On Fri, Oct 13, 2006 at 07:03:18AM -0000, [EMAIL PROTECTED] wrote:
> 
> Also see my reply to Russell below:
> 
> 
> >Russell Standish
> >
> >The Multiverse is defined as the set of consistent histories described
> >by the Schroedinger equation. I make the identification that a quantum
> >state is an observer moment, and the set of consistent quantum
> >histories is the set of observer histories. As such all observer
> >moments are in the Multiverse.
> >
> >But I appreciate this is not a widely held interpretation...
> 
> 
> Indeed so.  And there's a good reason why it isn't a widely held
> interpretation, as J.barbour explained in 'The End Of Time'.  In order
> to define 'the Multiverse' in terms of QM one needs a *static*
> wave-function solution for the entire universe (one which doesn't
> change) , whereas conventional QM solutions to real world problems are
> *dynamic* wave-function solutions (wave functions which evolve with
> time).  No one has yet succeeded in demonstrating a static
> wave-function solution for the entire universe.
> 

I haven't read Barbour's book, but if that is what he is saying, he
would be wrong. Consider a universe of a single electron living in a
potential well V(x)=|x|^2, x\in R^3. There is a well defined solution
\psi(t,x) = \sum_j <\psu_0|j><j| exp(-iE_j t) given the initial
condition \psi_0.

The function \psi: R x R^3 -> C is a static (time independent)
mathematical object (I wrote it the mathematicians write to emphasize
this point). Why wouldn't you identify this with the Multiverse of
that electron?

Now I am aware that several people (Hawking included I gather) have
proposed various "wave functions of the universe", which tend to be
solutions of the Wheeler de Witt equation, which is a time independent
equation. However, I'm not so interested in following that literature.

> See what I said above.  If the *same* QM state could be associated with
> *different* observer moments, then observer moments would not be
> reducible to QM states and the set of consistent quantum histories
> could not be said to be fully identified with the set of observer
> histories.
> 

If the same QM state is associated with different observer moments,
you must be talking about some non-functionalist approach to
consciousness. The QM state, by definition, contains all information
that can be extracted from observation.

Cheers 


-- 
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A/Prof Russell Standish                  Phone 0425 253119 (mobile)
Mathematics                              
UNSW SYDNEY 2052                         [EMAIL PROTECTED]             
Australia                                http://parallel.hpc.unsw.edu.au/rks
            International prefix  +612, Interstate prefix 02
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