From: Bruno Marchal 
Sent: Thursday, April 28, 2011 7:07 AM
To: everything-list@googlegroups.com 
Subject: Re: Quantum decoherence

On 27 Apr 2011, at 22:48, meekerdb wrote:

> On 4/27/2011 12:16 PM, Evgenii Rudnyi wrote:
>> Recently I have seen interpretation of quantum mechanics in terms  
>> of quantum decoherence, for example Decoherence and the Transition  
>> from Quantum to Classical by Wojciech H. Zurek. What is an attitude  
>> in general to this? Is this good? Is there a good text for a layman  
>> about such an approach?
>>
>> Evgenii
>>
>
> There's a good review paper by Max Schlosshauer
>
> http://arxiv.org/abs/quant-ph/0312059
>
> He later expanded it into a book.  Decoherence is a real, observed  
> physical process predicted by QM.  Interest in it is due to it's  
> role in explaining the appearance of the classical world.  It  
> explains the diagonalization of the reduced density matrix (the  
> density matrix after averaging over the unknown environment).  But  
> it doesn't explain the realization of just one of the diagonal  
> values with probabilities according to the Born rule.  Omnes and  
> some others point out that QM is a probabilistic theory and so  
> probabilities are all you can expect from it.
>
> There is also a problem in explaining the basis in which the density  
> matrix is diagonalized; this is know as the einselection problem.   
> Decoherence theory suggests some possible solutions to the  
> einselection problem but none are really worked out yet.


Yes. Decoherence is real, and can be explained entirely in the QM  
without collapse. It is a key ingredient of the Many-World  
Interpretation, and that is why those who dislike the MWI try to still  
add something to the decoherence effect. Basically decoherence comes  
from the contagion of the superposition state to the environment,  
which is a consequence of the linearity of tensor products and of the  
linear wave equation.

I am not sure there is a "basis problem". Basis are selected by  
universal-machine-tropic choice, and Zurek did provide explanation why  
the position basis in favored by our type of branch. Quantum states  
are relative states, and consciousness can find itself only on the  
branches which support stable self-reflexive machine abilities.

It is an open problem for me if other type of basis (than position)  
can play that role.

Bruno


http://iridia.ulb.ac.be/~marchal/


[SPK] 
    Hi Bruno,

    But are machine semantics restricted to a position basis mode of 
expression? I can see how this would do damage claims of universality! This is 
a open problem for me as well as my toy model is only framed in the position 
basis at the moment and I do not know how to generalize it at the moment, but I 
have seen hints in the C* algebra duality of Gel’fand. arxiv.org/pdf/0812.3601 
and www.mathstat.dal.ca/~p.l.lumsdaine/research/Lumsdaine-2009-Duality.pdf

    QM seems to demand that all possible basis be treated equally, there can be 
no preferred basis (via the linearity of the tensor product of Hilbert 
spaces?!); just as there can be no preferred reference frame in GR. 
http://www.physicsforums.com/showthread.php?t=362959 and 
http://plato.stanford.edu/entries/qm-everett/

“The preferred basis problem is arguably a more serious problem for a 
splitting-worlds reading of Everett. In order to explain our determinate 
measurement records, the theory requires one to choose a preferred basis so 
that observers have determinate records (or determinate experiences) in each 
term of the quantum-mechanical state as expressed in this basis. The problem is 
that not just any basis will do this. Making the total angular momentum of all 
the sheep in Austria determinate by choosing such a preferred basis to tell us 
when worlds split, would presumably do little to account for the determinate 
memory I have concerning what I just typed. But this is the problem, we do not 
really know what basis would make our most immediately accessible physical 
records, those records that determine our experiences and beliefs, determinate 
in every world. The problem of choosing which observable to make determinate is 
known as the preferred-basis problem.”


    That we humans have a bias toward the position basis may very well be an 
artifact of our physical senses. It is interesting to note that bases exists 
that are combinations of other bases. Some research by Aharonov et al in the so 
called Weak Measurement area shows some unusual implications of this: 
http://en.wikipedia.org/wiki/Weak_measurement 
    I suspect that the “basis problem” is just another version of the measure 
problem. What if communications between observers is constrained by a 
requirement that they share a common basis or at least commensurable bases. 
This seems to be implied by the way that all observables that can be defined on 
a given space-like surface must commute. If a given pair of observers have 
incompatible bases then we have some thing that looks/feels like curvature in 
information space!??? See Shun-Ichi Amari’s work 
http://videolectures.net/etvc08_amari_igaia/ (hat tip to Russell.)

Onward!

Stephen

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