On 10/19/2013 12:42 AM, Jason Resch wrote:




On Fri, Oct 18, 2013 at 6:09 PM, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>> wrote:

    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.


Is this a process to recover the probabilities of some observation from some point of view? I so will different probabilities be calculated if one takes a different basis?

There's only one basis in which the reduced matrix is diagonal - i.e. the 'classical basis'. But saying which basis this is from a fundamentally quantum standpoint (not relying on a classical world like Bohr) is part of "the basis problem".

    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".



Can you provide an example of how using a different basis leads to different conclusions? I very much appreciate your helping me to understand this problem.

If you choose a basis in which the density matrix is not diagonal, then there's no clear interpretation of it as probabilities. There are complex cross-terms that have not probabilistic interpretation.


        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.


But qubits don't exist in normal definitions of information or Turing machines. Sure, they can be modeled, but only by splitting the entire tape and Turing machine and having one of them read a 1 and the other read a 0. When you do this, you are talking about two different computational states, (you might as well model them as separate Turing machines/programs at this point) and hence you are talking about two different minds, not one mind that is conscious of a superpositional state.

I don't think that's right. A universal Turing machine can emulate a quantum Turing machine, it's just less efficient. But that's part of the point of Seth Lloyd's paper and of Scott Aaronson, that maybe efficiency is important. It's not in Bruno's theory, because if your computing the Everything, then time is part of the computation and not some outside measure against which to judge efficiency.

Brent


Jason

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