On 10/31/2011 6:01 AM, Nick Prince wrote:

On Oct 31, 5:30 am, meekerdb<meeke...@verizon.net>  wrote:
On 10/30/2011 5:13 PM, Nick Prince wrote:



On Oct 30, 8:56 pm, Russell Standish<li...@hpcoders.com.au>    wrote:
My point about the unitary evolution was that the clicking of the
Geiger counter is not a unitary process - and until you hear it, you remain in
superposition.
- Show quoted text -
I thought that in the everett interpretation everything was unitary?
best wishes
Nick
Right.  In Everett's interpretation Nick's consciousness exists in many 
superpositions and
there must be some additional mechanism of consciousness that accounts for the 
separation
of these conscious streams of experience.  This would be the same mechanism 
that collapses
the wave function in the Copenhagen interpretation - something like decoherence 
except
that when the cross terms become sufficiently small they become exactly zero.  
This would
be a "small" non-unitary step.  But it requires that there be distinguished 
variables in
which the density matrix becomes diagonal - the "pointer basis".

Brent

Hi Brent
Ok, after I'd posted the line above I thought again and wondered if my
misunderstanding of Russell's answer was that he was indicating that a
measurement made would cause the "click" which is essentally due to an
hermitian non unitary operator.  Yet in many accounts of the
measurement procedure they follow my resoning that the apparatus doing
the measuring, and the object being measured interact for some time
via a unitary operation i.e. obey the SE.  So I got confused.  I
understand that unitary operators are not observable operators yet
they do describe the evolution of a state from one to another (as does
the action of an observable operator) how do these accounts of the
measurement process end up being consistent with each other?  My
understanding of QM must be lacking here.

I read your answer but can't quite connect with it.  Why must there be
some additional mechanism of consciousness that accounts for the
separation
  of these conscious streams of experience? In two branches of the
multiverse can my consciousness  not be at the end of the
superposition that  I put in the original post.

exp(-iHt/hbar) (|s0>|a0>|Cons_0>


= exp(-iHt/hbar) (c1|s1>|a0>|Cons_0>  + c2|s2>|a0>|Cons_0>)  (3)

= (c1|s1>|a1>|Cons_1>  + c2|s2>|a2>|Cons_2>)

|s>  = system, |a>  = apparatus states
|Cons_i>  standing for conscious state of observer of the measurement.

This accounts for 3p viewponts.

I thought that 1p viewponts in any branch just change according to
some U(t) such that U(t) |cons_i(0)>  = |cons_i(t)>.  Can you (anyone)
help me to understand?

I don't think I understand it any better than you do. But ISTM we need a quantum theory of consciousness in order to write eqns like (3) above. In the standard theory it implies that there is some experience of both system states at the same time. A change of basis changes the labelling of 1 and 2. In other words, if the brain is in a superposition then there is *a* conscious experience of *both* states. If you deny this and postulate that consciousness must be unique (i.e. classical), as we directly experience it, then it seems you have gotten back to the theory that consciousness collapses the wave function.

To me, decoherence offers a better explanation, i.e. that the off diagonal terms in the density matrix become practically zero already at the brain level; or more accurately at the level of the detector of the particle that initiates breaking the vial. This explanation still has a problem though in that there must be some canonical pointer states in which the off diagonal terms become zero. I think it may be possible to justify a pointer basis; but it hasn't been found yet.

Brent


Best wishes

Nick



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