Stathis Papaioannou wrote:
> Brent Meeker writes (quoting Jason Resch):
>  
>  > > If many-worlds is true, consider for a second how many histories
>  > > lines (and copies of you) must have been created by now. The
>  > > universe had been branching into untold numbers of copies, untold
>  > > numbers of times each second, for billions of years before you were
>  > > born. While not every branch contains you, once you appeared in one
>  > > history line, a new copy of you has been created for every possible
>  > > outcome of every quantum event that happens anywhere in this
>  > > universe.
>  >
>  > I don't think this is the way to look at it. It's true that QM 
> predicts an uncountably infinite number of branchings, even for an 
> universe containing only a single unstable particle. But these 
> branchings don't produce different copies of Stathis. As a big 
> macroscopic object he is described by a reduced density matrix that has 
> only extremely tiny off-diagonal terms. So he is a stable entity against 
> these microscopic quantum events unless they are amplified so as to 
> change his macroscopic state - as for example if he heard a geiger 
> counter click. The microscopic events just add a little fuzz to his 
> reduced density matrix - and the same for all of the classical world.
>  >
>  > You might be interested in Greg Egan's excellent SF story "Singleton" 
> which is available online:
>  >
>  > ttp://gregegan.customer.netspace.net.au/MISC/SINGLETON/Singleton.html
>  >
>  > Egan says "People who professed belief in the MWI never seemed to 
> want to take it seriously, let alone personally." So he wrote a story in 
> which it is taken personally.
>  >
>  > Brent Meeker
> 
> Doesn't "a little fuzz" in an infinite number of branchings result in 
> every possibility actually manifesting an infinite number of times?

I don't think so.  Part of the trouble is that QM is based on continuum 
mathematics: in time, space, and probability.  So when we imagine it being 
simulated on a digital computer we're led to think of all these being integer 
valued (in suitable units).  So we think we can just talk about discrete states 
at discrete times.  But in fact I think we are implicitly relying on the time 
continuity in the computer; it that actually causes the computational process 
to occur.

The standard form of QM being based on real numbers can accommodate an infinite 
number of "branchings" with none of them significantly diverging from the 
classical result.  If you did a QM analysis of the orbit of the Earth you would 
not find the Earth diffusing away into space outside the solar system.  You 
would find its position to become infinitesimally uncertain about it's orbit 
and macroscopically uncertain in its position along its orbit.  It would only 
branch off into a truly different path if it were hit by an asteroid or 
similar.  Then QM would show two almost orthogonal histories.  Something 
similar would apply to a human life: it would proceed mostly as a classical 
system with occasional branches.  But exactly how the classical world arises 
from the quantum foundation is an unsolved problem

Brent Meeker


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