[ExI] Many Worlds (was: A Simulation Argument)

[Lee Corbin]

Damien writes

>>If it weren't for the "weird correlation", then there would actually be
>>four universes---inhabited respectively by the teams A-you & A-him,
>>A-you & B-him, B-you & A-him, and B-you & B-him---and each
>>such worthy would weep "alas there is no correlation between
>>what happens here and what happens there, our entanglementation
>>did fail".  But when entanglement succeeds, there are just the two
>>universes, and everyone celebrates the wonderous correlation,
>>except for the two pairs of unfortunates who didn't get any runtime,
>>Messrs. A-you & B-him and Messrs. B-you & A-him.
> 
> This certainly accords with my own intuition, and I find no 
> principled reason why "entanglement" isn't just an improbable 
> illusion in the MWI.

Illusion?  I imagine a very wide swath of flow lines, like
a river, all the flow lines representing completely identical
universes (indistinguishable universes).  Normally when
any binary possibility arises the large sheaf of lines or
stream of lines breaks into four sub-streams, having
approximately equal measure. On three simultaneous
events, they'd break up into eight streams, one for each
binary possibility.

In cases like this we speak of non-negligible probabilities.
Of course, there are always totally negligible little rivulets
that can break away, (e.g. a cow jumps over the moon).
But, again going back to AA, AB, BA, and BB, sure, 
maybe the AB stream and BA streams do exist, but they
are tiny. Why are there just two emergent possibilities
instead of four, and why are they called "entangled"?

Penrose on page 281 of "The Emperor's New Mind" has
the nicest explanation:

   Suppose that we have a physical system consisteing of two
   sub-systems A and B. For example, take A and B to be
   two different particles. Suppose that two (orthogonal)
   alternatives for the state of A are |alpha> or |rho>, whereas
   B's state might be |beta> or |sigma>. As we have seen above
   the general combined state would not simply be a product
   ('and') of a stateA with a state of B, but a superposition
   ('plus') of such products. [Hence my mantra of "at the bottom
   of things are amplitudes that add.]  We say that A and B are
   then "correlated".

   Let us take the state of the system to be

         |alpha>|beta>  +  |rho>|sigma>

   [By the way, you see here the fundamental assumption that
   Penrose makes from which everything follows. It took the
   physicists a long time in the twenties to find such a formula,
   such a concept, that if you just turn the crank and follow the
   rules, you get to make accurate predictions, even though
   they're just probabilistic ones.]
   Now perform a yes/no measurement on A that distinguishes
   |alpha> (YES) from |rho> (NO). What happens to B. If the
   measurement yields YES, then the resulting state must be

        |alpha>|beta>

   while if it yields NO, then it is 

        |rho>|sigma>

   Thus our measurement of A causes the state of B to jump:
   to |beta>, in the event of a YES answer, and to |sigma> in
   the event of a NO answer!  The particle B need not be 
   localized anywhere near A; they could be light-years apart.

So the behavior happens to follow the rules of what Penrose
elsewhere calls "the quantum mechanical 'and'", which is the
plus sign in the equation above. 

My wonder is that just two possibilities emerge. The math
prohibits "the unfortunates"   |alpha>|sigma> and |rho>|beta>
from existing.

> What prevents the "unfortunates" from existing?

In my original story, above, imagine that you experience |alpha>
here and then go far away to learn what your partners saw
at their end.  You will only find that they found |beta>, even
though intellectually you and they realize that another universe
holds their opposite numbers who saw |rho> and |sigma>
respectively.  But a you who experienced |alpha> and then
second hand experienced |sigma> (as he later interacts with the
locals at the distant location, and absorbs the results of their
experiment) does not exist.  Or exists only in negligible measure.

Lee