Classical states and decoherence

[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

 

[atyy]

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)

Yes, that's Bayesian in spirit. but it's so vague I don't really count it as Bayesian. It could just mean one can shift the Heisenberg cut etc. To me a proper Bayesian account needs a prior (either objective or subjective, I prefer subjective). Personally, I like Copenhagen because of this subjective spirit, but technically it's vague, It's really more like, we don't know what the wave function is - it is the subjective knowledge of objective properties :) But we never say what the properties are, except that FAPP it's the wave function!

Anyway, this maybe brings up a difference between textbook-style Copenhagen and the more modern Quantum Bayesianism. In Copenhagen, since the wave function is not real, but represents FAPP the state of a single system or the ensemble prepared by a procedure, one can do tomography and say that tomography is finding out an "unknown quantum state". However, if the quantum state is truly subjective, it cannot be unknown (if it is my subjective belief, by definition it cannot be unknown to me). So I think Quantum Bayesianism properly speaking does not describe tomography as finding out an "unknown quantum state".

 

[lucas_]

bhobba and atyy.. thanks for the many assistance...

last question for this thread... when you are sitting down looking at the computer screen reading this message. How big is the extend of the decoherence branches or outcomes (that didn't manifest at least to this world).. how many meters away from the chair are the other branches/outcomes or does it include running downstair to get a drink or going to the bathroom.. or is it only in the different positions of your body like your left foot over your knees or hands over head or tilting your head to to left or right that differs in each branches/outcomes? I'd like to know how to estimate the extend of the other branches/outcomes that didn't manifest or in other many worlds... tnx..

 

[atyy]

last question for this thread... when you are sitting down looking at the computer screen reading this message. How big is the extend of the decoherence branches or outcomes (that didn't manifest at least to this world).. how many meters away from the chair are the other branches/outcomes or does it include running downstair to get a drink or going to the bathroom.. or is it only in the different positions of your body like your left foot over your knees or hands over head or tilting your head to to left or right that differs in each branches/outcomes? I'd like to know how to estimate the extend of the other branches/outcomes that didn't manifest or in other many worlds... tnx..

In the most naive form of Many-Worlds, branching occurs whenever one performs a measurement. The other worlds are simply the other terms in the superposition following perfect decoherence, so they differ according to the measurement outcomes. If one is doing a spin experiment, the difference could be spin up or spin down. If one is doing a Schroedinger cat experiment, the difference is dead versus alive cat.

However, there is almost never (or never?) perfect decoherence in finite time, so branching requires some coarse graining. I don't know how this really works (or if it works at all), but the difference between worlds would then presumably depend on the coarse graining.

 

[lucas_]

In the most naive form of Many-Worlds, branching occurs whenever one performs a measurement. The other worlds are simply the other terms in the superposition following perfect decoherence, so they differ according to the measurement outcomes. If one is doing a spin experiment, the difference could be spin up or spin down. If one is doing a Schroedinger cat experiment, the difference is dead versus alive cat.

However, there is almost never (or never?) perfect decoherence in finite time, so branching requires some coarse graining. I don't know how this really works (or if it works at all), but the difference between worlds would then presumably depend on the coarse graining.

You have not answered my specific question. Let's ignore Many worlds for now. When you are sitting down in chair in front of computer, what could you be doing in other branches in Copenhagen, the ones that didn't get manifested.. as you know Copenhagen has only one outcome.. but what are the range of other outcomes that didn't occur.. could you be playing computer games instead of just reading this message in other outcomes, how could you estimate what else you could be doing.. let's assume no splitting occurs. I know in many worlds, each possible eigenvalues of your atoms split own worlds. I'm just focusing solely on the decoherence global superposition which didn't include the atoms splitting, what are the extend of it with this specific example of you sitting in computer?

 

[StevieTNZ]

You have not answered my specific question. Let's ignore Many worlds for now. When you are sitting down in chair in front of computer, what could you be doing in other branches in Copenhagen, the ones that didn't get manifested.. as you know Copenhagen has only one outcome.. but what are the range of other outcomes that didn't occur.. could you be playing computer games instead of just reading this message in other outcomes, how could you estimate what else you could be doing.. let's assume no splitting occurs. I know in many worlds, each possible eigenvalues of your atoms split own worlds. I'm just focusing solely on the decoherence global superposition which didn't include the atoms splitting, what are the extend of it with this specific example of you sitting in computer?

It all depends on what the solution to the fundamental Schrodinger equation predicts as possible states. I don't think anyone has solved the equation for the initial conditions, and the time thereafter, you propose.

 

[bhobba]

When you are sitting down in chair in front of computer, what could you be doing in other branches in Copenhagen,

Copenhagen doesn't have other branches - there is one outcome and one outcome only. Like flipping a coin - you get heads or tails - not one 'branch' with heads and another with tails.

But within MW I don't think the question you asked is answerable - I certainly can't do it.

If someone else wants to make a stab I am all ears.

Thanks
Bill

 

[lucas_]

Copenhagen doesn't have other branches - there is one outcome and one outcome only. Like flipping a coin - you get heads or tails - not one 'branch' with heads and another with tails.

But within MW I don't think the question you asked is answerable - I certainly can't do it.

If someone else wants to make a stab I am all ears.

Thanks
Bill

I know Copenhagen doesn't have branches. I was asking what are the extend of the eigenvalues before the collapse to our single outcome eigenvalues. Is this the right language to use to ask what are the other Copenhagen outcomes that didn't occur. So in the example of sitting in front of a computer. Are the other position eigenvalues only goes say 1 meter around you such that in the other unmanifested outcomes.. you could be reclining your back or something. Let's not complicate with many worlds.. just the other eigenvalues that didn't occur prior to the collapse of this outcome (please rewords these and what are the proper words to use?)

 

[bhobba]

Is this the right language to use to ask what are the other Copenhagen outcomes that didn't occur

They didn't occur because the foundational axiom I mentioned before implies they didn't occur - you have one outcome that is mapped to the POVM that determines the probability of that one outcome. Its a nonsense question to ask without reference to a specific interpretation that modifies that implicit assumption. The interpretation that does that is MW.

And you are still locked in language like collapse - QM does not have collapse - only some interpretations do.

Thanks
Bill

 

[lucas_]

They didn't occur because the foundational axiom I mentioned before implies they didn't occur - you have one outcome that is mapped to the POVM that determines the probability of that one outcome. Its a nonsense question to ask without reference to a specific interpretation that modifies that implicit assumption. The interpretation that does that is MW.

Thanks
Bill

You don't get what I was asking. The outcome is probabilistic and the rest didn't occur.. but because it's random, instead of these eigenvalues of position we get now.. it could be others, and these made up the initial probability distribution, I was asking what are the other probability distribution that didn't occur. Could it made the position eigenstate of your body be slightly to the right such that you are say 1 foot to the right in those outcome that didn't occur but could have occur. Do you understand what I'm saying?

 

[atyy]

You have not answered my specific question. Let's ignore Many worlds for now. When you are sitting down in chair in front of computer, what could you be doing in other branches in Copenhagen, the ones that didn't get manifested.. as you know Copenhagen has only one outcome.. but what are the range of other outcomes that didn't occur.. could you be playing computer games instead of just reading this message in other outcomes, how could you estimate what else you could be doing.. let's assume no splitting occurs. I know in many worlds, each possible eigenvalues of your atoms split own worlds. I'm just focusing solely on the decoherence global superposition which didn't include the atoms splitting, what are the extend of it with this specific example of you sitting in computer?

The answer isn't any different from Many-Worlds, since it's just a matter of whether only one outcome is realized or all outcomes are realized.

 

[bhobba]

You don't get what I was asking. The outcome is probabilistic and the rest didn't occur.. but because it's random, instead of these eigenvalues of position we get now.. it could be others, and these made up the initial probability distribution, I was asking what are the other probability distribution that didn't occur. Could it made the position eigenstate of your body be slightly to the right such that you are say 1 foot to the right in those outcome that didn't occur but could have occur. Do you understand what I'm saying?

In probability there is no probability that didn't occur. You don't know something with certainty so you assign a probability. When that something happens we know with a dead cert what the outcome is.

Look at it another way. Copenhagen is in fact compatible with quite a few different interpretations eg BM and MW. In BM everything is deterministic - probabilities are introduced due to lack of knowledge of initial conditions and in QM you can't know them exactly so you can only speak of probabilities - but everything is objective - there is no different possible outcome. In MW its the opposite - you don't actually get an outcome - we experience simply some aspect of this universal wave-function. Your query doesn't make sense in BM, only MW. Copenhagen is agnostic to it.

Thanks
Bill

 

[lucas_]

In probability there is no probability that didn't occur. You don't know something with certainty so you assign a probability. When that something happens we know with a dead cert what the outcome is.

Look at it another way. Copenhagen is in fact compatible with quite a few different interpretations eg BM and MW. In BM everything is deterministic - probabilities are introduced due to lack of knowledge of initial conditions and in QM you can't know them exactly so you can only speak of probabilities - but everything is objective - there is no different possible outcome. In MW its the opposite - you don't actually get an outcome - we experience simply some aspect of this universal wave-function. Your query doesn't make sense in BM, only MW. Copenhagen is agnostic to it.

Thanks
Bill

Let's take the case of double slit experiment. Copenhagen says it can pass any slits and be in any position, so we have the corresponding eigenstate and eigenvalues of positions in the detectors. But we only have one outcome, only one detector detects the emitted photon. The other unrealized eigenvalues are the other *possible* positions of the photons in the detector and which path. In the case of decoherence, there are quadtrillions and more of the interferences, but they still have eigenvalues. So how do you estimate the other unrealized eigenstates/eigenvalues similar to the double slit experiment where other detector positions have unrealized outcome? So if the range of the undetected photons in double slit is in the other side of the detectors at far left of the slit (instead of the realized outcome right side), what is the equivalent in terms of your sitting in computer, what is the unrealized position eigenstates in analogy to the double slit unrealized detections?

 

[lucas_]

The answer isn't any different from Many-Worlds, since it's just a matter of whether only one outcome is realized or all outcomes are realized.

There is a difference between Copenhagen and Many worlds, in Many Worlds, the Schroedinger Cat can be dead and alive in different branches (it can spawn worlds or split macroscopic branches). But in Copenhagen, this is not possible.. macroscopic branches or macrostate can't be spawned... unless you can show that dead cat and alive at are outcomes that can be realized in Copenhagen?

 

[bhobba]

Let's take the case of double slit experiment. Copenhagen says it can pass any slits and be in any position, so we have the corresponding eigenstate and eigenvalues of positions in the detectors.

It doesn't say that. It speaks only of observations - not going through slits or being in any position.

Here is the a correct quantum account of the double slit:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

If you want to discuss that can you reference that account please.

Thanks
Bill

 

[bhobba]

There is a difference between Copenhagen and Many worlds,

Copenhagen is a minimalist interpretation compatible with a number of others such as MW and BM. That's why your question makes no sense in Copenhagen - only in somthing like MW.

Thanks
Bill

 

[lucas_]

Copenhagen is a minimalist interpretation compatible with a number of others such as MW and BM. That's why your question makes no sense in Copenhagen - only in somthing like MW.

Thanks
Bill

Well. Maybe the following is how I imagine or assume it when I think of these things.. Many Worlds occur for a few seconds, then Copenhagen Collapse occur to them with only one World chosen whose outcome or selection is guided by Bohmian Pilot wave. This is what I imagine all these years. Is it not possible, is there no papers that mentioned it? and what is the flaw of the Unified Interpretations where you combine them together?

 

[bhobba]

Well. Maybe the following is how I imagine or assume it when I think of these things.. Many Worlds occur for a few seconds, then Copenhagen Collapse occur to them with only one World chosen whose outcome or selection is guided by Bohmian Pilot wave. This is what I imagine all these years. Is it not possible, is there no papers that mentioned it? and what is the flaw of the Unified Interpretations where you combine them together?

Why would you imagine such a weird world where interpretations change?

But that doesn't change anything. The question you asked only makes sense in MW or some similar interpretation.

Thanks
Bill

 

[lucas_]

Why would you imagine such a weird world where interpretations change?

But that doesn't change anything. The question you asked only makes sense in MW or some similar interpretation.

Thanks
Bill

So if Copenhagen/Ensemble are minimalist that need extra other, then we can say people who subscribe to Copenhagen/Ensemble are those who want to avoid the issues or hide them under the rug? Since you re one.. you admit you are a positivists who only focus on what you can measure? But since Many worlds and Bohmians don't seem likely. Then what are we left of?

Have you read Tegmark the Mathematical Universe? Here he says we are just simulations using the Copenhagen logarithm.. if true, then Tegmark Interpretation would complete Copenhagen as it would finally explain it all?

 

[bhobba]

So if Copenhagen/Ensemble are minimalist that need extra other,

Why you jump to the conclusion they need them I don't quite understand.

It goes back to the third part of the measurement problem mentioned previously - the problem of outcomes. Copenhagen, ensemble, etc makes no hypotheses why we get outcomes - they just accept it. Others like MW and BM do and they are compatible with those that don't specfy why.

The question you asked is only meaningful in interpretations similar to MW.

Thanks
Bill

 

[lucas_]

Why you jump to the conclusion they need them I don't quite understand.

It goes back to the third part of the measurement problem mentioned previously - the problem of outcomes. Copenhagen, ensemble, etc makes no hypotheses why we get outcomes - they just accept it. Others like MW and BM do and they are compatible with those that don't specfy why.

The question you asked is only meaningful in interpretations similar to MW.

Thanks
Bill

I mentioned "they need them" because I read it in the popular Maximilian decoherence paper where he stated

"3. The concept of classicality in the Copenhagen interpretation

...Based on the progress already achieved by the decoherence program, it is reasonable to anticipate that decoherence embedded in some additional interpretive structure could lead to a complete and consistent derivation of the classical world from quantum mechanical principles."

So what do you think are the possible "interpretive structure"? is he referring to Many Worlds or Bohmian?

 

[atyy]

There is a difference between Copenhagen and Many worlds, in Many Worlds, the Schroedinger Cat can be dead and alive in different branches (it can spawn worlds or split macroscopic branches). But in Copenhagen, this is not possible.. macroscopic branches or macrostate can't be spawned... unless you can show that dead cat and alive at are outcomes that can be realized in Copenhagen?

In Copenhagen, if there is uncontrolled decoherence, then the outcomes will be dead or alive.

 

[bhobba]

So what do you think are the possible "interpretive structure"? is he referring to Many Worlds or Bohmian?

I don't know from that how you get they need them. He is taking about it in the context of the three parts of the measurement problem and having an explanation for the so called problem of outcomes. But as I mentioned previously you can simply accept it and move on.

There are many possible candidates - even Quantum Darwinism you started out with may bear fruit and give a fully quantum explanation. Until there is a way to distinguish them experimentally your guess is as good as mine.

Thanks
Bill

 

[StevieTNZ]

I see my post hasn't been commented on, and in fact *I think* answers the question being posed.

 

[atyy]

I see my post hasn't been commented on, and in fact *I think* answers the question being posed.

It does, that's why I retreated to Schroedinger's cat.

 

[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.

Atyy. Something I want to ask for clarifications. It is stated in the Maximillian book page 86 that:

"By contrast, measurements on a closed quantum system will in general alter the state of the system.

It is therefore impossible to regard quantum states of a closed system as existing in the way that classical states do. This raises the question of how classical reality emerges from within the quantum substrate, i.e, how obserables are "objectified" in the above sense. The environment-induced superselection of preferred states discussed in the previous Section 2.8 has certainly made a significant contribution toward answering this question by explaining why only a certain subset of the possible states in the Hilbert space of the system are actually observable. Nonetheless, the problem sketched in the previous paragraph remains, as any direction measurement performed on the system would, in general, still alter the state of the system."

Then he mentioned quantum Darwinism where multiple observers can determine the state of the system from the environment fragments without directly perturbing the system. I'd like to clarify the following:

1. In the quantum substrate of system + environment, is our system a closed quantum system? If not, why does he worry that any direct measurement on the system would still alter the state of the system? In an open system, decoherence with environment can make the system unperturbable by any observer so why propose quantum Darwinism when even without this, the system can't be altered by any measurements of the observer?

2. In case you would say the quantum substrate and especially the system is a closed quantum system and perturbable by observer (is this what you believe?), then what experiments can you do that would directly perturb the system by maybe shining multiple lasers on them (here you can't say you are determining the state of the system by intercepting fragments in environment) such that you want to change the Hamiltonian from position to energy eigenstates such that the laser can make the object vanish in position and becoming pure energy eigenstates. Why is this not possible and how do you make it possible in the window for example?

3. Is quantum Darwinism still valid in Copenhagen, or only in the new Existential Interpretation?

Thank you.

 

[bhobba]

By contrast, measurements on a closed quantum system will in general alter the state of the system.

If what you are observing in the closed system is in a mixed state from entanglement where its 'components' are the eigenvalues of what's observing it there is no way to tell if it altered anything or not. This is one of the key points about decoherence explaining apparent collapse.

The point he is making relates to his issue three of the measurement problem - you don't know if it did or not ie you can only say it didn't change it if it was a proper mixed state - otherwise you can't say that - there is no way of telling - but you can't say it didn't alter the state of the system.

Schlosshauer's book contains very little detail on Quantum Darwinian. You really need to read Zureks paper:
http://arxiv.org/pdf/0903.5082v1.pdf

It focusses on the fact different observers don't observe exactly the same thing - they see different fragments - he shows they still 'see' the same thing.

Its a tacit assumption of the decoherence program all observer's will see the same outcome - he shows it must be the case. Ignorance ensemble takes the earliest point decoherence occurs and places the cut right there so the issue doesn't arise.

Thanks
Bill

 

[lucas_]

If what you are observing in the closed system is in a mixed state from entanglement where its 'components' are the eigenvalues of what's observing it there is no way to tell if it altered anything or not. This is one of the key points about decoherence explaining apparent collapse.

The point he is making relates to his issue three of the measurement problem - you don't know if it did or not ie you can only say it didn't change it if it was a proper mixed state - otherwise you can't say that - there is no way of telling - but you can't say it didn't alter the state of the system.

Schlosshauer's book contains very little detail on Quantum Darwinian. You really need to read Zureks paper:
http://arxiv.org/pdf/0903.5082v1.pdf

It focusses on the fact different observers don't observe exactly the same thing - they see different fragments - he shows they still 'see' the same thing.

Its a tacit assumption of the decoherence program all observer's will see the same outcome - he shows it must be the case. Ignorance ensemble takes the earliest point decoherence occurs and places the cut right there so the issue doesn't arise.

Thanks
Bill

But that passage in page 86 is about quantum Darwinism under the topic "2.9 Redundant Encoding of Information in the Environment and "Quantum Darwinism". Anyway. Can you give an example of what you are saying in "If what you are observing in the closed system is in a mixed state from entanglement where its 'components' are the eigenvalues of what's observing it there is no way to tell if it altered anything or not.". For example, let's take the case of an entangled electron with spin up and spin down. Say the spin up and spin down are components of the eigenvalues. What is the sense there is no way to tell if it's altered or not during observation? Please use this example of entangled electron pair, thanks.

 

[bhobba]

What is the sense there is no way to tell if it's altered or not during observation? Please use this example of entangled electron pair, thanks.

The system here is not the entangled electrons - its the entangled electrons AND the observational apparatus - that's where the decoherence occurs. It is the interaction with the observational apparatus that transforms the superposition of the up/down spin to a mixed state and breaks the entanglement with the other electron.

Note what I said:

If what you are observing in the closed system is in a mixed state from entanglement where its 'components' are the eigenvalues of what's observing it there is no way to tell if it altered anything or not. This is one of the key points about decoherence explaining apparent collapse.

It's not in a mixed state until decohered by the spin observational apparatus.

Actually in answering another query about this I noticed you can find the full gory detail in Chapter 7 of Susskind:
https://www.amazon.com/dp/0465036678/?tag=pfamazon01-20

It results from the fact if you observe one part of an entangled system it looks like a mixed state to what's observing it - the math is in the above.

Thanks
Bill

 

[lucas_]

The system here is not the entangled electrons - its the entangled electrons AND the observational apparatus - that's where the decoherence occurs. It is the interaction with the observational apparatus that transforms the superposition of the up/down spin to a mixed state and breaks the entanglement with the other electron.

Note what I said:It's not in a mixed state until decohered by the spin observational apparatus.

Actually in answering another query about this I noticed you can find the full gory detail in Chapter 7 of Susskind:
https://www.amazon.com/dp/0465036678/?tag=pfamazon01-20

It results from the fact if you observe one part of an entangled system it looks like a mixed state to what's observing it - the math is in the above.

Thanks
Bill

Ok. I will read it (but need to prioritize buying stuff). I just want to know what you mean you can't know if you alter them. Supposed you use apparatus that can measure spin up or down.. if it shows spin up.. and other observers apparatus show spin down.. you know they are altered, by the different results of different observers, do you agree with this?

 

[bhobba]

Ok. I will read it (but need to prioritize buying stuff). I just want to know what you mean you can't know if you alter them. Supposed you use apparatus that can measure spin up or down.. if it shows spin up.. and other observers apparatus show spin down.. you know they are altered, by the different results of different observers, do you agree with this?

Its simple. It's got to do with the difference between a proper and an improper mixed state. The mixed state is pu |u><u| + pd |d><d|. If you observe that with the up-down observable you will get |u><u| with probability pu and |d><d| with probability pd. Now is that because it was in state |u><u| with probability pd and similarly for |d><d|? If so the observation did nothing - no change. In interpretations like BM or GRW that actually is the case and is how they resolve the measurement problem. But they may not be true - the observation may have changed the mixed state to a pure one - there is no way of telling. Remember this is a mixed state - not a superposition - interference terms have been suppressed.

Thanks
Bill

 

[lucas_]

Its simple. It's got to do with the difference between a proper and an improper mixed state. The mixed state is Σ pu |u><u| + pd |d><d|. If you observe that with the up-down observable you will get |u><u| with probability pu and |d><d| with probability pd. Now is that because it was in state |u><u| with probability pd and similarly for |d><d|? If so the observation did nothing - no change. In interpretations like BM or GRW that actually is the case and is how they resolve the measurement problem. But they may not be true - the observation may have changed the mixed state to a pure one - there is no way of telling. Remember this is a mixed state - not a superposition - interference terms have been suppressed.

Thanks
Bill

is the "state |u><u| with probability pd and similarly for |d><d|" the improper mixed state in the example (noting that entangled electron with spin up and spin down are entangled so you can't use proper mixed state).. but why did you use proper mixed state in Σ pu |u><u| + pd |d><d|?

 

[bhobba]

is the "state |u><u| with probability pd and similarly for |d><d|" the improper mixed state in the example (noting that entangled electron with spin up and spin down are entangled so you can't use proper mixed state).. but why did you use proper mixed state in Σ pu |u><u| + pd |d><d|?

Both proper and improper mixed states are mathematically the same, pu |u><u| + pd |d><d| is proper or improper - you can't tell from observing it - only by knowing how it was prepared. |u><u| and |d><d| are pure - not mixed.

Thanks
Bill