Quantum decoherence

[Evgenii Rudnyi]

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

[meekerdb]

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.

Brent

[Bruno Marchal]

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/

[meekerdb]

I think more than "support" is needed - else you might find yourself the
the sole stable consciousness in a world full of quantum
superpositions. Steven Weinstein has shown this to be the generic case.
http://arxiv.org/abs/0807.3376v1

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

Max Schlosshauer points out that small systems (e.g. atoms) are stable
in energy-momentum eigenstates, not position eigenstates.

Brent

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

[Stephen Paul King]

[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

[Bruno Marchal]

Damned! I will have to look at this one.

Hmm... he made a lot of hypotheses which I can hardly judge (not being
a physicist). May be it will be shorter to stick with the comp body
problem.
Comp predicts that at some point physics must go wrong, unless they
explicitly take into account the self-reference logics. Remember that
comp entails that deriving physical laws from observation is already a
risky enterprise !

>
>>
>> It is an open problem for me if other type of basis (than position)
>> can play that role.
>
> Max Schlosshauer points out that small systems (e.g. atoms) are
> stable in energy-momentum eigenstates, not position eigenstates.

This might explain, with my remark just above, why life and mind does
not seem to appear on such small scale.

Bruno

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

[zprime21]

try stuart hammeroff and roger penrose collaboration....regarding
conciousness.

[Evgenii Rudnyi]

I have found the interview with Stuart Hameroff by googling

http://video.google.com/videoplay?docid=2911199841702354668

Do you mean something like this?

I am not sure that I find Hameroff's ideas impressive. I am personally
closer to Mike's agnosticism:

"What the WORLD is, if it exists (what does that mean?) what we call a
"universe" or "existence" is hazy. No outside view.".

I like a lot the reporter though, he is good, if the reporter had a
book, I would love to read it. As for the speaker, it would be an
interesting project for a psychologist to research what Hameroff himself
thinks about his statements and why. Some sort of physcoanalysis that
relates the viewpoints of the speaker to his infancy and childhood would
be good.

I believe that Bruno's statement

"But theology is a science, like biology, zoology, physics, etc. By
abandoning theology to the authoritative church, not only we have lost
the most fundamental science, but we have erect automatically another
science, physics, into a pseudo-theology, that is a science which acts
as a theology without saying."

would be also suitable here.

On 30.04.2011 02:47 zprime21 said the following:

[meekerdb]

Hameroff and Penrose's theory of consciousness can be summarized as
consciousness is a mystery, quantum gravity is a mystery, the two must
be the same.

Brent

[Bruno Marchal]

On 29 Apr 2011, at 04:03, Stephen Paul King wrote:

    Hi Bruno,

 

    But are machine semantics restricted to a position basis mode of expression?

That was the question I as asking. Probably not, but I am not sure. Even pure spin computations needs the use of position, at least for reading and writing memories. But this might be a human limitation, not a machine limitation.

I can see how this would do damage claims of universality!

Why? I don't see this at all. Remember that with comp the numbers are only dreaming space and position. Such notion are secondary and emerging from the numbers points of view.

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/

 

Yes. I agree. There are no preferres basis, like they are no preferred universal system. That is why I take the numbers.

“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.”

There is no splitting, both with Everett and comp. Only relative states. The 3-states are defined relatively to universal numbers., and the 1-states are defined relatively to infinities of universal numbers (the infinitely many competing below our substitution level). 

 

 

    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.

I think there is no basis problem. All versions of it  comes from a too much literal understanding of the notion of world or universe (which makes no sense with comp). 

Also, I think that the measure problem in QM is mainly solved by Gleason theorem. And the measurement problem is solved by Everett MW. I might be wrong (if Weinstein is correct, for example). Comp is far from being as clean as QM, though, but it should lead to QM, with perhaps some modification, which might solve the remaining problems.

Bruno

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