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Specifically, how can decoherence explain the appearance of flecks of metallic silver on a photographic plate when exposed to the very weak light of a distant star?

EDIT: Perhaps the advocates of decoherence need some context for this question. There is a certain definite quantity of energy on the order of one or two eV to drive the chemical reaction

2AgBr -> 2Ag + Br2

This is the reaction responsible for the fleck of silver on the photographic plate. The amount of energy is far greater than can be accounted for in any realistic time frame by the classical e-m wave energy of the light of a distant star.

Any explanation must explain where this energy comes from. How does "decoherence" claim to do this? I have heard over and over again that there is a matrix which is diagonalized, but no one has so much as volunteered to say just what matrix they are talking about. Is it, for example, the matrix of position states of the photon? Or perhaps it is the oxidation states of the silver atom? And I would really like a better explanation of how the matrix is "diagonalized" than to simply repeat that it is in "thermal contact with the environment."

EDIT: I have reviewed the comments again and I find that no one has come close to dealing with the question. I cannot find anything wrong in the way I have asked it so far, so I am posting this edit as my only means to prompt people to attempt an answer.

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Over the last few days I have posted questions unsuccessfully trying to elicit examples of what is meant by collapse of the wave function. No one has volunteered any such examples; however, some people have said there is no such thing as collapse because decoherence explains everything. This brings us to the present question. –  Marty Green May 23 '11 at 16:07
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I don't have time right now for a proper answer (which this question surely deserves) but I hope to come back with it later. For now, at the very least be sure to read wikipedia article and in particular this section. Especially focus on the fact that what appears as collapse (i.e. discontinuous jump in Hilbert space) is in fact caused by very coarse time resolution. If you look at it more closely, the evolution is unitary and the degrees of freedom "escape" into environment. –  Marek May 24 '11 at 5:35
    
Another point that I want to stress is that wave function collapse in the relativistic setting does not work at all if one assumes wave-function is an extended physical object. That is because different observers wouldn't necessarily agree on when the collapse happened. This again suggests that the whole collapse dogma is fishy and at best can be used only in certain situations (non-relativistic, long time scales, microscopic systems, ...). Another subject that it can't even begin to address is quantum/classical boundary (i.e. size of a system where genuine quantum properties appear). –  Marek May 24 '11 at 5:39
    
Yet another point is that decoherence is used to describe diagonalization of density matrix, but collapse is other story – it is “problem of definite outcome”. The last problem is not relevant with most practical applications. An analogue of the problem in classical case is a question – I know that probability of each face of dice is 1/6, but I want now to have a method to find precisely that particular face appears in given experiment. –  Alex 'qubeat' May 24 '11 at 12:00
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I would disagree slightly with @Marek when he says that discontinuous jumps are always caused by coarse time resolution. They can also be caused by not having access to the environment which is causing the system to decohere. Quantum jumps can appear naturally in solutions of the "master equation," which describes the interaction of a system with its environment. –  Peter Shor May 24 '11 at 23:44
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1 Answer

Almost phenomenologically, "the appearance of flecks of metallic silver on a photographic plate" is a thermodynamic transition that happens at different rates depending on the details of how the plate is prepared and on details of the exposure of the photographic plate. Such thermodynamic transitions are often correlated in nontrivial ways. All QM has to do to be Useful is to model or describe the statistics of the thermodynamic transitions. [Note that my introduction of the idea of a thermodynamic transition makes my claim here "theory-laden", not quite phenomenological, at least to that extent.]

Explanation is not necessary for Usefulness. One topic of research in Philosophy of Physics has been to try to determine what makes a model "explanatory", which IMO has been rather inconclusive. Models may be more or less Useful for many different reasons, including tractability and directness of reference between elements of the theory and elements of experimental signal data. Note that a class of models may seem explanatory for 50 years even if it is the phlogiston theory, if the model is superficially nice in whatever ways.

Which brings me to my Answer, which I'm pretty sure you won't find Useful, which is that Decoherence doesn't explain particularly well, whatever that means, partly because it's not a very tractable approach. Decoherence seems to have fairly direct referents, which perhaps is what makes it appeal to some people quite strongly. The same is true of "wave function collapse": it's possible to structure experimental data taking wave function collapse as a fundamental modeling strategy, but so far no-one has produced a mathematization that is enough more Useful than just dealing with the statistics of thermodynamic events. There are people who think it illuminates what we're doing with QM in ways that might lead to a better mathematical formulation of the whole theory, but, I think, nothing yet.

In a similar vein, you may notice that Particle Physics is more often called High Energy Physics than it used to be, which seems to me to reflect the realization, not uniformly acknowledged, that the explanation of tracks of obviously related thermodynamic events in detectors as "caused by particles" is weakened by the many low-energy experiments that show that the concept of a particle cannot be that simple. As of now, Quantum fields are as likely to be the locus of descriptions of experiments.

I'm curious whether you can knock down this argument, such as it is. I think you're looking at this all wrong, but of course it may be me. That I've worked on this for a long time doesn't guarantee much.

EDIT (a long comment, in response to Marty's comment that first mentions "Quantum Siphoning"): I take the Wave Function and operators to be a good way to generate probability measures. The empirical success comes from the probabilities being able to be good models for (or descriptions of) statistics of raw experimental data. I take it that probabilities do not cause individual events, they describe sets of events (propensity interpretations of probability notwithstanding). [If we go the Wigner function route --which I don't, except as a mathematical equivalence, because I think it obscures the relationship to empirical data-- the wave function is just a generalized probability function that sometimes has negative values.] If one wants to change probability distributions as a result of experience, instead of taking other approaches to statistics, then one should use something like Bayes' rule, which in general doesn't just change the probability from 0.615802 to 0 or to 1. "collapse" of the wave function adds an extra level of structure to the concept of a probability distribution that I think just doesn't fit well, as Mathematics. If people want to use "collapse", I think it has to be done somehow differently. It's possible that a propensity interpretation could work for you, but I think we would then quite quickly get far enough apart that we can't talk to each other.

I think I prefer my description of individual events (and we may just have to accept that this is a sticking point)-- that we should say that the individual events are "thermodynamic transitions", whatever that means, leaving a causal account of how that happens for the future. The concept of thermodynamic transitions is the historical concept from Physics that I think fits the case. A thermodynamic event implicitly invokes at least a large number, perhaps an infinite number of degrees of freedom, to explain what happens when there is an apparent discontinuity, it introduces a degree of complexity that is hard to manage mathematically, which definitely has its problems. Decoherence also introduces an infinite number of degrees of freedom, but I think by introducing the environment in the way it does it doesn't adequately embrace the complexity of the photographic plate. I think your description of what happens in a photographic plate accepts that complexity, but then looks to make "collapse" of a quantum state, which has nowhere near as much structure as the photographic plate, be an explanation of what is happening. It's important that it not be brushed under the table, but we can measure where and when thermodynamic events happen without knowing how they happen.

I hope that's helpful. I expect no-one else is listening!

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@Peter I'm gratified that you're interested in how I would counter your argument, but at the same time I wish I knew how you think I'm looking at it. As far as I'm understanding, you're simply saying that decoherence doesn't explain it. That's hardly an argument, and as such, I don't know why you'd expect me to try and knock it down. Did you understand that I posted this question as a kind of "put up or shut up" challenge to people who said that decoherence explains everything? –  Marty Green May 23 '11 at 19:57
    
Marty, that clarifies my thinking on your intentions some. There's enough mathematical work on decoherence to keep you reading it for a few years, if you engage with it. With that, "put up or shut up" sounds off, insofar as they sort of have already. They're working on their thing, I'm working on mine, everyone spends their time in whatever way they think useful. If you want to work on a different way to "explain" "wave function collapse", then you can. It will be called Physics, I guess, if it's seen as useful, in whatever way, by some number of Physicists. Sorry that's chicken and egg-ish. –  Peter Morgan May 23 '11 at 20:22
    
@Peter One of the very best math puzzles ever starts of with Mr. S and Mr. P facing each other. S is thinking about the sum of two numbers between 1 and 100, and P is thinking about their product. Neither knows what the numbers are. Mr S begins: I don't know what your number is. P replies And I don't know what yours is. S replies: Now I know what your number is. And S concludes: And now I know yours. In that vein, Peter, I'm glad you think you know what I'm thinking; but I'd still like to know what you think I'm thinking. –  Marty Green May 23 '11 at 20:33
    
@Marty, Hee! I fold, I guess. I never was good at poker. I'd already looked at your blog; backing off to try to see at least one of the wood or the trees, I looked some more. "Why I hate physics" but do it all the time? It's nicely concrete in a way I could sadly never do very well. I doubt I will ever do so well the sort-of-abstract thing I want to do. Your Questions have so far felt sideways to me; interesting, but I'm not quite getting where the itch is. For good or bad, I'm practically back-to-front myself, so I'm not complaining. My prejudices are pretty clearly getting in the way. –  Peter Morgan May 23 '11 at 21:09
    
@Peter I'm glad you found my blog, even though it's more just a collection of random articles than a blog. I hope you read my article on Quantum Siphoning: it's from March of 2010 and the link is marty-green.blogspot.com/2010/03/quantum-siphoning.html –  Marty Green May 23 '11 at 22:39
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