reality because we put the Heisenberg cut. Actually, I never heard of Bayesian probability until I'd already been well indoctrinated with Copenhagen.

And yes, I have no idea how Quantum Bayesianism differs from Copenhagen, except that Copenhagen is maybe more broad minded :) Eg. Copenhagen has no problem with Bohmian trajectories - it just doesn't know whether they are real or not :p

 

[atyy]

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.

It is a standard thing, but hard to find very explicitly. It is standard in Copenhagen to put a classical/quantum cut, and have the measurement outcome be on the classical side, and the quantum state be on the quantum side. It is also standard to define wave function collapse or state reduction as a rule which specifies the quantum state conditioned on a measurement outcome, which is of course a definite quantum outcome conditioned on a definite classical outcome.

You can find the language in:
Landau and Lifshitz (explicit about the classical/quantum cut, but the state reduction rule is an old-fashioned version based on repeatability)
Nielsen and Chuang (modern version of the state reduction rule, but classical/quantum cut only implicit in various comments throughout the book)
Heinosaari and Ziman (very explicit, but unclear as to whether state reduction is a postulate or derived)

 

[bhobba]

The Copenhagen I was indoctrinated with was agnostic about frequentist or Bayesian probability, since anything that works with Kolmogorov is ok :)

QM works with Kolmogorov just fine.

The reason its Bayesian like is you often see subjective used with regard to state in Copenhagen eg:

1. A system is completely described by a wave function ψ, representing an observer's subjective knowledge of the system. (Heisenberg)
2. The description of nature is essentially probabilistic, with the probability of an event related to the square of the amplitude of the wave function related to it. (The Born rule, after Max Born)
3. It is not possible to know the value of all the properties of the system at the same time; those properties that are not known with precision must be described by probabilities. (Heisenberg's uncertainty principle)
4. Matter exhibits a wave–particle duality. An experiment can show the particle-like properties of matter, or the wave-like properties; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.
5. Measuring devices are essentially classical devices, and measure only classical properties such as position and momentum.
6. The quantum mechanical description of large systems will closely approximate the classical description. (The correspondence principle of Bohr and Heisenberg).

Some parts are of course a crock eg wave-particle duality - but its pretty clear what the idea is.

In some accounts I have read they assume the wave-function is real - but obviously they haven't thought it through because as Ballentine correctly points out it leads to absurdities.

Thanks
Bill