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Does Decoherence Solve the Measurement Problem Completely

by Prathyush
Tags: measurement, quantum mechanics
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nanosiborg
#37
Nov28-12, 04:18 AM
P: 79
Quote Quote by tom.stoer View Post
give me a hint; where's a contradiction?
Not necessarily any contradictions but, for example, I said that ... quantum superposition is, in a most important sense, an expression of our ignorance of deep reality. To which you replied: Not necessarily; it could be an ontological feature ...

To which I would reply that I think the mathematics of quantum superposition, necessarily, does not correspond to any ontological feature of fundamental reality.

Which has to do with my currently favored notion that the mechanics of the deep reality are not fundamentally different than the mechanics of the reality that's amenable to our limited sensory apprehension. Which is based on the assumption that, even though there are emergent phenomena and emergent scale dependent organizing principles, there are nevertheless fundamental wave mechanical dynamical laws that hold for all behavioral scales.

In other words, I don't see any reason to believe that the fundamental laws governing the reality underlying instrumental behavior are essentially different than the fundamental laws governing instrumental behavior.

But you and others have offered many interesting comments that I really do need to reread and think about.

For now, I think we might agree that the math of decoherence doesn't provide any deeper understanding of nature than orthodox qm (and associated mathematical models) does -- and therefore is not a solution to the measurement problem.
Jazzdude
#38
Nov28-12, 04:38 AM
P: 184
Quote Quote by bhobba View Post
As Schlosshauer says it transforms a superposition into an 'improper' mixed state. Here improper means it mathematically looks exactly the same as a mixed state and no experiment can tell it from one but in reality it isn't. But it is this 'mimicking' of a mixed state that allows it to be interpreted as one, and as an interpretational thing solve the measurement problem. It doesn't by itself solve the measurement problem but by allowing the improper mixed states to be interpreted as proper ones does for all practical purposes. The wavefunction collapse issue is still there but swept under the rug so to speak.
If you say that a proper mixed state and an improper mixed state cannot be practically distinguished by experiment really means that they cannot be distinguished by quantum measurement. So you still need the quantum measurement postulate to argue like that, and that leaves you where you started. So this doesn't solve anything.
eloheim
#39
Nov28-12, 06:37 AM
P: 65
Quote Quote by tom.stoer View Post
Accortding to the QM formalism they are; according to my perception they aren't. That's the core of the problem. QM doesn't tell us what we will observe, it only tell's us something about the probabilities of observations. If there is a 50% probability for "dead" I will never observe these superpositions or mixed states. I will always either observe "dead" or "alive". But there is nothing in the QM formalism which tells us how the 50% in the density matrix become the 100% in my perception.
Sorry I should have posed the question less tounge-in-cheek. (And I agree that decoherence really doesn't address the ultimate measurement problem.) However, doesn't decoherence explain why you don't notice macroscopic superposition of the observer, i.e. because the wave-function evolves into multiple non-interacting components? (Not to mention the requisite (unresolved) issues of 'recovering the born rule', preferred basis, etc. if you stop there though.)

Quote Quote by tom.stoer View Post
The problem is deeper. If you insint on some ontological status of QM you immediately run into these problems. But if you give up an ontological interpretation and introduce "our ignorance of reality" then logically it follows that either QM is not complete in the description of nature or our understanding of QM is not complete. So the problem is not only a philosophical one but a physical one as well. We are feeling uncomfortable with the situation that there "is" or "seems to be" more than we can calculate. We can then never be sure where the problem resides and whether there may be a physical but yet unkown solution. I think your interpretation regarding "our ignorance of reality" is something we don't like b/c it may be an interpretation only.

The case of decoherence tells us that (partially !!) we can solve the measurement problem. And there's some hope - so we don't stop.
I could not agree more with the 'feel' of this, btw!..

Quote Quote by nanosiborg View Post
To which I would reply that I think the mathematics of quantum superposition, necessarily, does not correspond to any ontological feature of fundamental reality.
I don't think that makes sense. Researchers study, manipulate and make use of quantum superpositions all the time (quantum computation, etc.)
Maui
#40
Nov28-12, 07:08 AM
P: 724
Quote Quote by eloheim View Post
However, doesn't decoherence explain why you don't notice macroscopic superposition of the observer, i.e. because the wave-function evolves into multiple non-interacting components?


Yes, decoherence requires that there be interactionally-real components of the wavefunction which is in sync with your next statement:

I don't think that makes sense. Researchers study, manipulate and make use of quantum superpositions all the time (quantum computation, etc.)
bhobba
#41
Nov28-12, 07:38 AM
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Quote Quote by Jazzdude View Post
If you say that a proper mixed state and an improper mixed state cannot be practically distinguished by experiment really means that they cannot be distinguished by quantum measurement. So you still need the quantum measurement postulate to argue like that, and that leaves you where you started. So this doesn't solve anything.
By itself it does nothing - to resolve anything you have to use it in a compatible interpretation - that is the key. One compatible interpretation is decoherent histories (it automatically enforces that interpretations consistency condition) - but others exist (eg MWI) and are possible (eg a simple extension of the ensemble interpretation that I favor).

Thanks
Bill
bhobba
#42
Nov28-12, 08:07 AM
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Quote Quote by Maui View Post
Yes, decoherence requires that there be interactionally-real components of the wavefunction which is in sync with your next statement:
No, decoherence is interpretation independent. For example decoherent histories doesn't require that and yet it is central to it.

While it is applicable to any interpretation only for some is it central and if the wave function has 'interactionally real' components is not a common factor.

Thanks
Bill
nanosiborg
#43
Nov28-12, 02:39 PM
P: 79
Quote Quote by eloheim View Post
I don't think that makes sense. Researchers study, manipulate and make use of quantum superpositions all the time (quantum computation, etc.)
Yes, mathematically. It's part of a calculus that assigns values to possible measurement results. It's reasonable to infer that there are wavefunction components that correspond in some way to reality. It's not reasonable to infer that expressions of mutually exclusive measurement results refer to real ontological states.
Quantumental
#44
Nov28-12, 03:22 PM
P: 132
Quote Quote by nanosiborg View Post
Yes, mathematically. It's part of a calculus that assigns values to possible measurement results. It's reasonable to infer that there are wavefunction components that correspond in some way to reality. It's not reasonable to infer that expressions of mutually exclusive measurement results refer to real ontological states.
This used to be how I viewed the situation, but then what about PBR theorem?
bhobba
#45
Nov28-12, 03:26 PM
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Quote Quote by nanosiborg View Post
It's reasonable to infer that there are wavefunction components that correspond in some way to reality.
Just because it seems reasonable to you does not make it so - it does't seem reasonable to me BTW if you look carefully at the formalism - in fact if you do that you are lead down a slippery slope of problems such as the reality of wavefunction collapse. Guys like Bohr deliberately didn't do it for very good reasons. This was the exact point Einstein disagreed with Bohr. Einstein believed it represented something real and was incomplete.

Quote Quote by nanosiborg View Post
I like your take on this. And some others. My two cents is:
Quantum superposition is a mathematical representation, based on classical wave mechanics, of the extent of our knowledge of possible instrumental behaviors. Quantum superposition has the nonclassical character it does precisely because of our ignorance of the reality underlying instrumental behavior. That is, quantum superposition is, in a most important sense, an expression of our ignorance of deep reality.
You cant believe it sort of represents some kind of statistical knowledge of something real - a theorem (the now famous PBR Theorem the guy above referred to) says that is a no go:
http://xxx.lanl.gov/pdf/1111.3328v3.pdf

The superposition principle is not based on classical wave mechanics - it follows quite simply for pure states from the trace formula of QM - E(R) = Trace (pR) where p is the system state (ie a positive operator of trace 1).

Of course none of this proves its not real - it may well be - but if you believe so you need to face up to all sorts of issues.

Quote Quote by Quantumental View Post
This used to be how I viewed the situation, but then what about PBR theorem?
Exactly

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Bill
tom.stoer
#46
Nov28-12, 03:41 PM
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PBR theorem? this is new to me; seems that reading LQG and LHC Higgs papers is the wrong scope

bhobba
#47
Nov28-12, 04:17 PM
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Quote Quote by tom.stoer View Post
PBR theorem? this is new to me; seems that reading LQG and LHC Higgs papers is the wrong scope

It caused a real stir a while back but it has died down considerably since I think people have realised its a bit of a non issue.

Basically all its saying is if you believe the quantum state in some imperfect way, or even in a statistical sense, corresponds to something real then it is itself real. I always thought it was a bit weird believing otherwise anyway. There are also ways of evading it such as if you believe QM is incomplete then small blemishes like that don't really matter - that would be Einsteins view.

For a critical examination of it see:
http://arxiv.org/pdf/1203.4779.pdf

Added Later:

I forgot to mention the PBR theorem (as the above paper makes clear) only concerns interpretations/models where the underlying reality is not dependent on the state - that is also another out - and in fact quite a biggie.

Thanks
Bill
Maui
#48
Nov28-12, 04:40 PM
P: 724
Decoherence is said to be a thermodynamically irreversible process. So how does a H2O molecule in running water retain its classical-like properties in time? The evolution of the system would stop when the state loses coherence, then how does it move to the next state? There'd have to be a system in constant flux of becoming coherent then decoherent, coherent, decoherent... to mimick classical like behavior.





Quote Quote by bhobba
No, decoherence is interpretation independent. For example decoherent histories doesn't require that and yet it is central to it.

Yes, i've read claims that decoherence doesn't have to involve any real-world interaction(and nothing physical is decohering) but it seems like fitting the facts to the theory instead of changing the theory. Decoherence rates gave been measured and they vary depending on the setup so the states act in ways that do not imply they represent knowledge of the system. Does it make sense to say that by changing the temperature at which an atom is stored, you can decouple the atom from the environment and turn it into information about the system?
Quantumental
#49
Nov28-12, 04:58 PM
P: 132
Quote Quote by bhobba View Post
There are also ways of evading it such as if you believe QM is incomplete then small blemishes like that don't really matter - that would be Einsteins view.

But doesn't this theorem put restraints on whatever fundamental theory that lies beneath QM anyways?

I am in the "QM can't be 100% correct" group because none of the interpretations to date are satisfactory to me.
Collapse is just philosophically bad, indeterminism is not acceptable as a scientific explanation anymore than magic or God is. Plus the entire "when" does collapse occur is a problem.
de-Broglie Bohm is the best way to visualize QM and it sort of makes sense, but at the end of the day I don't buy it, it's just too ad hoc for me.
Everett is invalidated by the Born Rule and in addition you have the preferred basis issues.

So yeah, QM *HAS* to be wrong, but I would think that PBR's results will still have a impact on narrowing down the field of possible more fundamental theories? Just like Bells theorem restrict it.
bhobba
#50
Nov28-12, 05:21 PM
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Quote Quote by Maui View Post
Yes, i've read claims that decoherence doesn't have to involve any real-world interaction(and nothing physical is decohering) but it seems like fitting the facts to the theory instead of changing the theory. Decoherence rates gave been measured and they vary depending on the setup so the states act in ways that do not imply they represent knowledge of the system. Does it make sense to say that by changing the temperature at which an atom is stored, you can decouple the atom from the environment and turn it into information about the system?
Come again.

Decoherence is implied by the quantum formalism. It has nothing to do with if a quantum state is real, simply knowledge about observations or whatever.

There is no fitting of the facts to the theory. What there is is some interpretations that make use of decoherence and some that don't - that's all.

Thanks
Bill
bhobba
#51
Nov28-12, 05:31 PM
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Quote Quote by Quantumental View Post
But doesn't this theorem put restraints on whatever fundamental theory that lies beneath QM anyways?
No. If you believe QM is an approximation to a more fundamental theory then that theory simply has to give QM in some kind of limit. The theorems that apply to QM like PBR need not apply. In that case PBR is a sort of blemish on QM like acasual runaway solutions are a blemish on EM indicating its not fundamental.

Added Later:

Just to be clear other outs of PBR exist as well - it crucially depends on state independence.

Quote Quote by Quantumental View Post
I am in the "QM can't be 100% correct" group because none of the interpretations to date are satisfactory to me. Collapse is just philosophically bad, indeterminism is not acceptable as a scientific explanation anymore than magic or God is. Plus the entire "when" does collapse occur is a problem. de-Broglie Bohm is the best way to visualize QM and it sort of makes sense, but at the end of the day I don't buy it, it's just too ad hoc for me.

Everett is invalidated by the Born Rule and in addition you have the preferred basis issues.

So yeah, QM *HAS* to be wrong, but I would think that PBR's results will still have a impact on narrowing down the field of possible more fundamental theories? Just like Bells theorem restrict it.
I would be careful about letting your prejudices lead you to believe anything 'HAS' to be right or wrong. Choose an interpretation based on what makes most sense to you, or even reject them all, but don't think it must be like that - nature has a way of confounding that sort of view.

Thanks
Bill
tom.stoer
#52
Nov28-12, 06:33 PM
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We should make a clear distinction between
1) QM as a theory of nature = a formalism to predict experimental results
2) our ideas about or philosophy of reality
3) an interpretation of QM and its relation to 2)
4) the language we are using to talk about 1-4)
5) ...

Doing that I come to the conclusion that something in this web of relationships (1-4) evades our naive model of nature we have before starting to think about QM. But I would not dare to deduce that QM in the sense of (1) has to be wrong. QM has always proven to be "correct" in the sense of (1). The problems appear at the level of (2-4).

So why the hell should (1) be wrong and in which sense??
bhobba
#53
Nov28-12, 06:45 PM
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Quote Quote by tom.stoer View Post
So why the hell should (1) be wrong and in which sense??
IMHO no reason at all.

Thanks
Bill
tom.stoer
#54
Nov28-12, 06:56 PM
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of course, the question goes to Quantumental ;-)

Tom


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