From: scerir (scerir@libero.it)
Date: Thu Sep 19 2002 - 16:12:42 MDT
Lee Corbin:
> (Sorry that I'm about a week behind answering
> your posts, and about 3 of *your* posts behind,
> but I will catch up.)
Do not mind.
I'm years behind answering a post by Technotranscendence,
about Norberto Bobbio, and months behind answering a
post by Hal Finney, about the Poincaré sphere. :-)
> I bet the upshot will be that the MWI version which *does*
> appear to have simpler equations---but then I am an Everettista
> in your cute phrase ;-) --- will be just as satisfactory. But I still
> want to understand more of this amazing means of comparing
> the two interpretations.
In standard QM an instantaneous transfer of 'information' is not
possible. Philippe Eberhard ('Bell's theorem and the Different
Concepts of Locality', Nuovo Cimento, 46B, (1978), 392-419)
showed that. Actually he built a theorem, using a rather mathematical
definition of locality.
But in standard QM it is possible to 'teleport' some 'information'
(actually a quantum state, unknown too) by exploiting EPR
correlations, i.e. two entangled particles. Notice that a
quantum teleporting machine is the sum of two different
impossible machines: a classical teleporting machine, and
a quantum John Bell's telephone (a device using EPR pairs
to send FTL messages). It is weird, imo, that two impossible
machines, when combined, give a possible machine.
Now Alice wishes to give Bob the information about a quantum system,
i.e. the particle 1 prepared in an unknown quantum state. Alice lets this
particle interact with a couple of entangled particles, 2 and 3, of which
one, particle 3, was previously given to Bob and the other, particle
2, is used by her.
The unknown state of particle 1 has the form
|1> = a |+,1> + b |-,1>
EPR state of particles 2 and 3 has the form
|2&3> = |+,2>|-,3> - |-,2>|+,3>
The complete state of particles 1, 2 and 3 has the form
|1&2&3> = a |+,1>|+,2>|-,3> - a |+,1>|-,2>|+.3> +
b |-,1>|+,2>|-,3> - b |-,1>|-,2>|+,3>
which can also be written as
|1,2, one> * (-a |+,3> - b |-,3>) +
|1,2, two> * (-a |+,3> + b |-,3>) +
|1,2,three> * (a |-,3> + b |+,3>) +
|1,2, four> * (a |-,3> - b |+,3>)
Now in MWI Alice performs a measurement on particles 1 and 2
(at her side) and she obtains *all* these four possible states
|1,2, one>, |1,2, two>, |1,2,three>, |1,2, four>
This means that Bob, at his side, obtains, for the quantum state
of particle 3, which is the hands of Bob, all these four possible
states
(-a |+,3> - b |-,3>)
(-a |+,3> + b |-,3>)
(a |-,3> + b |+,3>)
(a |-,3> - b |+,3>)
Actually, in MWI, the measurement performed by Alice creates
four different worlds. In each of these worlds we can
find just one Alice and just one of these Alice's outcomes
|1,2, one>, |1,2, two>, |1,2,three>, |1,2, four>
and we can also find just one Bob and just one of these
states below, of particle 3, each one linked to an Alice's
outcome
(-a |+,3> - b |-,3>)
(-a |+,3> + b |-,3>)
(a |-,3> + b |+,3>)
(a |-,3> - b |+,3>)
Now notice that *one* of these four states is the *same* state
of the particle 1, except for an irrelevant phase factor.
Hence we can say that in MWI there is one world
(over four) in which Alice teleports, by quantum means,
instantaneously, without any classical channel, an unknown
quantum state, to Bob.
To say that Alice teleports instantaneously a quantum state
(which is information) might also mean that the quantum
state was already there, at Bob's side, in that particular
world.
Of course it is not impossible to build a model of an
asymmetrical splitting of worlds - a world has a 'large'
measure, another has a 'smaller' measure. It is also
possible to use the entanglement-swapping procedure,
which is much more powerful, hence build a net of .....
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