Does Decoherence Solve the Measurement Problem Completely

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

Quote by tom.stoer

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

Quote by 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??

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

Quantumental

Quote by bhobba

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

Quote by tom.stoer

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

Quote by Quantumental

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 wierd 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

Quote by bohm2

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 allowes 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

Quote by Quantumental

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*

Quote by Prathyush

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.

Quote by Prathyush

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.

Quote by Prathyush

Can it explain the behaviour of a photographic plate?

No.

Quote by Prathyush

What happens to the appratus after measurement?

Open question.

eloheim

Quote by Quantumental

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):

Quote by Jan-Markus Schwindt

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/ca...statistically/

http://mattleifer.info/2012/02/26/qu...e-pbr-theorem/

http://www.aps.org/units/gqi/newslet...d/vol6num3.pdf

http://mattleifer.wordpress.com/2007...ations-debate/

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

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

http://science.slashdot.org/story/11...hysical-object

http://blogs.discovermagazine.com/co.../#.ULb27oY4eso

http://www.physicsforums.com/showthr...551554&page=17

http://www.nature.com/news/quantum-t...dations-1.9392

http://motls.blogspot.com/2011/11/na...-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

Quote by nanosiborg

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:
http://www.amazon.com/Quantum-Mechan.../dp/9810241054

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

Quote by eloheim

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

Quote by Jacques Mallah

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 any one 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

Quote by tom.stoer

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

Quote by Quantumental

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

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tom.stoer Recognitions: Science Advisor	of course, the question goes to Quantumental ;-) Tom