On 12/29/2013 2:01 PM, Jason Resch wrote:



On Sun, Dec 29, 2013 at 1:47 AM, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>> wrote:

    On 12/28/2013 6:41 PM, Jason Resch wrote:



    On Sat, Dec 28, 2013 at 8:32 PM, meekerdb <meeke...@verizon.net
    <mailto:meeke...@verizon.net>> wrote:

        On 12/28/2013 4:45 PM, Jason Resch wrote:



        On Sat, Dec 28, 2013 at 7:12 PM, meekerdb <meeke...@verizon.net
        <mailto:meeke...@verizon.net>> wrote:

            On 12/27/2013 10:31 PM, Jason Resch wrote:

                To that I would add the purely epistemic "non-intepretation" of 
Peres
                and Fuchs.

            "No interpretation needed" -- I can interpret this in two ways, one 
way
            is to just take the math and equations literally (this leads to 
Everett),
            the other is "shut up and calculate", which leads no where really.



                    2. Determined by which observer? The cat is always either 
dead
                    or alive. It's just a matter of someone making a 
measurement to
                    find out.


                So are you saying that before the measurement the cat is neither
                alive nor dead, both alive and dead, or definitely alive or
                definitely dead?  If you, (and I think you are), saying that 
the cat
                is always definitely alive or definitely dead, then about about 
the
                radioactive atom? Is it ever in a state of being decayed and not
                decayed? If you say no, it sounds like you are denying the 
reality
                of the superposition, which some interpretations do, but then 
this
                leads to difficulties explaining how quantum computers work 
(which
                require the superposition to exist).

                Superposition is just a question of basis.  An eigenstate in one
                basis is a superposition in another.


            Can you provide a concrete example where some system can 
simultaneously
            be considered to be both in a superposition and not?  Is this like 
the
            superposition having collapsed for Wigner's friend while remaining 
for
            Wigner before he enters the room?


            ?? Every pure state can be written as a superposition of a complete 
set of
            basis states - that's just Hilbert space math.


        So then when is the system not in a superposition?

        When it's an incoherent mixture of pure states.


    What makes it incoherent though?

    If the density matrix is not a projection operator, i.e. rho^2 =/= rho, 
it's incoherent.

    But really I just meant that in theory there is a basis in which any given 
pure
    state is just (1,0,0,...).  In theory there is a 'dead&alive' basis in which
    Schrodinger's cat can be represented just like a spin-up state is a 
superposition is
    a spin-left basis.


So if someone keeps alternating between measuring the spin on the y axis, and then the spin on the x axis, are they not multiplying themselves continuously into diverging states (under MWI)? Even though these states only weakly interfere, are they not still superposed (that is, the particles involved in a simultaneous combination of possessing many different states for their properties)?

Right, according to Everett, the world state becomes a superposition of states of the form |x0,x1,...> where each xi is either +x, -x, +y, or -y. And per the Bucky Ball, Young's slit experiment, the spins don't have to observed by anyone. If the silver atom just goes thru the Stern-Gerlach apparatus and hits the laboratory wall, the superposition is still created. If it just goes out the window and into space...it's not so clear.


    An electron in a superposition, when measured, is still in a superposition
    according to MWI. It is just that the person doing the measurement is now 
also
    caught up in that superposition.

    The only thing that can destroy this superposition is to move everything 
back into
    the same state it was originally for all the possible diverged states, 
which should
    practically never happen for a superposition that has leaked into the 
environment.

    In Everett's interpretation a pure state can never evolve into a mixture 
because the
    evolution is via a Hermitian operator, the Hamiltonian.  Decoherence makes 
the
    submatrix corresponding to the system+instrument to approximate a mixture.  
That's
    why it can be interpreted as giving classical probabilities.


Are there pure states in Everett's interpretation? Doesn't one have to consider the wave function of the universe and consider it all the way into the past?

I suppose the universe could have started in a mixed state, but most cosmologists would invoke Ockham and assume it started in a pure state - which, assuming only unitary evolution, means it's still in a pure state. Of course since inflation there can be entanglements across event horizons, so FAPP that creates mixed states.


In any case, returning to the original point that began this tangent, do agree that QM interpretations which are anti-realist (or deny the reality of the superposition) are unable to describe where the intermediate computations that produce the answer to a quantum computation, take place?

They take place in a quantum computer.


What would Fuchs say about quantum computation?

It's a physical process whose outcome is predicted by QM.

Brent

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