# Re: many worlds interpretation

From: Mitchell Porter <mitch.domain.name.hidden>
Date: Fri, 20 Feb 1998 20:00:16 +1000 (EST)

WD:

> On Fri, Feb 20, 1998 at 02:48:25PM +1000, Mitchell Porter wrote:
> > WD:
> > > Ok, let me give my understanding of what a "world" is in MWI. Suppose we
> > > take the UWF and consider it as the superposition of two wavefunctions:
> > >
> > > PSI = c_0 PSI_0 + c_1 PSI_1.
> > >
> > > If from examining the time evolution of PSI, we can tell that there is
> > > very little interference between PSI_0 and PSI_1 after time t_1,
> >
> > Can you define what "interference" means here?
>
> I mean there's intereference between PSI_0 and PSI_1 at (r,t) if
>
> PSI*(r,t) PSI(r,t) dr <> |c_0| PSI_0*(r,t) PSI_0(r,t) + |c_1| PSI_1*(r,t)
> PSI_1(r,t) dr
>
> If for all r and t>t_1 the left side is approximately equal to the right
> side, then there is little inteference between PSI_0 and PSI_1 after time
> t_1.

Did you intend to use moduli squared, rather than moduli?
What motivates this expression?

In any case, in order make the condition that "there is little
interference" precise, you will need to say something like:

There is little interference when |LHS - RHS| < epsilon.

In other words, you will need to introduce an arbitrary parameter
into the definition of "world". I believe similar problems bedevil
attempts to derive the projection postulate from decoherence.

There was also something unspecified: what sort of functions
are PSI_0(r,t) and PSI_1(r,t)? For example, do you require that
they also be solutions to the Schroedinger equation? Or are they
just any time-varying functions at all?

-mitch
http://www.thehub.com.au/~mitch
Received on Fri Feb 20 1998 - 02:02:31 PST

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