Does Decoherence Solve the Measurement Problem Completely

[tom.stoer]

Thanks tom.stoer. I think I should reread your and others' comments and think about this some more.

give me a hint; where's a contradiction?

 

[nanosiborg]

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]

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]

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.)

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!..

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]

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]

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]

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]

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]

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]

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.

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 can't 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.

This used to be how I viewed the situation, but then what about PBR theorem?

Exactly

Thanks
Bill

 

[tom.stoer]

PBR theorem? this is new to me; seems that reading LQG and LHC Higgs papers is the wrong scope

 

[bhobba]

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 realized 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]

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.

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]

M

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]

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]

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.

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]

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]

So why the hell should (1) be wrong and in which sense??

IMHO no reason at all.

Thanks
Bill

 

[tom.stoer]

of course, the question goes to Quantumental ;-)

Tom

 

[bohm2]

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??

But can't (1) itself also be seen just as one more interpretation of QM (e.g. an instrumental approach).

 

[Quantumental]

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.

I do.

Belief in indeterminism is to me exactly like solipsism, sure I can never prove it wrong, it's logically coherent, but it explains nothing and I have no reason to think it's true.
For anyone believing in indeterminism, I wonder how you can justify the Born Rule. What sort of sense would it make for a genuinely indeterminate universe to care about a statistical rule like that of Born?
Why wouldn't particles just do whatever the hell they want at all times without obeying any laws what so ever. The fact that we observe a "rule" is to me philosophically requiring an explanation.
To me "random" is JUST as likely as inventing a God. So when you ask "why did the cat die?" I would say "God became allergic to felines" and take that just as seriously as "it just happened out of randomness".
If you followed up with "but why would God kill cats according to what we percieve as the Born Rule?" I would tell you: "God works in mysterious ways" and claim a Nobel Prize.
It's incoherent, stupid and not science. Science seeks explanations, if we had given up when we hit something that seems random we would have given up on trying to model ANYTHING, because EVERYTHING seems incomprehensible at first sight.
Imagine the first time someone pondered the rain, it would have to have seemed completely random, which is why most societies at the time believed in weather Gods, they saw no other explanation. I am 100% confident that reality is not indeterministic

 

[Quantumental]

1) QM as a theory of nature = a formalism to predict experimental results
...

So why the hell should (1) be wrong and in which sense??

I picked the wrong word, what I mean by wrong is that it's not 100% right, because it's incomplete.
So it's wrong in the same sense that Newtonian gravity is wrong. It works but it's not the final and fundamental model.

This is the same way I percieve QM given the fact that there is no way to make sense of QM unless you are willing to accept antirealistic-indeterminism on par with solipism, Bohm (non-local and surrealistic trajectories) or Many Worlds and be able to get the Born Rule out of Many Worlds.

 

[bhobba]

For anyone believing in indeterminism, I wonder how you can justify the Born Rule.

Actually its not that hard. It follows from the key assumption of additivity of expectation values as pointed out by Von Neumann's original hidden variable no go theorem. Its such a natural assumption it took a while to see it didn't necessarily apply to hidden variables - actually its more correct to say it took a while for the people that originally saw the issue (and a few did) to be heard above someone of Von Neumann's stature.

Later harder to evade theorems such as Gleasons also came along that also justifies it - but of course that is also evadeable since it rests on a crucial assumption of non-contextuality. I think contextuality is pretty weird but if you want determinism that's what you need.

I hasten to add me thinking the additivity of expectation values natural and contextuality weird means Jack Shite - nature does not have to respect my or anyone else's aesthetics.

Oh and since PBR has been mentioned I am glad I got the chance to post Schlosshauer's analysis of it which shows like contextuality and Von Neumann's theorem it also rests on hidden assumptions. Its very interesting how given a theory/interpretation that PBR applies to one can always construct one where it doesn't - and conversely. Its just goes to show how weird nature really is.

Thanks
Bill

 

[tom.stoer]

But can't (1) itself also be seen just as one more interpretation of QM (e.g. an instrumental approach).

No, not really.

An agnostic view regarding (1) would be that QM allows us to predict experimental results - end-of-story.

I agree that this seems to be incomplete b/c there is not reason "why" this works, there is no idea regarding reality or regarding a relation between the QM formalism and reality. And there it always a kind of 'interpretation' in the sense of "given this apparatus and an electron I have to use that formula with the following initial conditions".

All what I am sying is that these missing pieces - and I agree that this agnostic view is unsatisfactory and that there are missing pieves - are not on the level of (1).

Let's make a simple example: in classical mechanics we can count dead cats and alive cats (and such things) using Peanos axioms. Their consistency or inconsistency in the sense of Hilbert's second problem is to be discussed on the level of (1), the reason "why" we can use them is beyond level of (1).

Btw.: we never ask the question "why" things work as they do in classical mechanics. Why do we not ask this question? Why do we ask this question in QM? Is it really true that we have a full understanding of these ideas in classical mechanics? I am sure the answer is "no".

 

[tom.stoer]

If you followed up with "but why would God kill cats according to what we percieve as the Born Rule?" ... It's incoherent, stupid and not science. Science seeks explanations, ...

I understand what you are asking for. And I agree with you in some sense, and I am therefore interested in the same kind of questions.

All what I am saying is that these problems are strictly speaking not on the level of (1) as a pure mathematical formalism but beyond that level. And it is not clear that your interpretation of science (it's an interopretation, not a definition) is not the common view, at least not in quantum mechanics; many will agree that QM is not about "why" and not about "explanations". That does not mean that QM in the sense of (1) is incomplete or wrong. It just means that there are good reasons to go beyond (1) - and to be very careful when we should stop calling something science and when it becomes metaphysics (not with any negative connotation).

I think we should remeber where this discussion started. It was about the question regarding decoherence and the measurement problem. This thread (and many others) show that one problem is that decoherence comes with some context (interpretations, measurement problem, ...) and that in many presentations the facts (decoherence) and the context are presented as the same thing. So all what did was to decompose "decoherence as presented or perceived" in "decoherence as a fact derived from QM and demonstrated by experiments" and "context and interpretation of decoherence like measurement, many worlds, ...".

 

[nanosiborg]

As the Title describes, Is the measuremet problem completely solved by the decoherence Program?

No. No matter how the measurement problem is formulated it isn't solved by the "decoherence Program", as you put it.

In specific I would like the following question addressed.

Is there is clear explanation as to what it means to Record Infromation?

Yes. The physical referents of the term "recorded information" are amenable to our sensory apprehension.

Can it explain the behaviour of a photographic plate?

No.

What happens to the appratus after measurement?

Open question.

 

[eloheim]

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

Does this do anything for you? (And being in line with the thread title.) A small part of this (just to set up the issue):

How can the EI [Everett Interpretation] explain the observed probabilities in quantum measurements? I.e.,
why is the squared norm |ca|2 of a branch equivalent to the probability an observer
encounters for measuring the value a? If an observer performs the “same” (equivalent)
measurement many times, the state vector branches each time, and in the
end there will be a branch for each combined result of the measurements. Each
branch also contains one version of the observer. Each observer will conclude the
probability for each value a from the statistics of the individual results he got. One
can show that the norm of the part of the state vector corresponding to branches
where observers don’t get the right probabilities converges to zero when the number
of measurements is increased [2]. The remaining question is whether or not this
argument solves the problem (I think it does). In this paper, I will not deal with
the probability problem, so I won’t discuss this issue any further.

An argument against this resolution is that the limit only holds in the case of an infinite number of measurements (which seems unphysical). However, as Aguirre and Tegmark point out here, in a spatially infinite universe there actually will be an infinite number of such measurements being made. This is suggests to them the measurement problem can be resolved by appealing to a duality, of sorts, between the many worlds of quantum mechanics and cosmology.

 

[nanosiborg]

My understanding of the usual formulation of the quantum measurement problem is that it has to do with an apparent contradiction between the dynamics of quantum theory as described by the Schrodinger wave equation (and its wavefunction solutions), and the Born measurement axiom or postulate.

I call this the pseudo quantum measurement problem because I don't see any logical contradiction there.

That the underlying reality has something to do with wave shells expanding in media of unknown structure seems to me to be a most reasonable assumption. This is what the wave equation and wavefunctions have 'something' to do with (in the sense that they might be conceptually associated with an underlying reality), imo.

We place obstructions in the paths of the expanding wave shells and posit that the probability of whether or not a detection is recorded will be in direct proportion to the amplitudes (specifically, the squares of the amplitudes) of the wave fronts as they contact the obstructions. No problem there. This applies to waves in both particulate and nonparticulate media, and is understandable in terms of our limited sensory apprehension of nature.

What's less understood, or, not really understood at all, is the qualitative nature of the apparent particlelike properties of individual quantum detection results, which, in my view, is part of the real quantum measurement problem.

Decoherence cannot, imo, solve what I consider to be the real quantum measurement problem.

 

[nanosiborg]

By the way, thanks to all commenters, especially tom.stoer, bhobba, Quantumental, eloheim and bohm2 (apologies if I failed to mention other substantial commenters). I'm a recent graduate with a more than passing interest in the foundations of quantum theory, and modern physics in general. I've been doing a little homework and, for your convenience and amusement, here's a sampling of some of the reading and viewing that I've been doing with the help of the internet.

Some of it is beyond my current ability to fully understand (or maybe I'm just trying to read too fast). So, expect some questions ... and I hope they don't sound too naive.

http://mattleifer.info/2011/11/20/can-the-quantum-state-be-interpreted-statistically/

http://mattleifer.info/2012/02/26/quantum-times-article-on-the-pbr-theorem/

http://www.aps.org/units/gqi/newsletters/upload/vol6num3.pdf

http://mattleifer.wordpress.com/2007/04/11/why-is-many-worlds-winning-the-foundations-debate/

http://pirsa.org/displayFlash.php?id=12050021

http://dabacon.org/pontiff/?p=5912

http://science.slashdot.org/story/1...uantum-wavefunction-is-a-real-physical-object

http://blogs.discovermagazine.com/c...hysicality-of-the-quantum-state/#.ULb27oY4eso

https://www.physicsforums.com/showthread.php?t=551554&page=17

http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392

http://motls.blogspot.com/2011/11/nature-hypes-anti-qm-crackpot-paper-by.html

Distinct Quantum States Can Be Compatible with a Single State of Reality
http://arxiv.org/abs/1201.6554

On the reality of the quantum state
http://arxiv.org/abs/1111.3328

Exponential complexity and ontological theories of quantum mechanics
http://arxiv.org/abs/0711.4770

Strengths and Weaknesses of Quantum Computing
http://arxiv.org/abs/quant-ph/9701001

Einstein, incompleteness, and the epistemic view of quantum states
http://arxiv.org/abs/0706.2661

In defense of the epistemic view of quantum states: a toy theory
http://arxiv.org/abs/quant-ph/0401052

The paradigm of kinematics and dynamics must yield to causal structure
http://arxiv.org/abs/1209.0023

Formulating Quantum Theory as a Causally Neutral Theory of Bayesian Inference
http://arxiv.org/abs/1107.5849

 

[bhobba]

Some of it is beyond my current ability to fully understand (or maybe I'm just trying to read too fast). So, expect some questions ... and I hope they don't sound too naive.

Mate it looks like you are deadly serious in understanding this stuff - great to see.

The book to get is Ballentine - Quantum Mechanics - A Modern Development:
https://www.amazon.com/dp/9810241054/?tag=pfamazon01-20

Here you will find QM developed from just two axioms and Schrodengers equation derived (yes derived - not assumed) from its true basis - Galilean Invariance.

Take your time, go through it carefully, and you will come away with a really good understanding.

Thanks
Bill

 

[Quantumental]

An argument against this resolution is that the limit only holds in the case of an infinite number of measurements (which seems unphysical). However, as Aguirre and Tegmark point out here, in a spatially infinite universe there actually will be an infinite number of such measurements being made. This is suggests to them the measurement problem can be resolved by appealing to a duality, of sorts, between the many worlds of quantum mechanics and cosmology.

I don't think this really helps at all and I'll quote someone who has dealt with this

The frequency operator is the operator associated with the observable that is the number of cases in a series of experiments that a particular result occurs, divided by the total number of experiments. If is assumed that just the frequency itself is measured, and if the limit of the number of experiments is taken to infinity, the eigenvalue of this frequency operator is unique and equal to the Born Rule probability. The quantum system is then left in the eigenstate with that frequency; all other terms have zero amplitude, as shown by Finkelstein (1963) and Hartle (1968).

This scheme is irrelevant for two reasons. First, an infinite number of experiments can never be performed. As a result, terms of all possible frequencies remain in the superposition. Unless the Born Rule is assumed, there is no reason to discard branches of small amplitude. Assuming that they just disappear is equivalent to assuming collapse of the wavefunction.

Second, in real experiments, individual outcomes are recorded as well as the overall frequency. As a result, there are many branches with the same frequency and the amplitude of anyone branch tends towards zero as the number of experiments is increased. If one discards branches that approach zero amplitude in the limit of infinite experiments, then all branches should be discarded. Furthermore, prior to taking the infinite limit, the very largest individual branch is the one where the highest amplitude outcome of each individual experiment occurred, if there is one.

A more detailed critique of the frequency operator approach is given here(http://arxiv.org/abs/quant-ph/0409144).
The same basic approach of using infinite ensembles of measurements has been taken recently by certain Japanese physicists, Tanaka (who seems unaware of Hartle's work) and (seperately) Wada. Their work contains no significant improvements on the old, failed approach.

 

[Quantumental]

Btw.: we never ask the question "why" things work as they do in classical mechanics. Why do we not ask this question? Why do we ask this question in QM? Is it really true that we have a full understanding of these ideas in classical mechanics? I am sure the answer is "no".

The reason we don't ask why in classical mechanics is because we know it's not fundamental, the answer will always reduce to a more fundamental theory.
So for those who think that QM is *the* fundamental theory, they have to explain why everything occurs really.
If you ask why and their reply is simply: indeterminism!, then that suggests to me that they are not really interested in knowing why, but rather just want the math to work. That's fine if you are going to do technical work, but if you are seeking truth you can never be satisfied with "it just happens"

 

[bhobba]

If you ask why and their reply is simply: indeterminism!,

That's not my reply, which is Gleasons Theorem provides a pretty strong reason for QM being a statistical theory:
http://en.wikipedia.org/wiki/Gleason's_theorem

Gleason's theorem highlights a number of fundamental issues in quantum measurement theory. The fact that the logical structure of quantum events dictates the probability measure of the formalism is taken by some to demonstrate an inherent stochasticity in the very fabric of the world. To some researchers, such as Pitowski, the result is convincing enough to conclude that quantum mechanics represents a new theory of probability. Alternatively, such approaches as relational quantum mechanics make use of Gleason's theorem as an essential step in deriving the quantum formalism from information-theoretic postulates.

The theorem is often taken to rule out the possibility of hidden variables in quantum mechanics. This is because the theorem implies that there can be no bivalent probability measures, i.e. probability measures having only the values 1 and 0. Because the mapping is continuous on the unit sphere of the Hilbert space for any density operator W. Since this unit sphere is connected, no continuous function on it can take only the value of 0 and 1. But, a hidden variables theory which is deterministic implies that the probability of a given outcome is always either 0 or 1: either the electron's spin is up, or it isn't (which accords with classical intuitions). Gleason's theorem therefore seems to hint that quantum theory represents a deep and fundamental departure from the classical way of looking at the world, and that this departure is logical, not interpretational, in nature.

Of course it doesn't prove anything but for sure it is far from certain that in-determinism can not be fundamental - not certain at all.

Thanks
Bill

 

[tom.stoer]

the reason why we don't in classical mechanics is that classical mechanics fits to our perception whereas QM doesn't; QM was the first physical theory to which no Platonism, Aristotelism, Kantianism or any other XYZism had an answer; QM does not fit to the categories of our perception;

now there are two options
1) change nature
2) change our ideas about nature
for me 2) is acceptable, but that's a matter of taste ;-)

 

[Quantumental]

now there are two options
1) change nature
2) change our ideas about nature
for me 2) is acceptable, but that's a matter of taste ;-)

The problem is this: you could've said the same thing *ANYTIME* in history, remember that microscopes and telescopes are very recent in history.
Hell we can make it even more absurd.

Why should you assume that existence existed before you? Sure you might say "well my observations seem to be best accounted for by postulating that things were around before me."
After all, it makes little sense that existence surrounding you should try to decieve you into thinking that old things have been around for a long time if they hasn't.

But the same applies to Born Rule, there is no reason why something that is truly indeterminate should follow a statistical rule...
So with the same logic you reject the "the universe came into existence with me" hypothesis, I reject the "magic is the reason Born rule exists."