[EMAIL PROTECTED] wrote:
> 
> It's something of a semantic difference whether worlds should be said
> to fuse in the MWI.

Maybe, but you might also say that it's a semantic difference to
say that they split.  I'm saying that, if you allow that they split,
then, in the same sense, they also fuse.

 
> Consider a photon which passes through a two slit interference experiment.

Okay, yes, this is a good example.

> One way of describing it is to say that there are two worlds, one where
> the photon passes through one slit and one where it passes through the
> other.  Then the worlds fuse when the photons hit the screen and this
> is the cause of the interference.
> 
> Another way of describing it is that there is no split of worlds,
> that there is only one world in which the photon takes both paths (in
> some sense).  Only when there is a measurement which collapses the wave
> function do we get a new world.  In this view, if we put a detector
> at the slits which could tell which slit the photon passed through,
> the worlds would split when the detector was triggered.  In one world
> the detector would show the photon going through one slit, and in the
> other world it would show the photon going through the other slit.
> It is the act of measurement, an irreversible act of amplification,
> which causes worlds to split in this definition.

This begs the question:  what is a "world", anyway?  I use the word
to mean my "thread" -- the path that my conscious self weaves through
time.  *Everything else* is superposition.  I think that some people
don't appreciate the impact of superposition of worlds in MWI.
Everything that we observe, from
atoms to molecules to complex structures, owes it's stability to the
superposition of worlds.  Each electron attached to each atom is 
oscillating in some sense.  But what are the oscillations of?  Just
the wave function, which describes the probability density function
of the electron.  Thus the wave function is composed of the
superposition
of worlds.

Now when I consider propogating backwards from the present moment,
I don't accept that there are any fine distinctions between the
microscopic and macroscopic scales.  So if it's valid to consider
two worlds in the past, one in which some kid in some god-forsaken 
town in Australia poisoned a cat with cyanic acid, and another where 
he didn't, then it's also valid to consider the photon going through
one slit as one world, and the other slit as another world.

I'll admit that my conception of "world" is not fully clear to me.
It has always seemed kind of circular to me:  that particle wave
functions are superpositions of worlds, and worlds are collections
of particles.  But perhaps it's circularity is somehow fundamental.

 
> Both pictures are consistent and both use the concept of many worlds.
> It is just a matter of definition whether you want to say that parts of
> the state function which still are coherently entangled are separate
> worlds or not.
> 
> If you use the second definition, though, I think it is correct to say
> that worlds do not fuse.  Even a seemingly insignificant difference, if
> it occurs at the classical level, will produce a fundamentally different
> quantum wave function.
>  And in fact, given the chaotic nature of the
> classical world (where the flap of a butterfly's wings causes next year's
> hurricane), it is likely that there are no insigificant differences.

No, this is all wrong.  QM does not have this nonlinear chaotic
behavior.
If you take two quantum states in the past, w1 and w2, which differ by
a small amount, and then propogate them to the present, they will still
differ by a small amount.  But both will have gotten considerably 
"smeared out", and will consist of linear superpositions of lots of
different "worlds".  This smeared out state in each will contain a
non-zero
probability density for our "world".  That is, they overlap.

>From our vantage point, we can look backwards and say that there is a
branching tree of worlds in the past as well as the future.  It
doesn't have quite the same flavor as the future tree, however.
Past worlds where I was dead five minutes prior to now are
*extremely* unlikely, but not quite so unlikely in the future tree.
Any past world inconsistent with my memories is also unlikely.


> 
> Hal
> [EMAIL PROTECTED]




-- 
Chris Maloney
http://www.chrismaloney.com

"Knowledge is good"
-- Emil Faber

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