LizR wrote:
<mailto:bhkell...@optusnet.com.au>> wrote:
If we compare this to FPI in the MW Interpretation of quantum
mechanics we see that this is just a branch counting account of
quantum probabilities. Now it is well-known that this fails to
reproduce the correct quantum probabilities in MWI. So FPI as via
Step 3 and FPI as in MWI are intrinsically different.
Does the MWI predict an infinite number of branches from any given
measurement? I'm not sure (from FOR) that the MWI predicts branches at
all, so much as differentiation within a continuum? Maybe you could
expand on this. Why (to keep it simple) would a quantum experiment with
two possible outcomes not reproduce the correct probabilities in the
MWI? (Or is that a special case where it would?)
No, MWI does not predict an infinite number of branches for any
measurement. It predicts a number of branches equal to the number of
possible distinct outcomes for the measurement. The classical
duplication model of step 3 cannot reproduce quantum probabilities
because it relies on branch counting. There are only ever two branches
for a measurement in a 2-dim Hilberst space, but the probabilities can
take on any real values between 0 and 1. Foe a spin measurement with the
appropriate magnet orientation you can have a probability of 1/pi for Up
(and 1 - 1/pi for Down). This cannot be reproduced by observer
duplication as in step 3.
David Deutsh has his own peculiar take on many worlds. Most people would
consider his isea of a 'world' to be premature. In the developed MWI,
with decoherence, eiselection and the rest, a worl emerges only after
decoherence and orthogonalization. In this picture, worlds are disjoint
and can never interfere or recombine.
When we go to the full dovetailer stage we get multiple copies of
the same conscious instant. If we interpret these as repetitions of
the same quantum experiment (say a Stern-Gerlach spin measurement),
we get some sequences of Up and Down results.
I'm not sure I understand this. Why do we need to interpret these copies
(an infinite number, if the UD is able to run for an infinite time) as
repetitions of the experiment? Personally, I have only compared the MWI
with step 3 for John Clark's benefit, since he insists there is some
problem with pronouns in step 3, but not in the MWI. The extent to which
they are the same is that they produce both FPI from splitting or
differentiation of fungible observers. But at this stage there is no
need to take this any further. I'm just trying to help Mr Clark get his
head around this particular point, and since comp assumes classical
computation I wouldn't expect it to reproduce quantum probabilities
"simplistically" - if it's going to work, it needs to produce them as an
end result, not be expected to produce them until the entire logic of
the argument has been examined. (Bruno claims to have produced some sort
of quantum results at the far end of the comp argument, but I haven't
got that far myself.)
But in so far as the duplication ideas of Step 3 are involved, the
Born Rule of quantum probabilities will not be reproduced, since
that cannot be obtained by branch counting in the MWI.
OK. I believe that this is not the intention of step 3. It's only a
metaphorical comparison for people who suffer from pronoun trouble, or
only an exact comparison to the extent that both give a form of FPI. To
assume this is the final result is to be "too quick".
But it is introduced as an illustration of FPI, and the comparison with
MWI is made. I merely point out that this comparison is not valid.
As I said in a recent post, I think John Clark's trouble with the use of
personal pronouns stems from a hasty glossing of questions of personal
identity in brain substitution/duplication scenarios. I find Nozick's
closest continuer notion a useful starting point. He takes personal
identity to follow the closest continuer of the initial state, provided
there is no closer or tied continuation. If there is a tie (as in step
3), the rule is that two new persons are created. I think this solves
John's personal pronoun issue. However, this does need to be discussed
more fully.
Bruce
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