On 31 Oct 2011, at 18:13, meekerdb wrote:
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.
Why? Everett shows convincingly that, being a memory machine, when we
measure a superposition state, we just entangle ourself with the
superposition state, but this differentiate the consciousness/memory
of the machine, and she can feel the split. The theory of
consciousness used in Everett QM is simple mechanism. It is the major
interest of Everett.
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.
?
On the contrary. Everett QM applies the unitarity and the linearity to
each branch of the superposition, and the memory mechanism of the
machines reveals, from each machine points of view, a classical state.
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.
Decoherence is unitary. Decoherence is many worlds. The diagonal terms
get close to zero, but this does only mean that macroscopic quantum
erasing of memory is technically not doable, so that the branch of
realities diverge irreversibly (FAPP) and it is impossible to
macroscopically self-interfere. David Deutsch suggests that we might
do it with a possibly future quantum brain, though.
Bruno
Brent
Best wishes
Nick
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