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- Thread starter ThomasT
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Such as ... ?

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Since you're a Bohmian, id the "something else" you're referring to ignorance of which of the Everett many worlds is the "actual world"?

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bhobba

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Well its basically the wavefuntion collapse issue. Decoherence is the usual explanation these days. I believe it resolves it and in a very elegant way but opinions vary.

The conceptual reasoning behind it is its usually thought to be the only reasonable way you can define probabilities in a theory based on the principle of superposition eg see Gleasons Theorem. The reason you need probabilities is deterministic models turn out to be problematical eg see the Kochren Specker Theorem.

Thanks

Bill

The conceptual reasoning behind it is its usually thought to be the only reasonable way you can define probabilities in a theory based on the principle of superposition eg see Gleasons Theorem. The reason you need probabilities is deterministic models turn out to be problematical eg see the Kochren Specker Theorem.

Thanks

Bill

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Such as ... ?

Bohmian particle trajectories are certainly one possibility.Since you're a Bohmian, id the "something else" you're referring to ignorance of which of the Everett many worlds is the "actual world"?

Another possibility are additional axioms needed for the many-world interpretation to work. (For example, an axiom from which the Born rule can be explained.)

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Most papers on decoherence these days admit that decoherence is important but not sufficient to explain the collapse.Well its basically the wavefuntion collapse issue. Decoherence is the usual explanation these days.

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The only interpretation I need to make the connection between the QT formalism and real-world observations is Born's probabilistic interpretation of states, and there is no need for a collapse! So, I don't need an "explanation" for a collapse.

This is true in even stronger form for any additional elements in the formalism as in Bohm-de-Broglie pilot-wave interpretations. There I don't need to bother with unobservable trajectories; let alone any other esoterics like the "many-worlds" or "Princeton" interpretation.

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This is essentially the Ballentine statistical ensemble interpretation. It is indeed consistent, but still has some unappealing features which make it not universally accepted.The only interpretation I need to make the connection between the QT formalism and real-world observations is Born's probabilistic interpretation of states, and there is no need for a collapse!

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Fredrik

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All we need to make predictions about results of experiments, is the version of the Born rule that says for all observables A, and all pure states s, the average result in a long sequence of measurements of A, on systems that are all in the state |s>, will be <s|A|s>.

But to test those predictions, we also need to know what state to associate with the preparation procedure we're using. We need a rule that assigns states to preparation procedures. I'm not aware of anything other than the projection postulate that can do that.

**Edit:** I just need to make sure that we're talking about the same thing. What I just said is based on the assumption that the "projection postulate" is the rule that says that if we measure A and get the result *a*, and if the system wasn't destroyed by the measurement, then immediately after the measurement, it will be in an eigenstate of A with eigenvalue *a*. Let me know if you guys were actually talking about something else.

**Edit: 2** After reading Demystifier's post #2 again, I started thinking "Is decoherence another thing that can associate mathematical states with preparation procedures?". It seems to me that the answer is no. Decoherence is a prediction of the theory, but we don't even *have* a theory without the projection postulate.

But to test those predictions, we also need to know what state to associate with the preparation procedure we're using. We need a rule that assigns states to preparation procedures. I'm not aware of anything other than the projection postulate that can do that.

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bhobba

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Most papers on decoherence these days admit that decoherence is important but not sufficient to explain the collapse.

That's because the wrong question was asked. It for all practical purposes does explain it - there is no way to observationally tell the difference between a mixed state where each state is an eigenstate and wavefunction collapse.

Out of curiosity mind giving me some of those most papers - its not the view of the stuff I read such as Sholosshaurs book on decohrerence.

Thanks

Bill

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bhobba

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This is essentially the Ballentine statistical ensemble interpretation. It is indeed consistent, but still has some unappealing features which make it not universally accepted.

All interpretations suck in some way - it a matter of personal preference which you think sucks the least - I think the ensemble interpretation does that combined with decoherence - not that Ballentine is a big fan of decoherence.

Thanks

Bill

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bhobba

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Decoherence is a prediction of the theory, but we don't evenhavea theory without the projection postulate.

Indeed. But it does allow us to skirt problematical issues. For example the ensemble interpretation has problems with accepting the actual reality of the ensembles because the Kochen-Specker theorem means it can not be in an actual state that observation selects - but with decoherence it can.

Thanks

Bill

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Fair enough!All interpretations suck in some way - it a matter of personal preference which you think sucks the least - I think the ensemble interpretation does that combined with decoherence - not that Ballentine is a big fan of decoherence.

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I disagree. Even without the projection postulate, even without the Born rule, even without the probabilistic interpretation, we can calculate "reduced density matrices" as abstract mathematical objects governed by the Schrodinger equation. This is sufficient to predict decoherence, even if we have no idea what it means physically.Edit: 2After reading Demystifier's post #2 again, I started thinking "Is decoherence another thing that can associate mathematical states with preparation procedures?". It seems to me that the answer is no. Decoherence is a prediction of the theory, but we don't evenhavea theory without the projection postulate.

Of course, if you do have a probabilistic interpretation, then this further motivates you to calculate the reduced density matrix because then you know what is the meaning of it. But the point is - you can calculate it even without knowing about the probabilistic interpretation.

Besides, Bohmian interpretation is an example demonstrating that we can even have a full physical interpretation without the projection postulate.

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Fredrik

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I certainly didn't mean to suggest that the theory is guaranteed to remain broken even if we replace the projection postulate with something else. I don't know what that would be in Bohmian mechanics, but it has to be something. Every theory needs a rule that associates preparation procedures with mathematical things that can represent them.

The only thing I said (or rather inadvertently suggested, by my precise choice of words) that your argument seems to refute is that we need the full theory (=mathematics+correspondence rules) to find decoherence. I agree of course that decoherence is present in the purely mathematical part of the theory.

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I explained this starting with introductions of metaphysics, noting that purely mathematical laws of physics can only describe a mathematical universe, with a merely mathematical existence.

There needs to be something beyond mathematical laws to both provide for existence beyond mere mathematical existence, and for non-algorithmicity.

Because the mind's behavior cannot be purely algorithmic, for at least 2 reasons:

One is that, again, a purely algorithmic behavior cannot account for the notion that we "really exist" (that we have an authentic feeling of our existence, that morality makes real sense), because otherwise our existence would be purely mathematical, making any concept of probability devoid of any sense (since all possibilities equally exist mathematically, none of them can meaningfully be said more probable than another) and therefore in contradiction with the fact that such probability laws exist and have been verified.

The other is that the reasoning power of the mathematician can know things such as the consistency of ZF, that cannot be proven out of any formal system that can be reasonably assumed to be his. I am planning to soon add this point to my site on set theory and the foundations of mathematics - this will come after the many also very important things already there that you will surely not finish reading before I add it.

I observe that once started from these ideas and formalized them on the case of Markov processes, the principles of quantum physics can appear much more natural and intuitive, less paradoxical, than otherwise; and also the thermodynamical time orientation that comes from apparently nowhere is quite well explained in this view.

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bhobba

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noting that purely mathematical laws of physics can only describe a mathematical universe, with a merely mathematical existence.There needs to be something beyond mathematical laws to both provide for existence beyond mere mathematical existence, and for non-algorithmicity.

Here we go again with its only math stuff. What don't you get about system states being mapped to stuff out there like a particles position, momentum, spin, or whatever, and because of that is not purely mathematics? Do you believe the same thing about the points and lines of Euclidean Geometry? That's just math as well under your view. But suggest that to a surveyor and you are likely to get some weird looks.

That's not to denigrate the mind makes collapse view - Von Neumann thought so (so does Roger Penrose who goes a step further and believes he has found processes in the brain that do it) - its perfectly valid - just a bit too over determined for my tastes and not at all necessary. IMHO. However all interpretations suck in some way and its a matter of personal preference which one sucks the least.

Here is a Link about Penrose's views:

http://www.quantumconsciousness.org/penrose-hameroff/orchor.html [Broken]

BTW Markov processes can not be used as a model for QM - fundamental theorems show they always converge to a single state or cycle.

That is the essence of Quantum weirdness - in order to allow continuous transformations between states you must go to complex numbers - if not you get funny behavior like those of Markov chains. In fact a Wiener process (itself a Markov process) models QM if you do a Wick Rotation into complex numbers. Many people have been struck by this and have tried to figure out a way it can be used as an interpretation of QM but it has not proved successful.

Thanks

Bill

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Then I probably misunderstood you, because I agree with the above.

I certainly didn't mean to suggest that the theory is guaranteed to remain broken even if we replace the projection postulate with something else. I don't know what that would be in Bohmian mechanics, but it has to be something. Every theory needs a rule that associates preparation procedures with mathematical things that can represent them.

The only thing I said (or rather inadvertently suggested, by my precise choice of words) that your argument seems to refute is that we need the full theory (=mathematics+correspondence rules) to find decoherence. I agree of course that decoherence is present in the purely mathematical part of the theory.

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As a balance, I would suggest also to read a critique of the Zeilinger's information interpretation:I suggest you read the information interpretation (Zeilinger 1999+).

http://xxx.lanl.gov/abs/quant-ph/0604173

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i agree, is not enough.

Here is a paper that attempts to derive the Born rule using decoherence.

not so fast....

the paper

http://arxiv.org/pdf/quant-ph/0405161v2.pdf

...a recently discovered symmetry exhibited by entangled quantum systems...

....Envariance is enough to establish dynamical independence of preferred branches of the evolving state vector of the composite system, and, thus, to arrive at the {\it environment - induced superselection (einselection) of pointer states}, t

and a counterpoint

Probabilities from envariance?

http://arxiv.org/abs/quant-ph/0401180

It is argued that the reason why all attempts to do this have so far failed is that quantum states are fundamentally algorithms for computing correlations between possible measurement outcomes, rather than evolving ontological states.

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OK, sorry about that. What about this one?not so fast....

the paper

http://arxiv.org/pdf/quant-ph/0405161v2.pdf

...a recently discovered symmetry exhibited by entangled quantum systems...

....Envariance is enough to establish dynamical independence of preferred branches of the evolving state vector of the composite system, and, thus, to arrive at the {\it environment - induced superselection (einselection) of pointer states}, that was usually derived by an appeal to decoherence....

not from decoherence

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