Copenhagen Interpretation of Sleep / Unseen brain?

[bhobba]

Could someone explain how the need for such a factorization arises in the ensemble interpretation?

It doesnt.

I however chose the ignorance ensemble as an example purely because it popped into my head first. There is a tacit assumption in decoherence type interpretations that a factorisation can be found that gives standard QM predictions. Its pretty obvious it can in any situation - but it is an assumption.

Thanks
Bill

 

[bhobba]

Won't you just end up with standard Copenhagen with the cut of a particular observer?

It's different to Copenhagen, first in its use of decoherence, and secondly in its interpretation of probability.

Thanks
Bill

 

[ShayanJ]

It doesnt.

I however chose the ignorance ensemble as an example purely because it popped into my head first. There is a tacit assumption in decoherence type interpretations that a factorisation can be found that gives standard QM predictions. Its pretty obvious it can - but it is an assumption.

Thanks
Bill

I'm confused.
Your discussion with atyy is about this factorization and now you say there is no need for this factorization.
Another thing that confuses me is that you say there is no need for this factorization but then you go on to explain about an assumption about this factorization.
Also I don't understand what you mean by "decoherence type interpretation". Decoherence, as I understand it, is a part of QM formalism not of its interpretations. And I googled for it but there was only one result which was a thread here in PF where it was only mentioned with no explanation.

 

[bhobba]

Your discussion with atyy is about this factorization and now you say there is no need for this factorization.

Pull back a bit.

My discussion is if some simple interpretations exist whose logical consequences explain QM phenomena.

There are tons that do. Ensemble is one, Baysian is another, Decoherent Histories is another - I am sure you can think of others. To pin the issue down I simply chose ignorance ensemble. Because that interpretation uses decohohence then the factorisation problem becomes an issue ie you can always break a system into system being observed, what is doing the observation and/or environment. Some people claim that doesn't explain anything because the answer you get depends on that factorisation. It however is not an issue for the validity of the interpretation.

The Ensemble interpretation doesn't have that problem. It assumes QM is about system preparation and observations on the prepared system so the factorisation problem is not an issue. See figure one in the following:
http://arxiv.org/pdf/quant-ph/0101012.pdf

Thanks
Bill

 

[atyy]

It's different to Copenhagen, first in its use of decoherence, and secondly in its interpretation of probability.

Well, Copenhagen has decoherence too and it allows frequentist probability. It seems the difference is that in Copenhagen, the cut is subjective, ie. observer dependent. To remove the observer, it seems that you need an objective cut. So in your interpretation, there is simply an objective cut or factorization? In a way, you have objective collapse, so I don't see why you escape the problems of objective collapse theories like GRW or CSL.

 

[bhobba]

Well, Copenhagen has decoherence too and it allows frequentist probability. It seems the difference is that in Copenhagen, the cut is subjective, ie. observer dependent. To remove the observer, it seems that you need an objective cut. So in your interpretation, there is simply an objective cut or factorization? In a way, you have objective collapse, so I don't see why you escape the problems of objective collapse theories like GRW or CSL.

Any interpretation of QM has dechorence. Copenhagen however does not make explicit use of it. Ignorance ensemble does. Because it does you are making the tacit assumption what you are analysing can be factored into parts so decoherence works. For example a dust particle is decohered into a specific position by a few stray photons from the CBMR. But if you use a different factorisation do you get the same answer? Or no factorisation at all? Its not a problem because the assumption is you can always find one that gives standard QM.

Thanks
Bill

 

[atyy]

Any interpretation of QM has dechorence. Copenhagen however does not make explicit use of it. Ignorance ensemble does. Because it does you are making the tacit assumption what you are analysing can be factored into parts so decoherence works. For example a dust particle is decohered into a specific position by a few stray photons from the CBMR. But if you use a different factorisation do you get the same answer? Or no factorisation at all? Its not a problem because the assumption is you can always find one that gives standard QM.

Just to be clear, one postulates an objective factorization (F), and since decoherence is not perfect, one also postulates an objective criterion for how close to perfect decoherence the system comes before collapsing (let's call this criterion T)? Since only perfect decoherence defines a unique preferred basis, then the postulated objective criterion will also contain a postulated objective preferred basis (P)?

 

[Derek Potter]

Any interpretation of QM has dechorence. Copenhagen however does not make explicit use of it. Ignorance ensemble does. Because it does you are making the tacit assumption what you are analysing can be factored into parts so decoherence works. For example a dust particle is decohered into a specific position by a few stray photons from the CBMR. But if you use a different factorisation do you get the same answer?

Absolutely not. The very same photons decohere the particle into a unlocated momentum state. Why does standard QM assume that dust is located?

 

[bhobba]

Just to be clear, one postulates an objective factorization (F), and since decoherence is not perfect, one also postulates an objective criterion for how close to perfect decoherence the system comes before collapsing (let's call this criterion T)? Since only perfect decoherence defines a unique preferred basis, then the postulated objective criterion will also contain a postulated objective preferred basis (P)?

Yes to factorisation and a specified level below which its considered no interference occurs. But it is generally thought to explain the preferred basis problem.

Thanks
Bill

 

[bhobba]

Absolutely not. The very same photons decohere the particle into a unlocated momentum state. Why does standard QM assume that dust is located?

That's incorrect.

I was going to post the reference that gives the detail (its got to with the radial nature of such interactions) but before doing that can you post the full detail, and I do mean full mathematical detail, of the claim?

Thanks
Bill

 

[atyy]

Yes to factorisation and a specified level below which its considered no interference occurs. But it is generally thought to explain the preferred basis problem.

But can it really explain the preferred basis problem? The reason I am not sure is that only with perfect decoherence is the preferred basis uniquely specified, so if one specifies a criterion below which it is considered no interference occurs, one is essentially saying if I have the preferred basis, then I specify a criterion (T) below which I can set the off-diagonal terms in the matrix to zero. However, this seems to assume the existence of the preferred basis before already in order to specify the criterion (T).

 

[bhobba]

But can it really explain the preferred basis problem?

Its standard textbook stuff eg see 2.16 of Schlosshauer - Decocherence and The Quantum To Classical Transition.

The measurement problem has three parts

1. The preferred basis problem.
2. The problem of why its so hard to observe interefece
3. The problem of outcomes ie why do we get any outcomes at all.

As Schlosshauer says - page 113 - 'Its reasonable to conclude decoherence is capable of solving the first two problems, whereas the third is inherently linked to matters of interpretation'.

That's the exact basis of my claim decoherence has morphed the measurement problem to why we get any outcomes at all. Ignorance ensemble simply assumes it does - somehow.

Thanks
Bill

 

[atyy]

Its standard textbook stuff eg see 2.16 of Schlosshauer - Decocherence and The Quantum To Classical Transition.

The measurement problem has three parts

1. The preferred basis problem.
2. The problem of why its so hard to observe interefece
3. The problem of outcomes ie why do we get any outcomes at all.

As Schlosshauer says - page 113 - 'Its reasonable to conclude decoherence is capable of solving the first to problems, whereas the third is inherently linked to matters of interpretation'.

That's the exact basis of my claim decoherence has morphed the measurement problem to why we get any outcomes at all. Ignorance ensemble simply assumes it does - somehow.

Thanks
Bill

As I understand, one has to postulate (F), (T) and (P), but the sense is that one could imagine a postulate (P) which reproduces QM. One doesn't get the preferred basis for free when there is imperfect decoherence. For example, one proposal for (P) in the case of imperfect decoherence is the predictability sieve. Which criterion do you use?

 

[bhobba]

As I understand, one has to postulate (F), (T) and (P),

You mentioned T but can you detail what you mean by F and P?

Regarding T we don't have to specify a level below which off diagonal elements are considered zero - we simply need to assume such exists.

But this is getting way off topic. The issue here isn't exactly what assumptions any particular interpretation requires - the issue is such exist.

Thanks
Bill

 

[atyy]

You mentioned T but can you detail what you mean by F and P?

But this is getting way off topic. The issue here isn't exactly what assumptions any particular interpretation requires - the issue is such exist.

F is the postulate of factorization
T is the postulate that when the diagonal terms of the density matrix are small enough in a certain basis, they can be set to zero
P is the postulate of the basis used to define T

I used F for factorization, P for preferred basis, T for time of collapse.

Well, the reason I am asking about these is that this is the one example you use to show that there is at least one solution to the measurement problem for all quantum mechanics with no technical problems. Since it is certainly not a textbook interpretation, I'm trying to make sure I understand it.

 

[bhobba]

As Schlosshauer said - it is reasonable to assume decoherence explains P. Decoherence is based on F and T. I don't see any problem. To be precise when you work through a particular model you find some basis is singled out - by if I remember correctly the requirement is it stable wrt the particular Hamiltonian. That's why position is usually singled out - there is some general argument if the interaction is radial then the position pointer basis is stable (section 2.8.4 Schlosshauer).

Thanks
Bill

 

[1977ub]

So in the middle of the Sun, where it takes

To the average physicist - it won't come up. Philosophers may worry about it - but we don't discuss philosophy on this forum.

A brain is a classical object so QM isn't really relevant. It must be said though no one is really sure if some phenomena like conciousness doesn't crucially depend in some way on QM.

Thanks
Bill

To conceive of the world via reductionism, classical objects are made up of quantum phenomena - is this concern over what classical phenomena are "made of" a purely *philosophical* issue?

 

[atyy]

As Schlosshauer said - it is reasonable to assume decoherence explains P. Decoherence is based on F and T. I don't see any problem. To be precise when you work through a particular model you find some basis is singled out - by if I remember correctly the requirement is it stable wrt the particular Hamiltonian. That's why position is usually singled out - there is some general argument if the interaction is radial then the position pointer basis is stable (section 2.8.4 Schlosshauer).

Yes. The pointer basis is defined by a stability requirement, so the stability requirement is the postulate of a criterion that I am calling P.

 

[bhobba]

To conceive of the world via reductionism, classical objects are made up of quantum phenomena - is this concern over what classical phenomena are "made of" a purely *philosophical* issue?

Of course not.

And the Schlosshauer reference I gave before delves into it.

But that's not the question you asked, the answer to which is since the brain or body is being observed by the environment all the time that you have never seen your brain or are not consciously aware of your body during sleep is not relevant.

Thanks
Bill

 

[bhobba]

Yes. The pointer basis is defined by a stability requirement, so the stability requirement is the postulate of a criterion that I am calling P.

Then I don't follow your issue. You may not agree with the interpretation - or any particular interpretation - that's fine - I get that. The issue is does its conclusions follow from its premises ie is the interpretation a valid theory. If you can prove any interpretation invalid that would be very big news. Note I said prove - we have all sorts of words written about this interpretation having problems etc etc - but none is generally accepted as actually invalid.

However this sojourn into decoherence is not the issue so I will pick another - Quantum Bayesianism:
http://arxiv.org/pdf/1003.5209v1.pdf

Thanks
Bill

 

[atyy]

Then I don't follow your issue.

I am just trying to figure out your interpretation, and whether it solves the measurement problem. It may be correct but it is certainly not standard, not even by the research literature. For example, your interpretation is not mentioned in Schlosshauer's review.

You may not agree with the interpretation - or any particular interpretation - that's fine - I get that. The issue is does its conclusions follow from its premises ie is the interpretation a valid theory. If you can prove any interpretation invalid that would be very big news. Note I said prove - we have all sorts of words written about this interpretation having problems etc etc - but none is generally accepted as actually invalid.

No, I cannot agree with that. To solve a problem, the onus is on the intepretation to show that it is correct.

However this sojourn into decoherence is not the issue so I will pick another - Quantum Bayesianism:
http://arxiv.org/pdf/1003.5209v1.pdf

Quantum Bayesianism is a form of Copenhagen which basically asserts that the measurement problem is not a problem. That is certainly ok, but that is not what we are discussing, which is if the measurement problem is a problem, whether there are complete solutions to it.

So let's go back to your interpretation. Since P is your postulate of defining a pointer basis by a stability criterion, have we agreed that we pick F, P and T?

 

[Derek Potter]

That's incorrect.

Why am I not surprised?

I was going to post the reference that gives the detail (its got to with the radial nature of such interactions) but before doing that can you post the full detail, and I do mean full mathematical detail, of the claim?

Obviously not. I would, however, be interested to know why it is incorrect; that is, if you can dumb it down enough for me to grasp it.

 

[1977ub]

Of course not.

And the Schlosshauer reference I gave before delves into it.

But that's not the question you asked, the answer to which is since the brain or body is being observed by the environment all the time that you have never seen your brain or are not consciously aware of your body during sleep is not relevant.

Thanks
Bill

Perhaps not *more* relevant than other questions about what is "inside" of other matter - away from "measurement". If consciousness doesn't cause collapse (or doesn't do so in the approach of most physicists, then what does?)

For adherents of MWI, what "triggers" a branching ?

 

[atyy]

@bhobba, since you are using Schlosshauer as your reference, could you also explain why this passage does not indicate that there are open problems?

http://arxiv.org/abs/quant-ph/0312059 (p15)
"Finally, a fundamental conceptual difficulty of the decoherence-based approach to the preferred-basis prob-lem is the lack of a general criterion for what defines the systems and the “unobserved” degrees of freedom of the environment (see the discussion in Sec.III.A). While in many laboratory-type situations, the division into system and environment might seem straightforward, it is not clear a priori how quasiclassical observables can be defined through environment-induced superselection on a larger and more general scale, when larger parts of the universe are considered where the split into subsystems is not suggested by some specific system-apparatus-surroundings setup."

 

[bhobba]

Obviously not. I would, however, be interested to know why it is incorrect; that is, if you can dumb it down enough for me to grasp it.

Why obviously not? You made a statement - I am simply asking you to back it up. I will even accept a reference that gives the detail.

Added Later
To forestall this going around in circles you can find the detail in section 2.8.4 and chapter 3 of Schlosshauer.

But just as a general comment Derek you should be prepared to back up statements when you post what others are saying is incorrect with bold statements like 'Absolutely not'. If you can't do that its much better to say - I think such and such - can you give the detail of your claim.

Thanks
Bill

 

[bhobba]

[While in many laboratory-type situations, the division into system and environment might seem straightforward, it is not clear a priori how quasiclassical observables can be defined through environment-induced superselection on a larger and more general scale, when larger parts of the universe are considered where the split into subsystems is not suggested by some specific system-apparatus-surroundings setup."

Its the same factorisation problem in different language. The assumption is it can be done. Disproving decoherence would require you can show such a factorisation to explain a quantum observation does not exist.

Thanks
Bill

 

[atyy]

Its the same factorisation problem in different language. The assumption is it can be done. Disproving decoherence would require you can show such a factorisation to explain a quantum observation does not exist.

Yes. My point is that I'm trying to figure out your interpretation, and whether it solves the measurement problem, because as far as I know it is not published anywhere, not even in Schlosshauer.

So going back to figuring out your interpretation. Are we agreed that it postulates F, P and T criteria?

 

[bhobba]

It may be correct but it is certainly not standard, not even by the research literature.

It's standard. See the paper I have linked to many many times:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

See section 3.1:
(4) Ignorance interpretation: The mixed states we find by taking the partial trace over the environment can be interpreted as a proper mixture. Note that this is essentially a collapse postulate.

Whenever decoherence is discussed on this forum, and it has been discussed a lot, it always seems to get around to this factorisation issue.

Yes its a legit issue - but a fringe one.. It really only seems gain traction around here - there doesn't seem to be that much interest in it. The above review article doesn't mention it. Schlosshauer does but it doesn't have a lot on it - in fact I can't even really recall where it is like most of the things discussed here where I can easily find reference to it. The only reason I know its there is someone pointed out to me it was.

The factorisation issue does not disprove decoherence based interpretations. All its saying is the answer you get may depend on factorisation - not that a factorisation can't be found that gives standard QM predictions. I haven't even seen proof that a different factorisation gives a different answer in the cases that generally occur in practice such as detailed in Chapter 3 of Schlosshauer where he examines scattering models like photons decohering dust particles. But such is not the issue in disproving it - that would require showing something totally different - you can't break the system into what's observed and what's doing the observing.

I gave the argument before but for completeness here it is again. We will consider two systems A and B. A can be in state |a1> and |a2>. B in state |b1> abd |b2>. System B is the system being observed and system A is doing the observing. We have arranged things that if system A is in |a1> then B is in |b1> and similarly for |b2>.

Suppose we have the following superposition |p> = 1/√2|b1>|a1> + 1/√2|b2>|a2>. This is obviously an entangled system where system A is entangled with system B ie what is doing the observing is entangled with what is being observed. Obviously I chose that particular superposition purely for ease of exposition - it can be in any kind of superposition. It's a pure state. It remains in a pure state until observed ie until its interacted with.

But now we will do an observation on just system A with the observable A.

E(A) = <p|A|p> = 1/2 <a1|<b1|A|b1>|a1> + 1/2 <a1|<b1|A|b2>|a2> + 1/2 <a2|<b2|A|b1>|a1> + 1/2 <a2|<b2|A|b2>|a2>

Now here is the kicker - since you are only observing system A the observable A has no effect on the B system or its states. So we have:

<p|A|p> = 1/2 <Aa1|<b1|b1>|a1> + 1/2 <Aa1|<b1|b2>|a2> + 1/2 <Aa2|<b2|b1>|a1> + 1/2 <Aa2|<b2|b2>|a2> = 1/2 <a1|A|a1> + 1/2 <a2|A|a2>
= Trace((1/2|a1><a1| + 1/2|a2><a2|) A) = Trace (p' A)

Here p' is the mixed state 1/2|a1><a1| + 1/2|a2><a2|. Thus observing system A is equivalent to observing a system in the mixed state p' - which by definition is the state from |p> by doing a partial trace over B. The observation will of course give |a1> or |a2> and the entanglement will be broken so that if you get |a1> system B will be in |b1> and conversely. We still have collapse if you like that language - but now it has a different interpretation - you are not observing a pure state - but a mixed one. Its not a proper mixed state because its not prepared the way a proper mixed state is prepared - but the state is exactly the same. Any observable A will not be able to tell the difference. This means we, in a sense, can kid ourselves and say, somehow, its a proper mixed state. If it was a proper mixed state then prior to observation it is in state |a1> or state |a2> with probability of half. Prior to observation its in superposition - after it isnt. Until observed it continues in superposition - its simply because of the entanglement it can now be interpreted differently. By observing 'inside' the system - ie only observing system A - it is in a mixed state - not a proper one - but still a mixed state. Because of that it allows a different and clearer interpretation that avoids a lot of problems.

The factorisation issue does not disprove the above. Indeed the math is tight - its difficult to see how it could be disproved. What the factorisation issue is, is the claim that the answer we get depends on factorising the observed system and what is observed ie factoring it into system A and B. But the very existence of observations here in the macro world depends on a macro system interacting with a quantum system. If such was not possible QM in any interpretation would be in deep do do.

Thanks
Bill

 

[bhobba]

Are we agreed that it postulates F, P and T criteria?

I agree with the following:

1. That a system being observed by another system can be factored into the system being observed and what's doing the observing. The factorisation issue is you may get a different answer if you decompose it differently. That in no way challenges you can't decompose it into what is being observed and what does the observing by the very definition of what an observation is.

2. We assume there is a threshold below which interference effects are not detectable. You do not have to know what it is - simply such exists. The models I have seen such as in Chapter 3 of Schlosshauer all have the interference effects decaying to very low values very quickly. The obvious assumption is its way below what can be detected.

3. It is reasonable to believe it can solve the preferred basis problem. I don't think we have a general proof as yet. I have read in books like what I will link to at the end certain key theorems are lacking. However in the cases that occur in practice, such as those in Chapter 3 I mentioned previously, it does single out a preferred basis. The cases where it doesn't would seem rather pathological if there is no general theorem.
https://www.amazon.com/Understanding-Quantum-Mechanics-Roland-Omnès/dp/0691004358/ref=sr_1_3?s=books&ie=UTF8&qid=1436329923&sr=1-3

Thanks
Bill

 

[atyy]

Do you agree that the stability criterion needed to define the pointer basis is an additional postulate not found in standard QM, and hence I am justified in calling P a postulated criterion along with F and T?

 

[bhobba]

Do you agree that the stability criterion needed to define the pointer basis is an additional postulate not found in standard QM, and hence I am justified in calling P a postulated criterion along with F and T?

No.

Its obvious you can't have an observational outcome in a particular basis unless its stable. How would you even know the outcome?

Thanks
Bill

 

[atyy]

No.

Its obvious you can't have an observational outcome in a particular basis unless its stable. How would you even know the outcome?

Thanks
Bill

It isn't obvious. Dirac justified the projection postulate by saying that repeated measurement must give the same result. However, not all measurements have to be repeatable, eg. http://arxiv.org/abs/quant-ph/9603020v1 (bottom of p20-21).

At any rate, let's say one uses the predictability sieve as the stability criterion. That is certainly not part of standard QM.

 

[bhobba]

It isn't obvious.

Intuitively an observation is something that leaves a mark here in the macro world so must be robust wrt to the Hamiltonian ie is not changed as the system evolves.

As Schlosshauer says, page 76 'In fact, this ability of the apparatus to serve as a robust and faithful indicator of the state of the state of the system amounts the very definition of a measurement device'

It is this that is the key to solving the issue Schroedinger's cat was on about. Copenhagen did not give a precise definition of a measurement. Decoherence does. Using that its obvious the cat has nothing to do with anything - it happens at the particle detector.

Thanks
Bill

 

[Derek Potter]

Why obviously not? You made a statement - I am simply asking you to back it up. I will even accept a reference that gives the detail.

To forestall this going around in circles you can find the detail in section 2.8.4 and chapter 3 of Schlosshauer.

But just as a general comment Derek you should be prepared to back up statements when you post what others are saying is incorrect with bold statements like 'Absolutely not'. If you can't do that its much better to say - I think such and such - can you give the detail of your claim.
Thanks
Bill

Sure, But I wasn't aware I was contradicting you. I was answering what appeared to be a simple enough question. Of course the question is not simple, I had missed the point by miles, my answer was wrong anyway as well as irrelevant. My bad^N.

 

[atyy]

Intuitively an observation is something that leaves a mark here in the macro world so must be robust wrt to the Hamiltonian ie is not changed as the system evolves.

As Schlosshauer says, page 76 'In fact, this ability of the apparatus to serve as a robust and faithful indicator of the state of the state of the system amounts the very definition of a measurement device'

It is this that is the key to solving the issue Schroedinger's cat was on about. Copenhagen did not give a precise definition of a measurement. Decoherence does. Using that its obvious the cat has nothing to do with anything - it happens at the particle detector.

Is the predictability sieve the stability criterion? If it is not, please state the stability criterion exactly.