On 10/18/2013 1:45 PM, Jason Resch wrote:




On Fri, Oct 18, 2013 at 11:37 AM, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>> wrote:

    On 10/18/2013 12:42 AM, Jason Resch wrote:

          But that's not compatible with Bruno's idea of eliminating the 
physical - at
        least not unless he can solve the basis problem.


    Could you do me a favor and explain what the basis problem is in a way that 
a 6th
    grader could understand?  I've found all kinds of things said on it, and 
they all
    seem to be asking different things.

    For physicists, it's part of the problem of explaining the emergence of the
    classical world from the quantum world.  Decoherence can diagonalize 
(approximately)
    a reduced density matrix IN SOME BASIS.


Is this the same basis as in "momentum basis" and "position basis", or is it some other usage of the term?

Forgive my ignorance, but what does it mean to "diagonalize a reduced density 
matrix"?

It means to take an average over all the other variables except those of interest (i.e. the ones you measure). If you do this in a particular basis we think it makes the submatrix corresponding to those variables diagonal. Then it can be interpreted as the probabilities of the different values. Note that it is a mathematical operation that depends on choosing a basis, not a physical process. The MWI view is that this is a physical process - which it could be IF the basis was not an arbitrary choice but was somehow dictated by the physics. But so far there are only hand waving arguments that "it must be that way".

      Being diagonal in one basis means it's superposition in some other basis. 
 So for
    physicists the problem is saying what privileges or picks out the 
particular bases
    we see in experiments. Why do our instruments have needles that are in 
eigen states
    of position, while some other things (e.g. atoms) are in eigen states of 
energy or
    eigen states of momentum.  For physicists there are some suggestive, but 
not fully
    worked out answers to these questions, e.g. you get position eigenstates 
because the
    interaction term of the Hamiltonian is a function of position.  But those 
answers
    assume the physics.  If you want to reconstruct physics from experiences, 
you can't
    borrow the physical explanation to say why your experiences are classical.


I think the assumption that experiences are classical comes from the classicality of Turing machines (which are the supposed mechanism by which experiences are manifest).

I don't think there's anything either classical or quantum about Turing machines. They are just mathematical abstractions. And assuming they read and write qubits instead of bits doesn't change the range of things they can compute.

Brent

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