Does Decoherence Solve the Measurement Problem Completely

tom.stoer

One must still distinguish between the physical process of decoherence (selection of preferred pointer basis, effective diagonalization of the density matrix ρ' of the subsystem S') and its interpretation. What decoherence does is that it transforms the quantum probabilities into effective classical ones; but it does not tell us which particular result encoded in the diagonal matrix ρ' will be realized in one specific experiment. In terms of Schrödinger's cat: it explains the absence of coherent superpositions, but for one single cat in one single experiment it does not tell whether this specific cat will be dead or alive after opening the box.

Quantumental

Sure, but Occam Razor says "both" if there is no preferred basis problem. (ignoring the Born Rule problem at the moment)

tom.stoer

What do you mean by "both"? Both dead and alive?

Quantumental

Yes, Everett.

tom.stoer

but this does not follow mathematically from decoherence but is a (one of many) philosophical interpretation; and therefore decoherence does not fully solve the measurement problem

mfb

It follows from decoherence and the evolution of the wave function if you do not add collapses or other stuff.

tom.stoer

You are mixing up two different things, namely a) formalism and b) its (ontological) interpretation:
a) the "mathematical entities" (subspaces, ...) describing the dead cat and the alive cat are both "present" after decoherence in the density matrix - I agree
b) it is not a matter of physics but of philosophical interpretation whether this corresponds to something "ontologically real" in the sense of MWI, whether you want to add a "collapse" or whatever; physically this is a matter of taste b/c there is no experimental prediction to distinguish between all these interpretations, so it's philosophy or metaphysics (Ockhams razor is philosophy, not physics)

As a platonist believing in some abstract sense in the reality of the wave function and the specific cat as its realization I may also believe in MWI. As a positivist I will not believe in any reality but only in the results of my calculation and whether they agree with experimental results or not; they agree with experiments - fine - end-of-story (it is interesting that there are positivists arguing for MWI and against a collapse - which is a self-contradictory position).

Not even Ockhams razor is sufficient to decide b/c there are two choices:
1) add complexity to the ontological level in order to reduce the complexity of the interpretation => MWI
2) add complexity to the (not fully understood) explanation or interpretation in order to reduce complexity of the ontological level => collapos (b/c there is only one world = the observable world)
Ockhams razor doesn't tell you whether (1) or (2) is the correct reasoning b/c Ockhams razor is applied two different 'categories', namely
1) to 'interpretation'
2) to 'ontology'

So decoherence as a purely physical phenomenon cannot tell us anything regarding the metaphysical level. In order to deduce a metaphysical reasoning you have to have some metaphysical input - which is not present in the formalism of QM and decoherence.

Compare the following positions:
1) There are two branches of reality, both real in the same sense, one containing the dead cat and one containing the alive cat; and there are two observers in these two branchens ... In that sense everything that is present in the density operator does exist in the above mentioned sense.
2) blablabla regarding collaps ...
3) There is a density operator describing the probability to find a dead cat; but b/c w/o any observation of both cats at the same time - which we don't have - we do not have any indication whether they both exist in some still to be defined sense, so we decide not to ascribe any ontological meaning to the density operator (nor to wave functions etc.) We use the QM formalism as a model which approximately represents a subset of aspects of "reality" but which allowes us to predict results of a certain class of experiments

3) is an agnostic position. It does not allow us to explain in any sense why (!) physics (based on mathematics) is a successful description of reality - b/c neither do we make any statement regarding the relation between physics and reality, nor do we make any attempt to define 'reality'. But it still allowes us to use quantum mechanics including decoherence to derive experimentally testable and accurate predictions.

Any position that goes beyond (3) like MWI in the sense of (1) or collapse (2) adds some metaphysical reasoning beyond decoherence as a pure mathematical fact.

eloheim

I thought it was always possible, in principle, to discover whether or not superposition remains or a collapse has occurred as long as the relevant degrees of freedom in the environment are accounted for?

I wonder if detailed study of the line between "in principle" and "in practice" might reveal something here (based on limited information storage capacity in the universe).

tom.stoer

In the formalism of QM there is neither a collapse nor a branching into many worlds; there's only a single wave function with unitary time evolution (or a density matrix; but taking all d.o.f. into account there is not even the need to consider density matrices)

But when a human observes a pointer in an apparatus the pointer is not in any superposition, so there must be something like a collaps, a branching or whatever; and this is beyond the formalism of QM.

bhobba

Exactly.

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.

Thanks
Bill

jimgraber

Where does Schlosshauer say this?
I'd appreciate the reference. TIA. jimgraber

eloheim

Why are the pointer and observer not simply in superposition as well?

Nugatory

You've come full circle, back to Schrodinger's cat. I can set the experiment up so that in one position of the pointer I'm dead and in the other I'm alive; and now "simply in superposition" means a superposition of me dead and me alive. That's fine as far as the formalism of QM goes, and it makes perfect sense mathematically... But it's not a particularly useful description of anything.

bhobba

Page 49 Decoherence And The Quantum To Classical Transition.

Thanks
Bill

tom.stoer

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.

So QM doesn't tell us how potential results become actual (real) results. Even decoherence doesn't.

nanosiborg

I like your take on this. And some others. My two cents is:

QM is a probability calculus based on classical wave mechanical concepts of the reality underlying instrumental behavior which are inferred from the instrumental behavior. 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.

There is currently no extension or interpretation of QM (including decoherence) which explains instrumental behavior to the extent that that behavior can be predicted in any way other than assigning probabilites to the possiblities associated with any particular instrumental preparation.

Why there's only one observed experimental outcome rather than the multiple ones that might be entailed in a particular superposition isn't the question, imo. The question is, rather, eg., why was there a detection (as opposed to no detection) recorded during a certain interval. Decoherence can't answer this question, because the mathematics of decoherence doesn't tell us any more about the reality underlying instrumental behavior than can be inferred without applying the mathematics of decoherence.

Quantum amplitudes are superposed in accordance with the requirements of any consistent wave mechanical representation. Philosophical pseudo-problems and paradoxes arise due to assuming that quantum states are real ontological states, which is an assumption that has no direct evidentiary support.

The current state of affairs is that the math of quantum decoherence doesn't solve the real measurement problem. Imho, there will never be a solution to the real measurement problem.

It seems likely to me that some form of QM, ie. a probabilty calculus regarding instrumental behavior, is the best that can be hoped for -- and that the real quantum measurement problem will remain unsolved.

tom.stoer

nanosiborg, great, thanks.

A view comments:

Not necessarily; it could be an ontological feature, but see below ...

Decoherence (in the strict sense of the formalism) isn't an interpretation; it becomes an interpretation if we add something like MWI, or if we are sloppy in our discussions ...

Exactly. It explains a lot (classical probabilities, pointer basis, perhaps Born's rule), but not everything.

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.

Yes, that's one possibility.

Perhaps the whole discussion is misguided b/c decoherence adds a pseudo-solution in introducing the incoherent (classical) environment. It seems as if adding a classical environment could solve the quantum measurement problem (the discussion shows that it doesn't). But even if decoherence applies to most experiments (fapp) we must not forget about experiments which we could construct in principle, namely measurements where the apparatus is perfectly isolated from the environment and where the branching or collaps is not due to decoherence + XYZ. In that case we still have to deal with a small number of entangled d.o.f. and decoherence simply doesn't apply!