Is there an interpretation independent outcome problem?

[atyy]

And Tegmark's Mathematical Universe is MWI with every world picked out? :)

I've always assumed Tegmark just has really bad Calendar software, which get's April Fool's wrong quite often, due to the MWI effect.

Yes, you can probably assume that I think in MWI terms. But I wouldn't want to impose an interpretive framework on the measurement problem. If MW emerges, that's a bonus. I'm guessing one would then want to re-name it the Many Worlds Theorem.

Is there an interpretation independent description of the measurement problem? In a strict sense, and if one restricts to non-relativistic QM, no, since at least one interpretation does not have the problem. But let's go more loosely here.

The traditional statement of the problem is relative to Copenhagen, ie. how does one state QM without postulating a classical measurement apparatus or classical observer? Since even if BM or MWI are correct, Copenhagen can be derived from them, there is a good argument that Copenhagen is in some sense "interpretation-independent" as an effective theory. Examples of stating the measurement problem relative to Copenhagen are found in:
Landau and Lifshitz https://www.amazon.com/dp/0750635398/?tag=pfamazon01-20
Dirac http://blogs.scientificamerican.com/guest-blog/the-evolution-of-the-physicists-picture-of-nature/
Bell http://www.informationphilosopher.com/solutions/scientists/bell/Against_Measurement.pdf
Tsirelson http://www.tau.ac.il/~tsirel/download/nonaxio.html

Zurek states the measurement problem as a loose conglomerate of problems relative to both Copenhagen, as well as to trying to get an approach like unitary evolution without hidden variables to make sense: http://arxiv.org/abs/quant-ph/0306072

Leifer tries to state the measurement problem without reference to an interpretation, and his approach is strongly realist, and he indicates he believes both BM and MWI are coherent potential solutions: http://mattleifer.info/tag/decoherence/

Wallace also tries to state the measurement problem in an interpretation independent way: http://arxiv.org/abs/0712.0149

So does Schlosshauer. Of all the statements of the measurement problem, this is the only one I don't agree with: http://arxiv.org/abs/quant-ph/0312059

 

[Nugatory]

I've always assumed Tegmark just has really bad Calendar software, which get's April Fool's wrong quite often, due to the MWI effect.

 

[Derek Potter]

I've always assumed Tegmark just has really bad Calendar software, which get's April Fool's wrong quite often, due to the MWI effect.
Is there an interpretation independent description of the measurement problem? In a strict sense, and if one restricts to non-relativistic QM, no, since at least one interpretation does not have the problem. But let's go more loosely here.

I don't think I asked that! I asked why people say there is an outcome problem that is not resolved by decoherence. Perhaps the title of my post is misleading. My actual question is expanded in the text of the post and in post #12. Why is it people say that decoherence fails to account for outcomes? It appeared to me that the assumption of definite outcomes was the culprit. I was trying to ask whether the problem remains if we don't tie ourselves to an interpretation that makes such an assumption.

The traditional statement of the problem is relative to Copenhagen, ie. how does one state QM without postulating a classical measurement apparatus or classical observer? Since even if BM or MWI are correct, Copenhagen can be derived from them, there is a good argument that Copenhagen is in some sense "interpretation-independent" as an effective theory.

Copenhagen seems to mean different things to different people. If you mean the assumption that there is a classical world then of course superposition cannot provide definite outcomes from a superposition without postulating collapse. In which case the collapse does all the work and decoherence goes on the dole. In that sense, of course, decoherence doesn't solve the outcome problem, collapse gets there first and solves it by asserting outcomes axiomatically.
But saying that Copenhagen can be derived from BM or MWI is not quite true if this meaning of Copenhagen is used consistently. You would need to insert the all-important word "appearence": the appearence of definite outcomes and then, arguably, it is not Copenhagen but the appearence of Copenhagen :)

Examples of stating the measurement problem relative to Copenhagen are found in:
Landau and Lifshitz https://www.amazon.com/dp/0750635398/?tag=pfamazon01-20
Dirac http://blogs.scientificamerican.com/guest-blog/the-evolution-of-the-physicists-picture-of-nature/
Bell http://www.informationphilosopher.com/solutions/scientists/bell/Against_Measurement.pdf
Tsirelson http://www.tau.ac.il/~tsirel/download/nonaxio.html
Zurek states the measurement problem as a loose conglomerate of problems relative to both Copenhagen, as well as to trying to get an approach like unitary evolution without hidden variables to make sense: http://arxiv.org/abs/quant-ph/0306072
Leifer tries to state the measurement problem without reference to an interpretation, and his approach is strongly realist, and he indicates he believes both BM and MWI are coherent potential solutions: http://mattleifer.info/tag/decoherence/
Wallace also tries to state the measurement problem in an interpretation independent way: http://arxiv.org/abs/0712.0149
So does Schlosshauer. Of all the statements of the measurement problem, this is the only one I don't agree with: http://arxiv.org/abs/quant-ph/0312059

Well thanks for the links, some of which I have now skimmed, though it's taken me a good six hours so far! I liked Tsirelson's "Another, for whom we are not real" (LOL) which surely touches on MMWI and therefore excuses his polemical rhetoric. I also liked Bell's "I am not squeamish about delta functions", which will one day I shall undoubtedly adopt as a sig unless another of his marvellous aphorisms surpasses it. But, as they say, what has this to do with the price of cheese? I do not wish to sound ungrateful but I feel rather as if I have asked a question and been directed to a library "The answer's in there!" What are you actually saying - is the outcome problem easily removed by saying "We don't know there is a definite outcome, we only know there is an appearence of definite outcomes so measurement theory just needs to account for the appearence"? Thanks.

 

[atyy]

But, as they say, what has this to do with the price of cheese? I do not wish to sound ungrateful but I feel rather as if I have asked a question and been directed to a library "The answer's in there!".

Oh, it has nothing to do with the price of cheese. I thought you already got your answer in post #32, so I was just making tangential remarks.

 

[Derek Potter]

Oh, it has nothing to do with the price of cheese. I thought you already got your answer in post #32, so I was just making tangential remarks.

Heh-heh. Why am I not surprised? Good stuff.

I am so looking forwards to meeting Another, for whom we are not real. Presumably he lives not in Nirvana itself but right next door! FAPP, that is.

Yes, I think I have the answer too. People are saying that decoherence fails to square the circle! Why they should actually want it to do something which is obviously impossible (and unnecessary) still eludes me.

 

[Derek Potter]

So does Schlosshauer. Of all the statements of the measurement problem, this is the only one I don't agree with: http://arxiv.org/abs/quant-ph/0312059

What is it you disagree with?

 

[Ilja]

I should like to make it clear that it is not my position that decoherence does not resolve the problem; my question was, why do people say it doesn't?

Because decoherence requires an additional structure - a subdivision into system and environment, or system and observer, or so. Only if you have this splitting into different subspaces, you can start the mathematics of decoherence and obtain, say, a preferred basis in one of the subspaces. This splitting exists in a natural way in practical environments, where we have clear splitting into various systems we want to study and their less interesting environment. But all this practical environment is nothing fundamental. There is no fundamental natural splitting into what is an observer and what is environment or so. Thus, decoherence taken alone simply cannot solve any fundamental, conceptual problems. To work, it has to presuppose a background which essentially includes the whole classical part of Copenhagen.

 

[Derek Potter]

Because decoherence requires an additional structure - a subdivision into system and environment, or system and observer, or so. Only if you have this splitting into different subspaces, you can start the mathematics of decoherence and obtain, say, a preferred basis in one of the subspaces. This splitting exists in a natural way in practical environments, where we have clear splitting into various systems we want to study and their less interesting environment. But all this practical environment is nothing fundamental. There is no fundamental natural splitting into what is an observer and what is environment or so. Thus, decoherence taken alone simply cannot solve any fundamental, conceptual problems. To work, it has to presuppose a background which essentially includes the whole classical part of Copenhagen.

You seem to be saying there is a preferred factorization of the space as well as a preferred basis in one of the subspaces. Is that right? There seems to me to be a major difference between these two preferences. The emergence of a preferred basis in a subspace involves a physical process: actual decoherence. The preferred basis is a physical phenomenon: pointers physically point for example. I think we agree this happens. The factorization of the state space, however, is arbitrary: some factorizations may be more useful than others. I don't understand why the theory needs to be able to identify the observer/environment factorization. (Schrodinger's cat may be a flawed scenario but not because we can't tell from the picture what the cat's name is.) Surely the thing that matters is the fact that there is such a factorization, and that, whatever it may be, we can then create our interaction-entanglement-decoherence-improper mixed state sequence. I can't seem to see why this means there is an outcome problem. If you stop at the improper mixed state you've just shown that under certain factorizations, there will be an emergent appearence of definite outcomes. Anything beyond that - to create a proper mixed state - is optional interpretation. Why is the appearence of outcomes not sufficient? Oh well, my maths sucks so I'm probably missing a massive point - or ten. :/

 

[Ilja]

You seem to be saying there is a preferred factorization of the space as well as a preferred basis in one of the subspaces. Is that right?

No, I do not say there is such an animal as a preferred factorization. I say there would have to be such an animal if decoherence could solve any foundational problem.

There seems to me to be a major difference between these two preferences. The emergence of a preferred basis in a subspace involves a physical process: actual decoherence. The preferred basis is a physical phenomenon: pointers physically point for example. I think we agree this happens.

No. I agree with naming this "physical" only if there is, as a background, a physical subdivision into a particular system and its environment already given.

If no such physical subdivision is given, and one simply artificially splits somehow the Hilbert space into two parts, decoherence may formally happen, but will not correspond to anything physically meaningful. In particular, it will not lead to anything worth named "appearance".

The factorization of the state space, however, is arbitrary: some factorizations may be more useful than others.

Yes, and this is the problem. Decoherence does not explain which factorizations are physically useful and which are physically nonsensical. The factorization is assumed as given.

So, the possible choices are: Or you have to assume that there is some really, fundamentally preferred factorization - and then we have the fundamental problem which one. Which requires some additional structure, with physical importance.

Or one has to do something else, something more complex, which defines, out of what is given (the Hamilton operator?) not also a preferred basis in one part, but also the factorization itself. In this case, decoherence solves only one, the easier, part of the problem it is claimed to solve.

Moreover, the counterexample of http://arxiv.org/abs/0901.3262 suggests that there is no chance for this.

I don't understand why the theory needs to be able to identify the observer/environment factorization.

Because the only alternative is to postulate them as given, defined by something else - say, the classical part of the Copenhagen interpretation, which tells me that p measures "momentum" and q "position", and the meaning of "momentum" and "position" defined from classical physics.

But if we simply accept Copenhagen, then decoherence is a quite irrelevant triviality of no fundamental relevance at all - it is simply a computation of the probablity if we will see some quantum interference effects or not. It does not change a bit in the measurement problem.

 

[Derek Potter]

OK, Thanks Ilja. I'm going to have to chew on that because I think we differ somewhat on the logic rather than the physics - whether there is a problem or not and why anyone would make it the responsibility of decoherence to solve it - but it will take a lot of unravelling. Your explanation is nice and clear to read, so thanks a lot for that and I'll get back to you some time when I've thought about it.

 

[StevieTNZ]

From the phrases I was hoping you would take away the following points:

1. Decoherence causes interference to be suppressed, resulting in what looks like classical probabilities about something that exists, e.g. 50% of getting tails or heads when flipping a coin, with tails and heads actually existing on the coin (whether this is called a proper or improper mixture, I await Bernard's email).

I am in tears.

Sadly I will never hear from Bernard d'Espagnat regarding proper and improper mixtures. He passed away 1st August.