From: Bruno Marchal
Sent: Thursday, April 28, 2011 7:07 AM
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?
> There's a good review paper by Max Schlosshauer
> 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.
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
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.
“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:
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.)
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