On 28 Apr 2011, at 20:32, meekerdb wrote:

On 4/28/2011 4:07 AM, Bruno Marchal wrote:

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.

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


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/



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