The Refutation of Bohmian Mechanics

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In http://arxiv.org/pdf/0901.3262v2.pdf I have described this in some detail and constructed an explicit counterexample to the hope that one can derive it somehow given only the Hamilton operator.

Some quotes from Zurek (arXiv:quant-ph/9805065, arXiv:0707.2832):



It would be indeed useful, but, unfortunately for MWI, it is not possible. At least not without any additional physical structure.

So have you talked to him about this?
Last time I saw an interview with Zurek he was fairy confident in MWI, though he also said that it might be that you can get "it from bit" some other way.
 
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No. The quotes are from the papers I have cited.
From what I can tell he does not agree with you that this is not possible...
It seems he is perfectly fine with it?
 
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From what I can tell he does not agree with you that this is not possible...
It seems he is perfectly fine with it?
I don't even know if he has read my papers, so I cannot tell what he thinks about them.

I think my counterexamples show clearly that MWI needs additional structure. A strange fundamental "subdivision into systems" can provide such an additional structure. Once
Zurek has independently proposed such a subdivision as a natural postulate, it seems
reasonable to guess that he will not give it up.

But it is clearly an additional structure, which is not necessary in the Bohmian approach,
so that the "BM is MWI in denial" argument is clearly invalid.
 
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But it is clearly an additional structure, which is not necessary in the Bohmian approach,
so that the "BM is MWI in denial" argument is clearly invalid.
Why isn't the structure in the WF enough? I mean given functionalism there should be worlds in the empty pilot waves too?
 
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Why isn't the structure in the WF enough? I mean given functionalism there should be worlds in the empty pilot waves too?
I don't understand this functionalism. A function on something does not mean the existence
of this something. What do I think about unicorns? This depends on the unicorns - I have
a special preference for the invisible pink unicorn, while I consider other unicorns as boring.

So, it is a function of the state of unicorns, and it really exists in my mind. So, does it follow that unicorns exist?

The argument about the missing subdivision of the world into systems is of another type. This structure is necessary because, if one thinks about it, one can easily detect that all the MWI considerations assume that such a subdivision exists. And my example shows that different subdivisions lead to different physical predictions for the same Hamilton operator.
 
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I don't understand this functionalism. A function on something does not mean the existence
of this something. What do I think about unicorns? This depends on the unicorns - I have
a special preference for the invisible pink unicorn, while I consider other unicorns as boring.

So, it is a function of the state of unicorns, and it really exists in my mind. So, does it follow that unicorns exist?
What?
That is not functionalism at all.
The point is: if the wavefunction has a ontological existence as a pilot wave in the de-Broglie Bohm interpretation, then why doesn't the pilot wave give rise to worlds ?
If the pilot wave funciton exactly like a structure, then why isn't it structure?

The argument about the missing subdivision of the world into systems is of another type. This structure is necessary because, if one thinks about it, one can easily detect that all the MWI considerations assume that such a subdivision exists. And my example shows that different subdivisions lead to different physical predictions for the same Hamilton operator.
I'd love to learn more about this...
 
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What?
That is not functionalism at all.
The point is: if the wavefunction has a ontological existence as a pilot wave in the de-Broglie Bohm interpretation, then why doesn't the pilot wave give rise to worlds ?
If the pilot wave funciton exactly like a structure, then why isn't it structure?
My artificial unicorn-example was of similar nature. My ideas about unicorns have ontological
existence in any theory which assumes that human ideas correspond to states of neurons in the human's brain. So these ideas exist there, as a structure of my neurons.

But it does not follow that this structure of my neurons, even if it can be described by a function on the space of imaginable unicorns, gives rise to unicorns.

I'd love to learn more about this...
http://lanl.arxiv.org/abs/0901.3262 is the basic construction. The same Hamilton operator,
but nonetheless different physical predictions, because of different operators p,q or a different subdivision into systems.

http://lanl.arxiv.org/abs/0903.4657 is some argumentation why various quantum interpretations which are pure - that means, without any additional structure - are not viable.
 
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But it does not follow that this structure of my neurons, even if it can be described by a function on the space of imaginable unicorns, gives rise to unicorns.
I came directly from watching a video of imaginary unicorns to this. Golly.

Really.
 
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T. Seletskaia has pointed out to me Arnold Neumaier's paper "Bohmian mechanics contradicts quantum mechanics", discussed earlier in this thread.

So far as I can see, no-one made the analogy with momentum... If you want this sort of disagreement between Bohmian mechanics and quantum mechanics, you can just consider momentum. The distribution of momenta, exhibited by the Bohmian trajectories corresponding to a generic wavefunction, is not the same as the probability distribution for the momentum observable, predicted by QM for the same wavefunction.

To get a Bohmian, ontological, realist explanation of the quantum momentum operator, you have to include a physical interaction which "measures" the momentum, and you must consider the overall wavefunction for "original system" + "second system which interacts with the first". This is the sort of wavefunction considered e.g. in studies of measurement-induced decoherence; but here you are to consider the Bohmian trajectories corresponding to this overall wavefunction. When you do this, you once again have predictive agreement between QM and BM.

All this would be well-known to modern Bohmians. What's interesting here is that Arnold has found an analogous problem just involving position, which was supposed to be the part of Bohmian mechanics which matches with quantum mechanics in a direct and uncomplicated way. However, to find this problem, he had to consider correlations between position at different times. So we can refine our understanding as follows:

The single-time distribution for position is the same in Bohmian mechanics and quantum mechanics. The multi-time correlations for unmeasured position in Bohmian mechanics are not the same as the multi-time correlations for position in quantum mechanics, just as the distribution for the unmeasured momentum in Bohmian mechanics is not the same as the distribution for momentum in quantum mechanics. However, if there is a physical interaction such as is required for measurement, then multi-time correlations for measured position, and a distribution for measured momentum, are produced, which are the same as in QM. (This was the point of Marchildon's response.)

While I agree with Arnold's critics, who say that he is ignoring Bohmian measurement theory, I still think it's interesting to grasp the ways in which physical ontology, according to Bohmian mechanics, behaves differently than "quantum appearances" or "quantum intuition" suggest. Though I would not be surprised to learn that this is all old news for Bohmians who have specialized in issues of time (dwell time, time of flight, etc).
 

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However, if there is a physical interaction such as is required for measurement, then multi-time correlations for measured position, and a distribution for measured momentum, are produced, which are the same as in QM.
Let me just repeat and emphasize the most important sentence of your post.
 

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